Nothing
R/MGM.mxModel_helper.R
In nlpsem: Linear and Nonlinear Longitudinal Process in Structural Equation Modeling Framework
Defines functions
getMGM.mxModel
Documented in
getMGM.mxModel
#' @title Construct An Object of mxModel for Multivariate Latent Growth Curve Models or Multivariate Latent Change Score
#' Models To Be Evaluated
#'
#' @description This function builds up an object of mxModel for a multivariate latent growth curve model or a multivariate latent
#' change score model with user-specified functional form (including whether intrinsically nonlinear).
#'
#' @param dat A wide-format data frame, with each row corresponding to a unique ID. It contains the observed variables
#' with repeated measurements and occasions for multiple longitudinal outcomes. It takes the value passed from \code{getMGM()}.
#' @param t_var A vector of strings, with each element representing the prefix for column names related to the time
#' variable for the corresponding outcome variable at each study wave. It takes the value passed from \code{getMGM()}.
#' @param y_var A vector of strings, with each element representing the prefix for column names corresponding to a
#' particular outcome variable at each study wave. It takes the value passed from \code{getMGM()}.
#' @param curveFun A string specifying the functional form of the growth curve. Supported options for \code{y_model =
#' "LGCM"} include: \code{"linear"} (or \code{"LIN"}), \code{"quadratic"} (or \code{"QUAD"}), \code{"negative exponential"}
#' (or \code{"EXP"}), \code{"Jenss-Bayley"} (or \code{"JB"}), and \code{"bilinear spline"} (or \code{"BLS"}). Supported
#' options for \code{y_model = "LCSM"} include: \code{"quadratic"} (or \code{"QUAD"}), \code{"negative exponential"}
#' (or \code{"EXP"}), \code{"Jenss-Bayley"} (or \code{"JB"}), and \code{"nonparametric"} (or \code{"NonP"}). It takes the
#' value passed from \code{getMGM()}.
#' @param intrinsic A logical flag indicating whether to build an intrinsically nonlinear longitudinal model. It takes the
#' value passed from \code{getMGM()}.
#' @param records A list of numeric vectors, with each vector specifying the indices of the observed study waves for
#' the corresponding outcome variable. It takes the value passed from \code{getMGM()}.
#' @param y_model A string specifying how to fit the longitudinal outcome. Supported values are \code{"LGCM"} and \code{"LCSM"}.
#' It takes the value passed from \code{getMGM()}.
#' @param starts A list of initial values for the parameters, either takes the value passed from \code{getMGM()} or derived
#' by the helper function \code{getMULTI.initial()}.
#'
#' @return A pre-optimized mxModel for a multivariate latent growth curve model or a multivariate latent change
#' score model.
#'
#' @keywords internal
#'
getMGM.mxModel <- function(dat, t_var, y_var, curveFun, intrinsic, records, y_model, starts){
y_var_L <- tolower(y_var)
# Define manifest variables
traj_list <- list()
for (traj in 1:length(y_var)){
traj_list[[length(traj_list) + 1]] <- paste0(y_var[traj], records[[traj]])
}
manifests <- unlist(traj_list)
# Define variances and covariance(s) of residuals
RES <- COV <- list()
for (traj in 1:length(y_var)){
RES[[traj]] <- mxPath(from = traj_list[[traj]], to = traj_list[[traj]], arrows = 2, free = TRUE,
values = starts[[3]][traj, traj],
labels = paste0(y_var[traj], "_residuals"))
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
if (setequal(substr(traj_list[[traj_i]], 2, 2), substr(traj_list[[traj_j + 1]], 2, 2))){
COV[[traj_i + traj_j - 1]] <- mxPath(from = traj_list[[traj_i]], to = traj_list[[traj_j + 1]],
arrows = 2, free = TRUE, values = starts[[3]][traj_i, traj_j + 1],
labels = paste0(y_var[traj_i], y_var[traj_j + 1], "_RES"))
}
else{
T_common <- Reduce(intersect, list(substr(traj_list[[traj_i]], 2, 2), substr(traj_list[[traj_j + 1]], 2, 2)))
COV[[traj_i + traj_j - 1]] <- mxPath(from = paste0(y_var[traj_i], T_common),
to = paste0(y_var[traj_j + 1], T_common),
arrows = 2, free = TRUE, values = starts[[3]][traj_i, traj_j + 1],
labels = paste0(y_var[traj_i], y_var[traj_j + 1], "_RES"))
}
}
}
# Obtain factor loadigs for the specified trajectory model (either "LGCM" or "LCSM") and functional form
GF_loadings <- getMULTI.loadings(y_model = y_model, t_var = t_var, y_var = y_var, curveFun = curveFun,
intrinsic = intrinsic, records = records)
if (y_model == "LGCM"){
if (curveFun %in% c("linear", "LIN")){
latents <- paste0(rep(c("eta0", "eta1"), length(y_var)), rep(y_var, each = 2))
multi_label <- matrix(NA, nrow = length(latents), ncol = length(latents))
GF_MEAN <- GF_LOADINGS <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:2],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1")))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE,
labels = paste0("L1", records[[traj]], y_var[traj], "[1,1]")))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj], "_mueta1)"),
name = paste0(y_var[traj], "_mean0"))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj], "_psi01), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj], "_psi11))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi", c("00", "01", "01", "11")),
byrow = T, nrow = 2, ncol = 2)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ", y_var[traj_i], y_var[traj_j + 1], "_psi01), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ", y_var[traj_i], y_var[traj_j + 1], "_psi11))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi", c("00", "01", "10", "11")),
byrow = T, nrow = 2, ncol = 2)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 2 + 1):((traj - 1) * 2 + 2), ((traj - 1) * 2 + 1):((traj - 1) * 2 + 2)] <- gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 2 + 1):((traj_i - 1) * 2 + 2), (traj_j * 2 + 1):(traj_j * 2 + 2)] <- gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Growth Curve Model, Linear", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents, to = latents, arrows = 2, connect = "unique.pairs",
free = TRUE, values = t(starts[[2]])[row(t(starts[[2]])) >= col(t(starts[[2]]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L, psi_btw_L)
}
else if (curveFun %in% c("quadratic", "QUAD")){
latents <- paste0(rep(c("eta0", "eta1", "eta2"), length(y_var)), rep(y_var, each = 3))
multi_label <- matrix(NA, nrow = length(latents), ncol = length(latents))
GF_MEAN <- GF_LOADINGS <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1", "eta2"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:3],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1", "_mueta2")))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE,
labels = paste0("L1", records[[traj]], y_var[traj], "[1,1]")),
mxPath(from = paste0("eta2", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE,
labels = paste0("L2", records[[traj]], y_var[traj], "[1,1]")))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj],
"_mueta1, ", y_var[traj], "_mueta2)"),
name = paste0(y_var[traj], "_mean0"))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj],
"_psi01, ", y_var[traj], "_psi02), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj],
"_psi11, ", y_var[traj], "_psi12), ",
"cbind(", y_var[traj], "_psi02, ", y_var[traj],
"_psi12, ", y_var[traj], "_psi22))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi",
c("00", "01", "02", "01", "11", "12", "02", "12", "22")),
byrow = T, nrow = 3, ncol = 3)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ",
y_var[traj_i], y_var[traj_j + 1], "_psi01, ",
y_var[traj_i], y_var[traj_j + 1], "_psi02),",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11, ",
y_var[traj_i], y_var[traj_j + 1], "_psi12), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi20, ",
y_var[traj_i], y_var[traj_j + 1], "_psi21, ",
y_var[traj_i], y_var[traj_j + 1], "_psi22))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi",
c("00", "01", "02", "10", "11", "12", "20", "21", "22")),
byrow = T, nrow = 3, ncol = 3)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 3 + 1):((traj - 1) * 3 + 3), ((traj - 1) * 3 + 1):((traj - 1) * 3 + 3)] <- gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 3 + 1):((traj_i - 1) * 3 + 3), (traj_j * 3 + 1):(traj_j * 3 + 3)] <- gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Growth Curve Model, Quadratic", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents, to = latents, arrows = 2, connect = "unique.pairs",
free = TRUE, values = t(starts[[2]])[row(t(starts[[2]])) >= col(t(starts[[2]]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L, psi_btw_L)
}
else if (curveFun %in% c("negative exponential", "EXP")){
if (intrinsic){
latents <- paste0(rep(c("eta0", "eta1", "deltag"), length(y_var)), rep(y_var, each = 3))
multi_label <- matrix(NA, nrow = length(latents), ncol = length(latents))
GF_MEAN <- GF_LOADINGS <- GAMMA <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:2],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1")))
GAMMA[[traj]] <- mxMatrix("Full", 1, 1, free = TRUE, values = starts[[1]][[traj]][3],
labels = paste0(y_var[traj], "_slp_ratio"),
name = paste0(y_var[traj], "_mug"))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj], "_mueta1, ",
y_var[traj], "_slp_ratio)"),
name = paste0(y_var[traj], "_mean0"))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE,
labels = paste0("L1", records[[traj]], y_var[traj], "[1,1]")),
mxPath(from = paste0("deltag", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 0,
labels = paste0("L2", records[[traj]], y_var[traj], "[1,1]")))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj],
"_psi01, ", y_var[traj], "_psi0g), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj],
"_psi11, ", y_var[traj], "_psi1g), ",
"cbind(", y_var[traj], "_psi0g, ", y_var[traj],
"_psi1g, ", y_var[traj], "_psigg))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi",
c("00", "01", "0g", "01", "11", "1g", "0g", "1g", "gg")),
byrow = T, nrow = 3, ncol = 3)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ",
y_var[traj_i], y_var[traj_j + 1],
"_psi01, ", y_var[traj_i], y_var[traj_j + 1], "_psi0g),",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11, ",
y_var[traj_i], y_var[traj_j + 1], "_psi1g), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psig0, ",
y_var[traj_i], y_var[traj_j + 1], "_psig1, ",
y_var[traj_i], y_var[traj_j + 1], "_psigg))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi",
c("00", "01", "0g", "10", "11", "1g", "g0", "g1", "gg")),
byrow = T, nrow = 3, ncol = 3)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 3 + 1):((traj - 1) * 3 + 3), ((traj - 1) * 3 + 1):((traj - 1) * 3 + 3)] <-
gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 3 + 1):((traj_i - 1) * 3 + 3), (traj_j * 3 + 1):(traj_j * 3 + 3)] <-
gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Growth Curve Model, Negative Exponential (random ratio)", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents, to = latents, arrows = 2, connect = "unique.pairs",
free = TRUE, values = t(starts[[2]])[row(t(starts[[2]])) >= col(t(starts[[2]]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, GAMMA, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L, psi_btw_L)
}
else if (!intrinsic){
latents <- paste0(rep(c("eta0", "eta1"), length(y_var)), rep(y_var, each = 2))
multi_label <- matrix(NA, nrow = length(latents), ncol = length(latents))
GF_MEAN <- GF_LOADINGS <- GAMMA <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:2],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1")))
GAMMA[[traj]] <- mxMatrix("Full", 1, 1, free = TRUE, values = starts[[1]][[traj]][3],
labels = paste0(y_var[traj], "_slp_ratio"),
name = paste0(y_var[traj], "_mug"))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj], "_mueta1, ",
y_var[traj], "_slp_ratio)"),
name = paste0(y_var[traj], "_mean0"))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE,
labels = paste0("L1", records[[traj]], y_var[traj], "[1,1]")))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj], "_psi01), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj], "_psi11))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi", c("00", "01", "01", "11")),
byrow = T, nrow = 2, ncol = 2)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ",
y_var[traj_i], y_var[traj_j + 1], "_psi01), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi", c("00", "01", "10", "11")),
byrow = T, nrow = 2, ncol = 2)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 2 + 1):((traj - 1) * 2 + 2), ((traj - 1) * 2 + 1):((traj - 1) * 2 + 2)] <-
gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 2 + 1):((traj_i - 1) * 2 + 2), (traj_j * 2 + 1):(traj_j * 2 + 2)] <-
gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Growth Curve Model, Negative Exponential (fixed ratio)", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents, to = latents, arrows = 2, connect = "unique.pairs", free = TRUE,
values = t(starts[[2]][c(1:2, 4:5), c(1:2, 4:5)])[row(t(starts[[2]][c(1:2, 4:5), c(1:2, 4:5)])) >=
col(t(starts[[2]][c(1:2, 4:5), c(1:2, 4:5)]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, GAMMA, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L, psi_btw_L)
}
}
else if (curveFun %in% c("Jenss-Bayley", "JB")){
if (intrinsic){
latents <- paste0(rep(c("eta0", "eta1", "eta2", "deltag"), length(y_var)), rep(y_var, each = 4))
multi_label <- matrix(NA, nrow = length(latents), ncol = length(latents))
GF_MEAN <- GF_LOADINGS <- GAMMA <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1", "eta2"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:3],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1", "_mueta2")))
GAMMA[[traj]] <- mxMatrix("Full", 1, 1, free = TRUE, values = starts[[1]][[traj]][4],
labels = paste0(y_var[traj], "_acc_ratio"),
name = paste0(y_var[traj], "_mug"))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj], "_mueta1, ",
y_var[traj], "_mueta2, ", y_var[traj], "_acc_ratio)"),
name = paste0(y_var[traj], "_mean0"))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 0,
labels = paste0("L1", records[[traj]], y_var[traj], "[1,1]")),
mxPath(from = paste0("eta2", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 0,
labels = paste0("L2", records[[traj]], y_var[traj], "[1,1]")),
mxPath(from = paste0("deltag", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 0,
labels = paste0("L3", records[[traj]], y_var[traj], "[1,1]")))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj], "_psi01, ",
y_var[traj], "_psi02, ", y_var[traj], "_psi0g), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj], "_psi11, ",
y_var[traj], "_psi12, ", y_var[traj], "_psi1g), ",
"cbind(", y_var[traj], "_psi02, ", y_var[traj], "_psi12, ",
y_var[traj], "_psi22, ", y_var[traj], "_psi2g), ",
"cbind(", y_var[traj], "_psi0g, ", y_var[traj], "_psi1g, ",
y_var[traj], "_psi2g, ", y_var[traj], "_psigg))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi", c("00", "01", "02", "0g", "01", "11", "12", "1g",
"02", "12", "22", "2g", "0g", "1g", "2g", "gg")),
byrow = T, nrow = 4, ncol = 4)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ",
y_var[traj_i], y_var[traj_j + 1], "_psi01, ",
y_var[traj_i], y_var[traj_j + 1], "_psi02, ",
y_var[traj_i], y_var[traj_j + 1], "_psi0g), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11, ",
y_var[traj_i], y_var[traj_j + 1], "_psi12, ",
y_var[traj_i], y_var[traj_j + 1], "_psi1g), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi20, ",
y_var[traj_i], y_var[traj_j + 1], "_psi21, ",
y_var[traj_i], y_var[traj_j + 1], "_psi22, ",
y_var[traj_i], y_var[traj_j + 1], "_psi2g), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psig0, ",
y_var[traj_i], y_var[traj_j + 1], "_psig1, ",
y_var[traj_i], y_var[traj_j + 1], "_psig2, ",
y_var[traj_i], y_var[traj_j + 1], "_psigg))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi",
c("00", "01", "02", "0g", "10", "11", "12", "1g",
"20", "21", "22", "2g", "g0", "g1", "g2", "gg")),
byrow = T, nrow = 4, ncol = 4)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 4 + 1):((traj - 1) * 4 + 4), ((traj - 1) * 4 + 1):((traj - 1) * 4 + 4)] <-
gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 4 + 1):((traj_i - 1) * 4 + 4), (traj_j * 4 + 1):(traj_j * 4 + 4)] <-
gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Growth Curve Model, Jenss Bayley (random ratio)", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents, to = latents, arrows = 2, connect = "unique.pairs",
free = TRUE, values = t(starts[[2]])[row(t(starts[[2]])) >= col(t(starts[[2]]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, GAMMA, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L, psi_btw_L)
}
else if (!intrinsic){
latents <- paste0(rep(c("eta0", "eta1", "eta2"), length(y_var)), rep(y_var, each = 3))
multi_label <- matrix(NA, nrow = length(latents), ncol = length(latents))
GF_MEAN <- GF_LOADINGS <- GAMMA <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1", "eta2"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:3],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1", "_mueta2")))
GAMMA[[traj]] <- mxMatrix("Full", 1, 1, free = TRUE, values = starts[[1]][[traj]][4],
labels = paste0(y_var[traj], "_acc_ratio"),
name = paste0(y_var[traj], "_mug"))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj], "_mueta1, ",
y_var[traj], "_mueta2, ", y_var[traj], "_acc_ratio)"),
name = paste0(y_var[traj], "_mean0"))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 0,
labels = paste0("L1", records[[traj]], y_var[traj], "[1,1]")),
mxPath(from = paste0("eta2", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 0,
labels = paste0("L2", records[[traj]], y_var[traj], "[1,1]")))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj], "_psi01, ",
y_var[traj], "_psi02), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj], "_psi11, ",
y_var[traj], "_psi12), ",
"cbind(", y_var[traj], "_psi02, ", y_var[traj], "_psi12, ",
y_var[traj], "_psi22))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi", c("00", "01", "02", "01", "11", "12",
"02", "12", "22")),
byrow = T, nrow = 3, ncol = 3)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ",
y_var[traj_i], y_var[traj_j + 1], "_psi01, ",
y_var[traj_i], y_var[traj_j + 1], "_psi02), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11, ",
y_var[traj_i], y_var[traj_j + 1], "_psi12), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi20, ",
y_var[traj_i], y_var[traj_j + 1], "_psi21, ",
y_var[traj_i], y_var[traj_j + 1], "_psi22))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi",
c("00", "01", "02", "10", "11", "12",
"20", "21", "22")),
byrow = T, nrow = 3, ncol = 3)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 3 + 1):((traj - 1) * 3 + 3), ((traj - 1) * 3 + 1):((traj - 1) * 3 + 3)] <-
gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 3 + 1):((traj_i - 1) * 3 + 3), (traj_j * 3 + 1):(traj_j * 3 + 3)] <-
gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Growth Curve Model, Jenss Bayley (fixed ratio)", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents, to = latents, arrows = 2, connect = "unique.pairs", free = TRUE,
values = t(starts[[2]][c(1:3, 5:7), c(1:3, 5:7)])[row(t(starts[[2]][c(1:3, 5:7), c(1:3, 5:7)])) >=
col(t(starts[[2]][c(1:3, 5:7), c(1:3, 5:7)]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, GAMMA, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L, psi_btw_L)
}
}
else if (curveFun %in% c("bilinear spline", "BLS")){
if (intrinsic){
latents <- paste0(rep(c("eta0s", "eta1s", "eta2s", "deltag"), length(y_var)), rep(y_var, each = 4))
multi_label <- matrix(NA, nrow = length(latents), ncol = length(latents))
GF_MEAN <- GF_LOADINGS <- GAMMA <- list()
func_L <- grad_L <- mean_s_L <- psi_s_L <- mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_s_L <- psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0s", "eta1s", "eta2s"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:3],
labels = paste0(y_var[traj], c("_mueta0s", "_mueta1s", "_mueta2s")))
GAMMA[[traj]] <- mxMatrix("Full", 1, 1, free = TRUE, values = starts[[1]][[traj]][4],
labels = paste0(y_var[traj], "_knot"),
name = paste0(y_var[traj], "_mug"))
mean_s_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0s, ", y_var[traj], "_mueta1s, ",
y_var[traj], "_mueta2s, ", y_var[traj], "_knot)"),
name = paste0(y_var[traj], "_mean_s"))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0s", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1s", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 0,
labels = paste0("L1", records[[traj]], y_var[traj], "[1,1]")),
mxPath(from = paste0("eta2s", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 0,
labels = paste0("L2", records[[traj]], y_var[traj], "[1,1]")),
mxPath(from = paste0("deltag", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 0,
labels = paste0("L3", records[[traj]], y_var[traj], "[1,1]")))
func_L[[length(func_L) + 1]] <- mxAlgebraFromString(paste0("rbind(cbind(1, -", y_var[traj], "_mug, ", y_var[traj], "_mug, 0), ",
"cbind(0, 1, -1, 0), ", "cbind(0, 1, 1, 0)", ", cbind(0, 0, 0, 1))"),
name = paste0("func", y_var[traj]))
grad_L[[length(grad_L) + 1]] <- mxAlgebraFromString(paste0("rbind(cbind(1, -", y_var[traj], "_mug, ", y_var[traj], "_mug, 0), ",
"cbind(0, 1, -1, 0), ", "cbind(0, 1, 1, 0)", ", cbind(0, 0, 0, 1))"),
name = paste0("grad", y_var[traj]))
psi_s_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00s, ", y_var[traj], "_psi01s, ",
y_var[traj], "_psi02s, ", y_var[traj], "_psi0gs), ",
"cbind(", y_var[traj], "_psi01s, ", y_var[traj], "_psi11s, ",
y_var[traj], "_psi12s, ", y_var[traj], "_psi1gs), ",
"cbind(", y_var[traj], "_psi02s, ", y_var[traj], "_psi12s, ",
y_var[traj], "_psi22s, ", y_var[traj], "_psi2gs), ",
"cbind(", y_var[traj], "_psi0gs, ", y_var[traj], "_psi1gs, ",
y_var[traj], "_psi2gs, ", y_var[traj], "_psiggs))"),
name = paste0(y_var[traj], "_psi_s"))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(func", y_var[traj], " %*% ", y_var[traj],
"_mean_s)"), name = paste0(y_var[traj], "_mean0"))
psi_L[[traj]] <- mxAlgebraFromString(paste0("grad", y_var[traj], " %*% ", y_var[traj], "_psi_s",
" %*% t(grad", y_var[traj], ")"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi", c("00s", "01s", "02s", "0gs", "01s", "11s", "12s", "1gs",
"02s", "12s", "22s", "2gs", "0gs", "1gs", "2gs", "ggs")),
byrow = T, nrow = 4, ncol = 4)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_s_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi01s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi02s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi0gs), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi12s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi1gs), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi20s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi21s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi22s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi2gs), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psig0s, ",
y_var[traj_i], y_var[traj_j + 1], "_psig1s, ",
y_var[traj_i], y_var[traj_j + 1], "_psig2s, ",
y_var[traj_i], y_var[traj_j + 1], "_psiggs))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi_s"))
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("grad", y_var[traj_i], " %*% ",
y_var[traj_i], y_var[traj_j + 1], "_psi_s",
" %*% t(grad", y_var[traj_j + 1], ")"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi",
c("00s", "01s", "02s", "0gs", "10s", "11s", "12s", "1gs",
"20s", "21s", "22s", "2gs", "g0s", "g1s", "g2s", "ggs")),
byrow = T, nrow = 4, ncol = 4)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 4 + 1):((traj - 1) * 4 + 4), ((traj - 1) * 4 + 1):((traj - 1) * 4 + 4)] <-
gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 4 + 1):((traj_i - 1) * 4 + 4), (traj_j * 4 + 1):(traj_j * 4 + 4)] <-
gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Growth Curve Model, Bilinear Spline (random knot)", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents, to = latents, arrows = 2, connect = "unique.pairs",
free = TRUE, values = t(starts[[2]])[row(t(starts[[2]])) >= col(t(starts[[2]]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, GAMMA, func_L, grad_L, mean_s_L, psi_s_L, psi_btw_s_L,
GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L, psi_btw_L)
}
else if (!intrinsic){
latents <- paste0(rep(c("eta0s", "eta1s", "eta2s"), length(y_var)), rep(y_var, each = 3))
multi_label <- matrix(NA, nrow = length(latents), ncol = length(latents))
GF_MEAN <- GF_LOADINGS <- GAMMA <- list()
func_L <- grad_L <- mean_s_L <- psi_s_L <- mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_s_L <- psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0s", "eta1s", "eta2s"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:3],
labels = paste0(y_var[traj], c("_mueta0s", "_mueta1s", "_mueta2s")))
GAMMA[[traj]] <- mxMatrix("Full", 1, 1, free = TRUE, values = starts[[1]][[traj]][4],
labels = paste0(y_var[traj], "_knot"),
name = paste0(y_var[traj], "_mug"))
mean_s_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0s, ", y_var[traj], "_mueta1s, ",
y_var[traj], "_mueta2s)"),
name = paste0(y_var[traj], "_mean_s"))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0s", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1s", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 0,
labels = paste0("L1", records[[traj]], y_var[traj], "[1,1]")),
mxPath(from = paste0("eta2s", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 0,
labels = paste0("L2", records[[traj]], y_var[traj], "[1,1]")))
func_L[[length(func_L) + 1]] <- mxAlgebraFromString(paste0("rbind(cbind(1, -", y_var[traj], "_mug, ", y_var[traj], "_mug), ",
"cbind(0, 1, -1), ", "cbind(0, 1, 1))"),
name = paste0("func", y_var[traj]))
grad_L[[length(grad_L) + 1]] <- mxAlgebraFromString(paste0("rbind(cbind(1, -", y_var[traj], "_mug, ", y_var[traj], "_mug), ",
"cbind(0, 1, -1), ", "cbind(0, 1, 1))"),
name = paste0("grad", y_var[traj]))
psi_s_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00s, ", y_var[traj], "_psi01s, ",
y_var[traj], "_psi02s), ",
"cbind(", y_var[traj], "_psi01s, ", y_var[traj], "_psi11s, ",
y_var[traj], "_psi12s), ",
"cbind(", y_var[traj], "_psi02s, ", y_var[traj], "_psi12s, ",
y_var[traj], "_psi22s))"),
name = paste0(y_var[traj], "_psi_s"))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(func", y_var[traj], " %*% ", y_var[traj],
"_mean_s, ", y_var[traj], "_knot)"),
name = paste0(y_var[traj], "_mean0"))
psi_L[[traj]] <- mxAlgebraFromString(paste0("grad", y_var[traj], " %*% ", y_var[traj], "_psi_s",
" %*% t(grad", y_var[traj], ")"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi", c("00s", "01s", "02s", "01s", "11s", "12s",
"02s", "12s", "22s")),
byrow = T, nrow = 3, ncol = 3)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_s_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi01s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi02s), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi12s), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi20s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi21s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi22s))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi_s"))
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("grad", y_var[traj_i], " %*% ",
y_var[traj_i], y_var[traj_j + 1], "_psi_s",
" %*% t(grad", y_var[traj_j + 1], ")"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi",
c("00s", "01s", "02s", "10s", "11s", "12s", "20s", "21s", "22s")),
byrow = T, nrow = 3, ncol = 3)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 3 + 1):((traj - 1) * 3 + 3), ((traj - 1) * 3 + 1):((traj - 1) * 3 + 3)] <-
gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 3 + 1):((traj_i - 1) * 3 + 3), (traj_j * 3 + 1):(traj_j * 3 + 3)] <-
gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Growth Curve Model, Bilinear Spline (fixed knot)", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents, to = latents, arrows = 2, connect = "unique.pairs", free = TRUE,
values = t(starts[[2]][c(1:3, 5:7), c(1:3, 5:7)])[row(t(starts[[2]][c(1:3, 5:7), c(1:3, 5:7)])) >=
col(t(starts[[2]][c(1:3, 5:7), c(1:3, 5:7)]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, GAMMA, func_L, grad_L, mean_s_L, psi_s_L, psi_btw_s_L,
GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L, psi_btw_L)
}
}
}
else if (y_model == "LCSM"){
# Obtain additional parameters (derived) for the specified functional form
AddPara <- getMULTI.addpara(dat = dat, y_var = y_var, curveFun = curveFun, intrinsic = intrinsic,
t_var = t_var, records = records, starts = starts)
# Define latent variables in addition to growth factors
L_list <- D_list <- list()
for (traj in 1:length(y_var)){
L_list[[traj]] <- paste0("l", y_var_L[traj], records[[traj]])
D_list[[traj]] <- paste0("d", y_var_L[traj], records[[traj]][-1])
}
PATH_L_L <- PATH_SLP_L <- PATH_AUTO_L <- list()
for (traj in 1:length(y_var)){
# Define paths from latent true scores to observed scores
PATH_L_L[[traj]] <- mxPath(from = paste0("l", y_var_L[traj], records[[traj]]),
to = paste0(y_var[[traj]], records[[traj]]), arrows = 1, free = FALSE, values = 1)
# Define paths from latent instantaneous rate of change at each measurement to true scores
PATH_SLP_L[[traj]] <- mxPath(from = paste0("d", y_var_L[traj], records[[traj]][-1]),
to = paste0("l", y_var_L[traj], records[[traj]][-1]),
arrows = 1, free = FALSE, values = 0,
labels = paste0(y_var[traj], "lag", records[[traj]][-1], "[1,1]"))
# Define autoregressive paths
PATH_AUTO_L[[traj]] <- mxPath(from = paste0("l", y_var_L[traj], records[[traj]][-length(records[[traj]])]),
to = paste0("l", y_var_L[traj], records[[traj]][-1]), arrows = 1,
free = FALSE, values = 1)
}
if (curveFun %in% c("nonparametric", "NonP")){
latents <- c(paste0(rep(c("eta0", "eta1"), length(y_var)), rep(y_var, each = 2)),
unlist(L_list), unlist(D_list))
multi_label <- matrix(NA, nrow = 2 * length(y_var), ncol = 2 * length(y_var))
GF_MEAN <- GF_LOADINGS <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:2],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1")))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0", y_var[traj]),
to = paste0("l", y_var_L[traj], records[[traj]][1]),
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]),
to = paste0("d", y_var_L[traj], records[[traj]][-1]),
arrows = 1, free = c(F, rep(T, length(records[[traj]]) - 2)),
values = c(1, starts[[4]][[traj]][-1]),
labels = paste0(y_var[traj], "_rel_rate",
1:(length(records[[traj]]) - 1))))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj], "_mueta1)"),
name = paste0(y_var[traj], "_mean0"))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj], "_psi01), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj], "_psi11))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi", c("00", "01", "01", "11")),
byrow = T, nrow = 2, ncol = 2)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ", y_var[traj_i], y_var[traj_j + 1], "_psi01), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ", y_var[traj_i], y_var[traj_j + 1], "_psi11))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi", c("00", "01", "10", "11")),
byrow = T, nrow = 2, ncol = 2)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 2 + 1):((traj - 1) * 2 + 2), ((traj - 1) * 2 + 1):((traj - 1) * 2 + 2)] <- gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 2 + 1):((traj_i - 1) * 2 + 2), (traj_j * 2 + 1):(traj_j * 2 + 2)] <- gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Change Score Model, Nonparametric", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents[1:(length(y_var) * 2)], to = latents[1:(length(y_var) * 2)],
arrows = 2, connect = "unique.pairs", free = TRUE, values = t(starts[[2]])[row(t(starts[[2]])) >= col(t(starts[[2]]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, AddPara, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L, psi_btw_L,
PATH_L_L, PATH_SLP_L, PATH_AUTO_L)
}
else if (curveFun %in% c("quadratic", "QUAD")){
latents <- c(paste0(rep(c("eta0", "eta1", "eta2"), length(y_var)), rep(y_var, each = 3)),
unlist(L_list), unlist(D_list))
multi_label <- matrix(NA, nrow = 3 * length(y_var), ncol = 3 * length(y_var))
GF_MEAN <- GF_LOADINGS <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1", "eta2"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:3],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1", "_mueta2")))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0", y_var[traj]),
to = paste0("l", y_var_L[traj], records[[traj]][1]),
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]),
to = paste0("d", y_var_L[traj], records[[traj]][-1]),
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta2", y_var[traj]),
to = paste0("d", y_var_L[traj], records[[traj]][-1]),
arrows = 1, free = FALSE, values = 0,
labels = paste0(y_var[traj], "L2", records[[traj]][-1], "[1,1]")))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj],
"_mueta1, ", y_var[traj], "_mueta2)"),
name = paste0(y_var[traj], "_mean0"))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj],
"_psi01, ", y_var[traj], "_psi02), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj],
"_psi11, ", y_var[traj], "_psi12), ",
"cbind(", y_var[traj], "_psi02, ", y_var[traj],
"_psi12, ", y_var[traj], "_psi22))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi",
c("00", "01", "02", "01", "11", "12", "02", "12", "22")),
byrow = T, nrow = 3, ncol = 3)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ",
y_var[traj_i], y_var[traj_j + 1], "_psi01, ",
y_var[traj_i], y_var[traj_j + 1], "_psi02),",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11, ",
y_var[traj_i], y_var[traj_j + 1], "_psi12), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi20, ",
y_var[traj_i], y_var[traj_j + 1], "_psi21, ",
y_var[traj_i], y_var[traj_j + 1], "_psi22))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi",
c("00", "01", "02", "10", "11", "12", "20", "21", "22")),
byrow = T, nrow = 3, ncol = 3)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 3 + 1):((traj - 1) * 3 + 3), ((traj - 1) * 3 + 1):((traj - 1) * 3 + 3)] <- gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 3 + 1):((traj_i - 1) * 3 + 3), (traj_j * 3 + 1):(traj_j * 3 + 3)] <- gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Change Score Model, Quadratic", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents[1:(length(y_var) * 3)], to = latents[1:(length(y_var) * 3)],
arrows = 2, connect = "unique.pairs", free = TRUE, values = t(starts[[2]])[row(t(starts[[2]])) >= col(t(starts[[2]]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, AddPara, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L, psi_btw_L,
PATH_L_L, PATH_SLP_L, PATH_AUTO_L)
}
else if (curveFun %in% c("negative exponential", "EXP")){
if (intrinsic){
latents <- c(paste0(rep(c("eta0", "eta1", "deltag"), length(y_var)), rep(y_var, each = 3)),
unlist(L_list), unlist(D_list))
multi_label <- matrix(NA, nrow = 3 * length(y_var), ncol = 3 * length(y_var))
GF_MEAN <- GF_LOADINGS <- GAMMA <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:2],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1")))
GAMMA[[traj]] <- mxMatrix("Full", 1, 1, free = TRUE, values = starts[[1]][[traj]][3],
labels = paste0(y_var[traj], "_slp_ratio"),
name = paste0(y_var[traj], "_mug"))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj], "_mueta1, ",
y_var[traj], "_slp_ratio)"),
name = paste0(y_var[traj], "_mean0"))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0", y_var[traj]),
to = paste0("l", y_var_L[traj], records[[traj]][1]),
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]),
to = paste0("d", y_var_L[traj], records[[traj]][-1]),
arrows = 1, free = FALSE, values = 0,
labels = paste0(y_var[traj], "L1", records[[traj]][-1], "[1,1]")),
mxPath(from = paste0("deltag", y_var[traj]),
to = paste0("d", y_var_L[traj], records[[traj]][-1]),
arrows = 1, free = FALSE, values = 0,
labels = paste0(y_var[traj], "L2", records[[traj]][-1], "[1,1]")))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj],
"_psi01, ", y_var[traj], "_psi0g), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj],
"_psi11, ", y_var[traj], "_psi1g), ",
"cbind(", y_var[traj], "_psi0g, ", y_var[traj],
"_psi1g, ", y_var[traj], "_psigg))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi",
c("00", "01", "0g", "01", "11", "1g", "0g", "1g", "gg")),
byrow = T, nrow = 3, ncol = 3)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ",
y_var[traj_i], y_var[traj_j + 1],
"_psi01, ", y_var[traj_i], y_var[traj_j + 1], "_psi0g),",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11, ",
y_var[traj_i], y_var[traj_j + 1], "_psi1g), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psig0, ",
y_var[traj_i], y_var[traj_j + 1], "_psig1, ",
y_var[traj_i], y_var[traj_j + 1], "_psigg))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi",
c("00", "01", "0g", "10", "11", "1g", "g0", "g1", "gg")),
byrow = T, nrow = 3, ncol = 3)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 3 + 1):((traj - 1) * 3 + 3), ((traj - 1) * 3 + 1):((traj - 1) * 3 + 3)] <-
gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 3 + 1):((traj_i - 1) * 3 + 3), (traj_j * 3 + 1):(traj_j * 3 + 3)] <-
gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Change Score Model, Negative Exponential", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents[1:(length(y_var) * 3)], to = latents[1:(length(y_var) * 3)],
arrows = 2, connect = "unique.pairs", free = TRUE,
values = t(starts[[2]])[row(t(starts[[2]])) >= col(t(starts[[2]]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, AddPara, GAMMA, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L,
psi_btw_L, PATH_L_L, PATH_SLP_L, PATH_AUTO_L)
}
else if (!intrinsic){
latents <- c(paste0(rep(c("eta0", "eta1"), length(y_var)), rep(y_var, each = 2)),
unlist(L_list), unlist(D_list))
multi_label <- matrix(NA, nrow = 2 * length(y_var), ncol = 2 * length(y_var))
GF_MEAN <- GF_LOADINGS <- GAMMA <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:2],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1")))
GAMMA[[traj]] <- mxMatrix("Full", 1, 1, free = TRUE, values = starts[[1]][[traj]][3],
labels = paste0(y_var[traj], "_slp_ratio"),
name = paste0(y_var[traj], "_mug"))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj], "_mueta1, ",
y_var[traj], "_slp_ratio)"),
name = paste0(y_var[traj], "_mean0"))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0", y_var[traj]),
to = paste0("l", y_var_L[traj], records[[traj]][1]),
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]),
to = paste0("d", y_var_L[traj], records[[traj]][-1]),
arrows = 1, free = FALSE, values = 0,
labels = paste0(y_var[traj], "L1", records[[traj]][-1], "[1,1]")))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj], "_psi01), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj], "_psi11))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi", c("00", "01", "01", "11")),
byrow = T, nrow = 2, ncol = 2)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ",
y_var[traj_i], y_var[traj_j + 1], "_psi01), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi", c("00", "01", "10", "11")),
byrow = T, nrow = 2, ncol = 2)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 2 + 1):((traj - 1) * 2 + 2), ((traj - 1) * 2 + 1):((traj - 1) * 2 + 2)] <-
gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 2 + 1):((traj_i - 1) * 2 + 2), (traj_j * 2 + 1):(traj_j * 2 + 2)] <-
gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Change Score Model, Negative Exponential", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents[1:(length(y_var) * 2)], to = latents[1:(length(y_var) * 2)],
arrows = 2, connect = "unique.pairs", free = TRUE,
values = t(starts[[2]][c(1:2, 4:5), c(1:2, 4:5)])[row(t(starts[[2]][c(1:2, 4:5), c(1:2, 4:5)])) >=
col(t(starts[[2]][c(1:2, 4:5), c(1:2, 4:5)]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, AddPara, GAMMA, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L,
psi_btw_L, PATH_L_L, PATH_SLP_L, PATH_AUTO_L)
}
}
else if (curveFun %in% c("Jenss-Bayley", "JB")){
if (intrinsic){
latents <- c(paste0(rep(c("eta0", "eta1", "eta2", "deltag"), length(y_var)), rep(y_var, each = 4)),
unlist(L_list), unlist(D_list))
multi_label <- matrix(NA, nrow = 4 * length(y_var), ncol = 4 * length(y_var))
GF_MEAN <- GF_LOADINGS <- GAMMA <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1", "eta2"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:3],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1", "_mueta2")))
GAMMA[[traj]] <- mxMatrix("Full", 1, 1, free = TRUE, values = starts[[1]][[traj]][4],
labels = paste0(y_var[traj], "_acc_ratio"),
name = paste0(y_var[traj], "_mug"))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj], "_mueta1, ",
y_var[traj], "_mueta2, ", y_var[traj], "_acc_ratio)"),
name = paste0(y_var[traj], "_mean0"))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0", y_var[traj]),
to = paste0("l", y_var_L[traj], records[[traj]][1]),
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]),
to = paste0("d", y_var_L[traj], records[[traj]][-1]),
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta2", y_var[traj]),
to = paste0("d", y_var_L[traj], records[[traj]][-1]),
arrows = 1, free = FALSE, values = 0,
labels = paste0(y_var[traj], "L2", records[[traj]][-1], "[1,1]")),
mxPath(from = paste0("deltag", y_var[traj]),
to = paste0("d", y_var_L[traj], records[[traj]][-1]), arrows = 1, free = FALSE, values = 0,
labels = paste0(y_var[traj], "L3", records[[traj]][-1], "[1,1]")))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj], "_psi01, ",
y_var[traj], "_psi02, ", y_var[traj], "_psi0g), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj], "_psi11, ",
y_var[traj], "_psi12, ", y_var[traj], "_psi1g), ",
"cbind(", y_var[traj], "_psi02, ", y_var[traj], "_psi12, ",
y_var[traj], "_psi22, ", y_var[traj], "_psi2g), ",
"cbind(", y_var[traj], "_psi0g, ", y_var[traj], "_psi1g, ",
y_var[traj], "_psi2g, ", y_var[traj], "_psigg))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi", c("00", "01", "02", "0g", "01", "11", "12", "1g",
"02", "12", "22", "2g", "0g", "1g", "2g", "gg")),
byrow = T, nrow = 4, ncol = 4)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ",
y_var[traj_i], y_var[traj_j + 1], "_psi01, ",
y_var[traj_i], y_var[traj_j + 1], "_psi02, ",
y_var[traj_i], y_var[traj_j + 1], "_psi0g), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11, ",
y_var[traj_i], y_var[traj_j + 1], "_psi12, ",
y_var[traj_i], y_var[traj_j + 1], "_psi1g), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi20, ",
y_var[traj_i], y_var[traj_j + 1], "_psi21, ",
y_var[traj_i], y_var[traj_j + 1], "_psi22, ",
y_var[traj_i], y_var[traj_j + 1], "_psi2g), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psig0, ",
y_var[traj_i], y_var[traj_j + 1], "_psig1, ",
y_var[traj_i], y_var[traj_j + 1], "_psig2, ",
y_var[traj_i], y_var[traj_j + 1], "_psigg))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi",
c("00", "01", "02", "0g", "10", "11", "12", "1g",
"20", "21", "22", "2g", "g0", "g1", "g2", "gg")),
byrow = T, nrow = 4, ncol = 4)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 4 + 1):((traj - 1) * 4 + 4), ((traj - 1) * 4 + 1):((traj - 1) * 4 + 4)] <-
gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 4 + 1):((traj_i - 1) * 4 + 4), (traj_j * 4 + 1):(traj_j * 4 + 4)] <-
gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Change Score Model, Jenss Bayley (random ratio)", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents[1:(length(y_var) * 4)], to = latents[1:(length(y_var) * 4)],
arrows = 2, connect = "unique.pairs",
free = TRUE, values = t(starts[[2]])[row(t(starts[[2]])) >= col(t(starts[[2]]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, AddPara, GAMMA, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L,
psi_btw_L, PATH_L_L, PATH_SLP_L, PATH_AUTO_L)
}
else if (!intrinsic){
latents <- c(paste0(rep(c("eta0", "eta1", "eta2"), length(y_var)), rep(y_var, each = 3)),
unlist(L_list), unlist(D_list))
multi_label <- matrix(NA, nrow = 3 * length(y_var), ncol = 3 * length(y_var))
GF_MEAN <- GF_LOADINGS <- GAMMA <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1", "eta2"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:3],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1", "_mueta2")))
GAMMA[[traj]] <- mxMatrix("Full", 1, 1, free = TRUE, values = starts[[1]][[traj]][4],
labels = paste0(y_var[traj], "_acc_ratio"),
name = paste0(y_var[traj], "_mug"))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj], "_mueta1, ",
y_var[traj], "_mueta2, ", y_var[traj], "_acc_ratio)"),
name = paste0(y_var[traj], "_mean0"))
GF_LOADINGS[[length(GF_LOADINGS) + 1]] <- list(mxPath(from = paste0("eta0", y_var[traj]),
to = paste0("l", y_var_L[traj], records[[traj]][1]),
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]),
to = paste0("d", y_var_L[traj], records[[traj]][-1]),
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta2", y_var[traj]),
to = paste0("d", y_var_L[traj], records[[traj]][-1]),
arrows = 1, free = FALSE, values = 0,
labels = paste0(y_var[traj], "L2", records[[traj]][-1], "[1,1]")))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj], "_psi01, ",
y_var[traj], "_psi02), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj], "_psi11, ",
y_var[traj], "_psi12), ",
"cbind(", y_var[traj], "_psi02, ", y_var[traj], "_psi12, ",
y_var[traj], "_psi22))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi", c("00", "01", "02", "01", "11", "12",
"02", "12", "22")),
byrow = T, nrow = 3, ncol = 3)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ",
y_var[traj_i], y_var[traj_j + 1], "_psi01, ",
y_var[traj_i], y_var[traj_j + 1], "_psi02), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11, ",
y_var[traj_i], y_var[traj_j + 1], "_psi12), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi20, ",
y_var[traj_i], y_var[traj_j + 1], "_psi21, ",
y_var[traj_i], y_var[traj_j + 1], "_psi22))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi",
c("00", "01", "02", "10", "11", "12",
"20", "21", "22")),
byrow = T, nrow = 3, ncol = 3)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 3 + 1):((traj - 1) * 3 + 3), ((traj - 1) * 3 + 1):((traj - 1) * 3 + 3)] <-
gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 3 + 1):((traj_i - 1) * 3 + 3), (traj_j * 3 + 1):(traj_j * 3 + 3)] <-
gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Change Score Model, Jenss Bayley (fixed ratio)", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents[1:(length(y_var) * 3)], to = latents[1:(length(y_var) * 3)],
arrows = 2, connect = "unique.pairs", free = TRUE,
values = t(starts[[2]][c(1:3, 5:7), c(1:3, 5:7)])[row(t(starts[[2]][c(1:3, 5:7), c(1:3, 5:7)])) >=
col(t(starts[[2]][c(1:3, 5:7), c(1:3, 5:7)]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, AddPara, GAMMA, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L,
psi_btw_L, PATH_L_L, PATH_SLP_L, PATH_AUTO_L)
}
}
}
return(model_mx)
}
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Defines functions getMGM.mxModel
Documented in getMGM.mxModel
#' @title Construct An Object of mxModel for Multivariate Latent Growth Curve Models or Multivariate Latent Change Score
#' Models To Be Evaluated
#'
#' @description This function builds up an object of mxModel for a multivariate latent growth curve model or a multivariate latent
#' change score model with user-specified functional form (including whether intrinsically nonlinear).
#'
#' @param dat A wide-format data frame, with each row corresponding to a unique ID. It contains the observed variables
#' with repeated measurements and occasions for multiple longitudinal outcomes. It takes the value passed from \code{getMGM()}.
#' @param t_var A vector of strings, with each element representing the prefix for column names related to the time
#' variable for the corresponding outcome variable at each study wave. It takes the value passed from \code{getMGM()}.
#' @param y_var A vector of strings, with each element representing the prefix for column names corresponding to a
#' particular outcome variable at each study wave. It takes the value passed from \code{getMGM()}.
#' @param curveFun A string specifying the functional form of the growth curve. Supported options for \code{y_model =
#' "LGCM"} include: \code{"linear"} (or \code{"LIN"}), \code{"quadratic"} (or \code{"QUAD"}), \code{"negative exponential"}
#' (or \code{"EXP"}), \code{"Jenss-Bayley"} (or \code{"JB"}), and \code{"bilinear spline"} (or \code{"BLS"}). Supported
#' options for \code{y_model = "LCSM"} include: \code{"quadratic"} (or \code{"QUAD"}), \code{"negative exponential"}
#' (or \code{"EXP"}), \code{"Jenss-Bayley"} (or \code{"JB"}), and \code{"nonparametric"} (or \code{"NonP"}). It takes the
#' value passed from \code{getMGM()}.
#' @param intrinsic A logical flag indicating whether to build an intrinsically nonlinear longitudinal model. It takes the
#' value passed from \code{getMGM()}.
#' @param records A list of numeric vectors, with each vector specifying the indices of the observed study waves for
#' the corresponding outcome variable. It takes the value passed from \code{getMGM()}.
#' @param y_model A string specifying how to fit the longitudinal outcome. Supported values are \code{"LGCM"} and \code{"LCSM"}.
#' It takes the value passed from \code{getMGM()}.
#' @param starts A list of initial values for the parameters, either takes the value passed from \code{getMGM()} or derived
#' by the helper function \code{getMULTI.initial()}.
#'
#' @return A pre-optimized mxModel for a multivariate latent growth curve model or a multivariate latent change
#' score model.
#'
#' @keywords internal
#'
getMGM.mxModel <- function(dat, t_var, y_var, curveFun, intrinsic, records, y_model, starts){
y_var_L <- tolower(y_var)
# Define manifest variables
traj_list <- list()
for (traj in 1:length(y_var)){
traj_list[[length(traj_list) + 1]] <- paste0(y_var[traj], records[[traj]])
}
manifests <- unlist(traj_list)
# Define variances and covariance(s) of residuals
RES <- COV <- list()
for (traj in 1:length(y_var)){
RES[[traj]] <- mxPath(from = traj_list[[traj]], to = traj_list[[traj]], arrows = 2, free = TRUE,
values = starts[[3]][traj, traj],
labels = paste0(y_var[traj], "_residuals"))
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
if (setequal(substr(traj_list[[traj_i]], 2, 2), substr(traj_list[[traj_j + 1]], 2, 2))){
COV[[traj_i + traj_j - 1]] <- mxPath(from = traj_list[[traj_i]], to = traj_list[[traj_j + 1]],
arrows = 2, free = TRUE, values = starts[[3]][traj_i, traj_j + 1],
labels = paste0(y_var[traj_i], y_var[traj_j + 1], "_RES"))
}
else{
T_common <- Reduce(intersect, list(substr(traj_list[[traj_i]], 2, 2), substr(traj_list[[traj_j + 1]], 2, 2)))
COV[[traj_i + traj_j - 1]] <- mxPath(from = paste0(y_var[traj_i], T_common),
to = paste0(y_var[traj_j + 1], T_common),
arrows = 2, free = TRUE, values = starts[[3]][traj_i, traj_j + 1],
labels = paste0(y_var[traj_i], y_var[traj_j + 1], "_RES"))
}
}
}
# Obtain factor loadigs for the specified trajectory model (either "LGCM" or "LCSM") and functional form
GF_loadings <- getMULTI.loadings(y_model = y_model, t_var = t_var, y_var = y_var, curveFun = curveFun,
intrinsic = intrinsic, records = records)
if (y_model == "LGCM"){
if (curveFun %in% c("linear", "LIN")){
latents <- paste0(rep(c("eta0", "eta1"), length(y_var)), rep(y_var, each = 2))
multi_label <- matrix(NA, nrow = length(latents), ncol = length(latents))
GF_MEAN <- GF_LOADINGS <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:2],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1")))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE,
labels = paste0("L1", records[[traj]], y_var[traj], "[1,1]")))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj], "_mueta1)"),
name = paste0(y_var[traj], "_mean0"))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj], "_psi01), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj], "_psi11))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi", c("00", "01", "01", "11")),
byrow = T, nrow = 2, ncol = 2)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ", y_var[traj_i], y_var[traj_j + 1], "_psi01), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ", y_var[traj_i], y_var[traj_j + 1], "_psi11))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi", c("00", "01", "10", "11")),
byrow = T, nrow = 2, ncol = 2)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 2 + 1):((traj - 1) * 2 + 2), ((traj - 1) * 2 + 1):((traj - 1) * 2 + 2)] <- gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 2 + 1):((traj_i - 1) * 2 + 2), (traj_j * 2 + 1):(traj_j * 2 + 2)] <- gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Growth Curve Model, Linear", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents, to = latents, arrows = 2, connect = "unique.pairs",
free = TRUE, values = t(starts[[2]])[row(t(starts[[2]])) >= col(t(starts[[2]]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L, psi_btw_L)
}
else if (curveFun %in% c("quadratic", "QUAD")){
latents <- paste0(rep(c("eta0", "eta1", "eta2"), length(y_var)), rep(y_var, each = 3))
multi_label <- matrix(NA, nrow = length(latents), ncol = length(latents))
GF_MEAN <- GF_LOADINGS <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1", "eta2"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:3],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1", "_mueta2")))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE,
labels = paste0("L1", records[[traj]], y_var[traj], "[1,1]")),
mxPath(from = paste0("eta2", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE,
labels = paste0("L2", records[[traj]], y_var[traj], "[1,1]")))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj],
"_mueta1, ", y_var[traj], "_mueta2)"),
name = paste0(y_var[traj], "_mean0"))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj],
"_psi01, ", y_var[traj], "_psi02), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj],
"_psi11, ", y_var[traj], "_psi12), ",
"cbind(", y_var[traj], "_psi02, ", y_var[traj],
"_psi12, ", y_var[traj], "_psi22))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi",
c("00", "01", "02", "01", "11", "12", "02", "12", "22")),
byrow = T, nrow = 3, ncol = 3)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ",
y_var[traj_i], y_var[traj_j + 1], "_psi01, ",
y_var[traj_i], y_var[traj_j + 1], "_psi02),",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11, ",
y_var[traj_i], y_var[traj_j + 1], "_psi12), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi20, ",
y_var[traj_i], y_var[traj_j + 1], "_psi21, ",
y_var[traj_i], y_var[traj_j + 1], "_psi22))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi",
c("00", "01", "02", "10", "11", "12", "20", "21", "22")),
byrow = T, nrow = 3, ncol = 3)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 3 + 1):((traj - 1) * 3 + 3), ((traj - 1) * 3 + 1):((traj - 1) * 3 + 3)] <- gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 3 + 1):((traj_i - 1) * 3 + 3), (traj_j * 3 + 1):(traj_j * 3 + 3)] <- gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Growth Curve Model, Quadratic", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents, to = latents, arrows = 2, connect = "unique.pairs",
free = TRUE, values = t(starts[[2]])[row(t(starts[[2]])) >= col(t(starts[[2]]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L, psi_btw_L)
}
else if (curveFun %in% c("negative exponential", "EXP")){
if (intrinsic){
latents <- paste0(rep(c("eta0", "eta1", "deltag"), length(y_var)), rep(y_var, each = 3))
multi_label <- matrix(NA, nrow = length(latents), ncol = length(latents))
GF_MEAN <- GF_LOADINGS <- GAMMA <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:2],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1")))
GAMMA[[traj]] <- mxMatrix("Full", 1, 1, free = TRUE, values = starts[[1]][[traj]][3],
labels = paste0(y_var[traj], "_slp_ratio"),
name = paste0(y_var[traj], "_mug"))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj], "_mueta1, ",
y_var[traj], "_slp_ratio)"),
name = paste0(y_var[traj], "_mean0"))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE,
labels = paste0("L1", records[[traj]], y_var[traj], "[1,1]")),
mxPath(from = paste0("deltag", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 0,
labels = paste0("L2", records[[traj]], y_var[traj], "[1,1]")))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj],
"_psi01, ", y_var[traj], "_psi0g), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj],
"_psi11, ", y_var[traj], "_psi1g), ",
"cbind(", y_var[traj], "_psi0g, ", y_var[traj],
"_psi1g, ", y_var[traj], "_psigg))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi",
c("00", "01", "0g", "01", "11", "1g", "0g", "1g", "gg")),
byrow = T, nrow = 3, ncol = 3)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ",
y_var[traj_i], y_var[traj_j + 1],
"_psi01, ", y_var[traj_i], y_var[traj_j + 1], "_psi0g),",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11, ",
y_var[traj_i], y_var[traj_j + 1], "_psi1g), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psig0, ",
y_var[traj_i], y_var[traj_j + 1], "_psig1, ",
y_var[traj_i], y_var[traj_j + 1], "_psigg))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi",
c("00", "01", "0g", "10", "11", "1g", "g0", "g1", "gg")),
byrow = T, nrow = 3, ncol = 3)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 3 + 1):((traj - 1) * 3 + 3), ((traj - 1) * 3 + 1):((traj - 1) * 3 + 3)] <-
gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 3 + 1):((traj_i - 1) * 3 + 3), (traj_j * 3 + 1):(traj_j * 3 + 3)] <-
gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Growth Curve Model, Negative Exponential (random ratio)", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents, to = latents, arrows = 2, connect = "unique.pairs",
free = TRUE, values = t(starts[[2]])[row(t(starts[[2]])) >= col(t(starts[[2]]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, GAMMA, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L, psi_btw_L)
}
else if (!intrinsic){
latents <- paste0(rep(c("eta0", "eta1"), length(y_var)), rep(y_var, each = 2))
multi_label <- matrix(NA, nrow = length(latents), ncol = length(latents))
GF_MEAN <- GF_LOADINGS <- GAMMA <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:2],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1")))
GAMMA[[traj]] <- mxMatrix("Full", 1, 1, free = TRUE, values = starts[[1]][[traj]][3],
labels = paste0(y_var[traj], "_slp_ratio"),
name = paste0(y_var[traj], "_mug"))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj], "_mueta1, ",
y_var[traj], "_slp_ratio)"),
name = paste0(y_var[traj], "_mean0"))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE,
labels = paste0("L1", records[[traj]], y_var[traj], "[1,1]")))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj], "_psi01), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj], "_psi11))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi", c("00", "01", "01", "11")),
byrow = T, nrow = 2, ncol = 2)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ",
y_var[traj_i], y_var[traj_j + 1], "_psi01), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi", c("00", "01", "10", "11")),
byrow = T, nrow = 2, ncol = 2)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 2 + 1):((traj - 1) * 2 + 2), ((traj - 1) * 2 + 1):((traj - 1) * 2 + 2)] <-
gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 2 + 1):((traj_i - 1) * 2 + 2), (traj_j * 2 + 1):(traj_j * 2 + 2)] <-
gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Growth Curve Model, Negative Exponential (fixed ratio)", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents, to = latents, arrows = 2, connect = "unique.pairs", free = TRUE,
values = t(starts[[2]][c(1:2, 4:5), c(1:2, 4:5)])[row(t(starts[[2]][c(1:2, 4:5), c(1:2, 4:5)])) >=
col(t(starts[[2]][c(1:2, 4:5), c(1:2, 4:5)]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, GAMMA, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L, psi_btw_L)
}
}
else if (curveFun %in% c("Jenss-Bayley", "JB")){
if (intrinsic){
latents <- paste0(rep(c("eta0", "eta1", "eta2", "deltag"), length(y_var)), rep(y_var, each = 4))
multi_label <- matrix(NA, nrow = length(latents), ncol = length(latents))
GF_MEAN <- GF_LOADINGS <- GAMMA <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1", "eta2"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:3],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1", "_mueta2")))
GAMMA[[traj]] <- mxMatrix("Full", 1, 1, free = TRUE, values = starts[[1]][[traj]][4],
labels = paste0(y_var[traj], "_acc_ratio"),
name = paste0(y_var[traj], "_mug"))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj], "_mueta1, ",
y_var[traj], "_mueta2, ", y_var[traj], "_acc_ratio)"),
name = paste0(y_var[traj], "_mean0"))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 0,
labels = paste0("L1", records[[traj]], y_var[traj], "[1,1]")),
mxPath(from = paste0("eta2", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 0,
labels = paste0("L2", records[[traj]], y_var[traj], "[1,1]")),
mxPath(from = paste0("deltag", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 0,
labels = paste0("L3", records[[traj]], y_var[traj], "[1,1]")))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj], "_psi01, ",
y_var[traj], "_psi02, ", y_var[traj], "_psi0g), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj], "_psi11, ",
y_var[traj], "_psi12, ", y_var[traj], "_psi1g), ",
"cbind(", y_var[traj], "_psi02, ", y_var[traj], "_psi12, ",
y_var[traj], "_psi22, ", y_var[traj], "_psi2g), ",
"cbind(", y_var[traj], "_psi0g, ", y_var[traj], "_psi1g, ",
y_var[traj], "_psi2g, ", y_var[traj], "_psigg))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi", c("00", "01", "02", "0g", "01", "11", "12", "1g",
"02", "12", "22", "2g", "0g", "1g", "2g", "gg")),
byrow = T, nrow = 4, ncol = 4)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ",
y_var[traj_i], y_var[traj_j + 1], "_psi01, ",
y_var[traj_i], y_var[traj_j + 1], "_psi02, ",
y_var[traj_i], y_var[traj_j + 1], "_psi0g), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11, ",
y_var[traj_i], y_var[traj_j + 1], "_psi12, ",
y_var[traj_i], y_var[traj_j + 1], "_psi1g), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi20, ",
y_var[traj_i], y_var[traj_j + 1], "_psi21, ",
y_var[traj_i], y_var[traj_j + 1], "_psi22, ",
y_var[traj_i], y_var[traj_j + 1], "_psi2g), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psig0, ",
y_var[traj_i], y_var[traj_j + 1], "_psig1, ",
y_var[traj_i], y_var[traj_j + 1], "_psig2, ",
y_var[traj_i], y_var[traj_j + 1], "_psigg))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi",
c("00", "01", "02", "0g", "10", "11", "12", "1g",
"20", "21", "22", "2g", "g0", "g1", "g2", "gg")),
byrow = T, nrow = 4, ncol = 4)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 4 + 1):((traj - 1) * 4 + 4), ((traj - 1) * 4 + 1):((traj - 1) * 4 + 4)] <-
gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 4 + 1):((traj_i - 1) * 4 + 4), (traj_j * 4 + 1):(traj_j * 4 + 4)] <-
gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Growth Curve Model, Jenss Bayley (random ratio)", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents, to = latents, arrows = 2, connect = "unique.pairs",
free = TRUE, values = t(starts[[2]])[row(t(starts[[2]])) >= col(t(starts[[2]]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, GAMMA, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L, psi_btw_L)
}
else if (!intrinsic){
latents <- paste0(rep(c("eta0", "eta1", "eta2"), length(y_var)), rep(y_var, each = 3))
multi_label <- matrix(NA, nrow = length(latents), ncol = length(latents))
GF_MEAN <- GF_LOADINGS <- GAMMA <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1", "eta2"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:3],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1", "_mueta2")))
GAMMA[[traj]] <- mxMatrix("Full", 1, 1, free = TRUE, values = starts[[1]][[traj]][4],
labels = paste0(y_var[traj], "_acc_ratio"),
name = paste0(y_var[traj], "_mug"))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj], "_mueta1, ",
y_var[traj], "_mueta2, ", y_var[traj], "_acc_ratio)"),
name = paste0(y_var[traj], "_mean0"))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 0,
labels = paste0("L1", records[[traj]], y_var[traj], "[1,1]")),
mxPath(from = paste0("eta2", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 0,
labels = paste0("L2", records[[traj]], y_var[traj], "[1,1]")))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj], "_psi01, ",
y_var[traj], "_psi02), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj], "_psi11, ",
y_var[traj], "_psi12), ",
"cbind(", y_var[traj], "_psi02, ", y_var[traj], "_psi12, ",
y_var[traj], "_psi22))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi", c("00", "01", "02", "01", "11", "12",
"02", "12", "22")),
byrow = T, nrow = 3, ncol = 3)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ",
y_var[traj_i], y_var[traj_j + 1], "_psi01, ",
y_var[traj_i], y_var[traj_j + 1], "_psi02), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11, ",
y_var[traj_i], y_var[traj_j + 1], "_psi12), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi20, ",
y_var[traj_i], y_var[traj_j + 1], "_psi21, ",
y_var[traj_i], y_var[traj_j + 1], "_psi22))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi",
c("00", "01", "02", "10", "11", "12",
"20", "21", "22")),
byrow = T, nrow = 3, ncol = 3)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 3 + 1):((traj - 1) * 3 + 3), ((traj - 1) * 3 + 1):((traj - 1) * 3 + 3)] <-
gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 3 + 1):((traj_i - 1) * 3 + 3), (traj_j * 3 + 1):(traj_j * 3 + 3)] <-
gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Growth Curve Model, Jenss Bayley (fixed ratio)", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents, to = latents, arrows = 2, connect = "unique.pairs", free = TRUE,
values = t(starts[[2]][c(1:3, 5:7), c(1:3, 5:7)])[row(t(starts[[2]][c(1:3, 5:7), c(1:3, 5:7)])) >=
col(t(starts[[2]][c(1:3, 5:7), c(1:3, 5:7)]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, GAMMA, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L, psi_btw_L)
}
}
else if (curveFun %in% c("bilinear spline", "BLS")){
if (intrinsic){
latents <- paste0(rep(c("eta0s", "eta1s", "eta2s", "deltag"), length(y_var)), rep(y_var, each = 4))
multi_label <- matrix(NA, nrow = length(latents), ncol = length(latents))
GF_MEAN <- GF_LOADINGS <- GAMMA <- list()
func_L <- grad_L <- mean_s_L <- psi_s_L <- mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_s_L <- psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0s", "eta1s", "eta2s"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:3],
labels = paste0(y_var[traj], c("_mueta0s", "_mueta1s", "_mueta2s")))
GAMMA[[traj]] <- mxMatrix("Full", 1, 1, free = TRUE, values = starts[[1]][[traj]][4],
labels = paste0(y_var[traj], "_knot"),
name = paste0(y_var[traj], "_mug"))
mean_s_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0s, ", y_var[traj], "_mueta1s, ",
y_var[traj], "_mueta2s, ", y_var[traj], "_knot)"),
name = paste0(y_var[traj], "_mean_s"))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0s", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1s", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 0,
labels = paste0("L1", records[[traj]], y_var[traj], "[1,1]")),
mxPath(from = paste0("eta2s", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 0,
labels = paste0("L2", records[[traj]], y_var[traj], "[1,1]")),
mxPath(from = paste0("deltag", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 0,
labels = paste0("L3", records[[traj]], y_var[traj], "[1,1]")))
func_L[[length(func_L) + 1]] <- mxAlgebraFromString(paste0("rbind(cbind(1, -", y_var[traj], "_mug, ", y_var[traj], "_mug, 0), ",
"cbind(0, 1, -1, 0), ", "cbind(0, 1, 1, 0)", ", cbind(0, 0, 0, 1))"),
name = paste0("func", y_var[traj]))
grad_L[[length(grad_L) + 1]] <- mxAlgebraFromString(paste0("rbind(cbind(1, -", y_var[traj], "_mug, ", y_var[traj], "_mug, 0), ",
"cbind(0, 1, -1, 0), ", "cbind(0, 1, 1, 0)", ", cbind(0, 0, 0, 1))"),
name = paste0("grad", y_var[traj]))
psi_s_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00s, ", y_var[traj], "_psi01s, ",
y_var[traj], "_psi02s, ", y_var[traj], "_psi0gs), ",
"cbind(", y_var[traj], "_psi01s, ", y_var[traj], "_psi11s, ",
y_var[traj], "_psi12s, ", y_var[traj], "_psi1gs), ",
"cbind(", y_var[traj], "_psi02s, ", y_var[traj], "_psi12s, ",
y_var[traj], "_psi22s, ", y_var[traj], "_psi2gs), ",
"cbind(", y_var[traj], "_psi0gs, ", y_var[traj], "_psi1gs, ",
y_var[traj], "_psi2gs, ", y_var[traj], "_psiggs))"),
name = paste0(y_var[traj], "_psi_s"))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(func", y_var[traj], " %*% ", y_var[traj],
"_mean_s)"), name = paste0(y_var[traj], "_mean0"))
psi_L[[traj]] <- mxAlgebraFromString(paste0("grad", y_var[traj], " %*% ", y_var[traj], "_psi_s",
" %*% t(grad", y_var[traj], ")"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi", c("00s", "01s", "02s", "0gs", "01s", "11s", "12s", "1gs",
"02s", "12s", "22s", "2gs", "0gs", "1gs", "2gs", "ggs")),
byrow = T, nrow = 4, ncol = 4)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_s_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi01s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi02s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi0gs), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi12s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi1gs), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi20s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi21s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi22s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi2gs), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psig0s, ",
y_var[traj_i], y_var[traj_j + 1], "_psig1s, ",
y_var[traj_i], y_var[traj_j + 1], "_psig2s, ",
y_var[traj_i], y_var[traj_j + 1], "_psiggs))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi_s"))
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("grad", y_var[traj_i], " %*% ",
y_var[traj_i], y_var[traj_j + 1], "_psi_s",
" %*% t(grad", y_var[traj_j + 1], ")"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi",
c("00s", "01s", "02s", "0gs", "10s", "11s", "12s", "1gs",
"20s", "21s", "22s", "2gs", "g0s", "g1s", "g2s", "ggs")),
byrow = T, nrow = 4, ncol = 4)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 4 + 1):((traj - 1) * 4 + 4), ((traj - 1) * 4 + 1):((traj - 1) * 4 + 4)] <-
gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 4 + 1):((traj_i - 1) * 4 + 4), (traj_j * 4 + 1):(traj_j * 4 + 4)] <-
gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Growth Curve Model, Bilinear Spline (random knot)", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents, to = latents, arrows = 2, connect = "unique.pairs",
free = TRUE, values = t(starts[[2]])[row(t(starts[[2]])) >= col(t(starts[[2]]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, GAMMA, func_L, grad_L, mean_s_L, psi_s_L, psi_btw_s_L,
GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L, psi_btw_L)
}
else if (!intrinsic){
latents <- paste0(rep(c("eta0s", "eta1s", "eta2s"), length(y_var)), rep(y_var, each = 3))
multi_label <- matrix(NA, nrow = length(latents), ncol = length(latents))
GF_MEAN <- GF_LOADINGS <- GAMMA <- list()
func_L <- grad_L <- mean_s_L <- psi_s_L <- mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_s_L <- psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0s", "eta1s", "eta2s"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:3],
labels = paste0(y_var[traj], c("_mueta0s", "_mueta1s", "_mueta2s")))
GAMMA[[traj]] <- mxMatrix("Full", 1, 1, free = TRUE, values = starts[[1]][[traj]][4],
labels = paste0(y_var[traj], "_knot"),
name = paste0(y_var[traj], "_mug"))
mean_s_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0s, ", y_var[traj], "_mueta1s, ",
y_var[traj], "_mueta2s)"),
name = paste0(y_var[traj], "_mean_s"))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0s", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1s", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 0,
labels = paste0("L1", records[[traj]], y_var[traj], "[1,1]")),
mxPath(from = paste0("eta2s", y_var[traj]), to = traj_list[[traj]],
arrows = 1, free = FALSE, values = 0,
labels = paste0("L2", records[[traj]], y_var[traj], "[1,1]")))
func_L[[length(func_L) + 1]] <- mxAlgebraFromString(paste0("rbind(cbind(1, -", y_var[traj], "_mug, ", y_var[traj], "_mug), ",
"cbind(0, 1, -1), ", "cbind(0, 1, 1))"),
name = paste0("func", y_var[traj]))
grad_L[[length(grad_L) + 1]] <- mxAlgebraFromString(paste0("rbind(cbind(1, -", y_var[traj], "_mug, ", y_var[traj], "_mug), ",
"cbind(0, 1, -1), ", "cbind(0, 1, 1))"),
name = paste0("grad", y_var[traj]))
psi_s_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00s, ", y_var[traj], "_psi01s, ",
y_var[traj], "_psi02s), ",
"cbind(", y_var[traj], "_psi01s, ", y_var[traj], "_psi11s, ",
y_var[traj], "_psi12s), ",
"cbind(", y_var[traj], "_psi02s, ", y_var[traj], "_psi12s, ",
y_var[traj], "_psi22s))"),
name = paste0(y_var[traj], "_psi_s"))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(func", y_var[traj], " %*% ", y_var[traj],
"_mean_s, ", y_var[traj], "_knot)"),
name = paste0(y_var[traj], "_mean0"))
psi_L[[traj]] <- mxAlgebraFromString(paste0("grad", y_var[traj], " %*% ", y_var[traj], "_psi_s",
" %*% t(grad", y_var[traj], ")"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi", c("00s", "01s", "02s", "01s", "11s", "12s",
"02s", "12s", "22s")),
byrow = T, nrow = 3, ncol = 3)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_s_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi01s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi02s), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi12s), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi20s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi21s, ",
y_var[traj_i], y_var[traj_j + 1], "_psi22s))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi_s"))
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("grad", y_var[traj_i], " %*% ",
y_var[traj_i], y_var[traj_j + 1], "_psi_s",
" %*% t(grad", y_var[traj_j + 1], ")"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi",
c("00s", "01s", "02s", "10s", "11s", "12s", "20s", "21s", "22s")),
byrow = T, nrow = 3, ncol = 3)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 3 + 1):((traj - 1) * 3 + 3), ((traj - 1) * 3 + 1):((traj - 1) * 3 + 3)] <-
gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 3 + 1):((traj_i - 1) * 3 + 3), (traj_j * 3 + 1):(traj_j * 3 + 3)] <-
gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Growth Curve Model, Bilinear Spline (fixed knot)", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents, to = latents, arrows = 2, connect = "unique.pairs", free = TRUE,
values = t(starts[[2]][c(1:3, 5:7), c(1:3, 5:7)])[row(t(starts[[2]][c(1:3, 5:7), c(1:3, 5:7)])) >=
col(t(starts[[2]][c(1:3, 5:7), c(1:3, 5:7)]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, GAMMA, func_L, grad_L, mean_s_L, psi_s_L, psi_btw_s_L,
GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L, psi_btw_L)
}
}
}
else if (y_model == "LCSM"){
# Obtain additional parameters (derived) for the specified functional form
AddPara <- getMULTI.addpara(dat = dat, y_var = y_var, curveFun = curveFun, intrinsic = intrinsic,
t_var = t_var, records = records, starts = starts)
# Define latent variables in addition to growth factors
L_list <- D_list <- list()
for (traj in 1:length(y_var)){
L_list[[traj]] <- paste0("l", y_var_L[traj], records[[traj]])
D_list[[traj]] <- paste0("d", y_var_L[traj], records[[traj]][-1])
}
PATH_L_L <- PATH_SLP_L <- PATH_AUTO_L <- list()
for (traj in 1:length(y_var)){
# Define paths from latent true scores to observed scores
PATH_L_L[[traj]] <- mxPath(from = paste0("l", y_var_L[traj], records[[traj]]),
to = paste0(y_var[[traj]], records[[traj]]), arrows = 1, free = FALSE, values = 1)
# Define paths from latent instantaneous rate of change at each measurement to true scores
PATH_SLP_L[[traj]] <- mxPath(from = paste0("d", y_var_L[traj], records[[traj]][-1]),
to = paste0("l", y_var_L[traj], records[[traj]][-1]),
arrows = 1, free = FALSE, values = 0,
labels = paste0(y_var[traj], "lag", records[[traj]][-1], "[1,1]"))
# Define autoregressive paths
PATH_AUTO_L[[traj]] <- mxPath(from = paste0("l", y_var_L[traj], records[[traj]][-length(records[[traj]])]),
to = paste0("l", y_var_L[traj], records[[traj]][-1]), arrows = 1,
free = FALSE, values = 1)
}
if (curveFun %in% c("nonparametric", "NonP")){
latents <- c(paste0(rep(c("eta0", "eta1"), length(y_var)), rep(y_var, each = 2)),
unlist(L_list), unlist(D_list))
multi_label <- matrix(NA, nrow = 2 * length(y_var), ncol = 2 * length(y_var))
GF_MEAN <- GF_LOADINGS <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:2],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1")))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0", y_var[traj]),
to = paste0("l", y_var_L[traj], records[[traj]][1]),
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]),
to = paste0("d", y_var_L[traj], records[[traj]][-1]),
arrows = 1, free = c(F, rep(T, length(records[[traj]]) - 2)),
values = c(1, starts[[4]][[traj]][-1]),
labels = paste0(y_var[traj], "_rel_rate",
1:(length(records[[traj]]) - 1))))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj], "_mueta1)"),
name = paste0(y_var[traj], "_mean0"))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj], "_psi01), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj], "_psi11))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi", c("00", "01", "01", "11")),
byrow = T, nrow = 2, ncol = 2)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ", y_var[traj_i], y_var[traj_j + 1], "_psi01), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ", y_var[traj_i], y_var[traj_j + 1], "_psi11))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi", c("00", "01", "10", "11")),
byrow = T, nrow = 2, ncol = 2)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 2 + 1):((traj - 1) * 2 + 2), ((traj - 1) * 2 + 1):((traj - 1) * 2 + 2)] <- gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 2 + 1):((traj_i - 1) * 2 + 2), (traj_j * 2 + 1):(traj_j * 2 + 2)] <- gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Change Score Model, Nonparametric", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents[1:(length(y_var) * 2)], to = latents[1:(length(y_var) * 2)],
arrows = 2, connect = "unique.pairs", free = TRUE, values = t(starts[[2]])[row(t(starts[[2]])) >= col(t(starts[[2]]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, AddPara, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L, psi_btw_L,
PATH_L_L, PATH_SLP_L, PATH_AUTO_L)
}
else if (curveFun %in% c("quadratic", "QUAD")){
latents <- c(paste0(rep(c("eta0", "eta1", "eta2"), length(y_var)), rep(y_var, each = 3)),
unlist(L_list), unlist(D_list))
multi_label <- matrix(NA, nrow = 3 * length(y_var), ncol = 3 * length(y_var))
GF_MEAN <- GF_LOADINGS <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1", "eta2"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:3],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1", "_mueta2")))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0", y_var[traj]),
to = paste0("l", y_var_L[traj], records[[traj]][1]),
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]),
to = paste0("d", y_var_L[traj], records[[traj]][-1]),
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta2", y_var[traj]),
to = paste0("d", y_var_L[traj], records[[traj]][-1]),
arrows = 1, free = FALSE, values = 0,
labels = paste0(y_var[traj], "L2", records[[traj]][-1], "[1,1]")))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj],
"_mueta1, ", y_var[traj], "_mueta2)"),
name = paste0(y_var[traj], "_mean0"))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj],
"_psi01, ", y_var[traj], "_psi02), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj],
"_psi11, ", y_var[traj], "_psi12), ",
"cbind(", y_var[traj], "_psi02, ", y_var[traj],
"_psi12, ", y_var[traj], "_psi22))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi",
c("00", "01", "02", "01", "11", "12", "02", "12", "22")),
byrow = T, nrow = 3, ncol = 3)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ",
y_var[traj_i], y_var[traj_j + 1], "_psi01, ",
y_var[traj_i], y_var[traj_j + 1], "_psi02),",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11, ",
y_var[traj_i], y_var[traj_j + 1], "_psi12), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi20, ",
y_var[traj_i], y_var[traj_j + 1], "_psi21, ",
y_var[traj_i], y_var[traj_j + 1], "_psi22))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi",
c("00", "01", "02", "10", "11", "12", "20", "21", "22")),
byrow = T, nrow = 3, ncol = 3)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 3 + 1):((traj - 1) * 3 + 3), ((traj - 1) * 3 + 1):((traj - 1) * 3 + 3)] <- gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 3 + 1):((traj_i - 1) * 3 + 3), (traj_j * 3 + 1):(traj_j * 3 + 3)] <- gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Change Score Model, Quadratic", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents[1:(length(y_var) * 3)], to = latents[1:(length(y_var) * 3)],
arrows = 2, connect = "unique.pairs", free = TRUE, values = t(starts[[2]])[row(t(starts[[2]])) >= col(t(starts[[2]]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, AddPara, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L, psi_btw_L,
PATH_L_L, PATH_SLP_L, PATH_AUTO_L)
}
else if (curveFun %in% c("negative exponential", "EXP")){
if (intrinsic){
latents <- c(paste0(rep(c("eta0", "eta1", "deltag"), length(y_var)), rep(y_var, each = 3)),
unlist(L_list), unlist(D_list))
multi_label <- matrix(NA, nrow = 3 * length(y_var), ncol = 3 * length(y_var))
GF_MEAN <- GF_LOADINGS <- GAMMA <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:2],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1")))
GAMMA[[traj]] <- mxMatrix("Full", 1, 1, free = TRUE, values = starts[[1]][[traj]][3],
labels = paste0(y_var[traj], "_slp_ratio"),
name = paste0(y_var[traj], "_mug"))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj], "_mueta1, ",
y_var[traj], "_slp_ratio)"),
name = paste0(y_var[traj], "_mean0"))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0", y_var[traj]),
to = paste0("l", y_var_L[traj], records[[traj]][1]),
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]),
to = paste0("d", y_var_L[traj], records[[traj]][-1]),
arrows = 1, free = FALSE, values = 0,
labels = paste0(y_var[traj], "L1", records[[traj]][-1], "[1,1]")),
mxPath(from = paste0("deltag", y_var[traj]),
to = paste0("d", y_var_L[traj], records[[traj]][-1]),
arrows = 1, free = FALSE, values = 0,
labels = paste0(y_var[traj], "L2", records[[traj]][-1], "[1,1]")))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj],
"_psi01, ", y_var[traj], "_psi0g), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj],
"_psi11, ", y_var[traj], "_psi1g), ",
"cbind(", y_var[traj], "_psi0g, ", y_var[traj],
"_psi1g, ", y_var[traj], "_psigg))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi",
c("00", "01", "0g", "01", "11", "1g", "0g", "1g", "gg")),
byrow = T, nrow = 3, ncol = 3)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ",
y_var[traj_i], y_var[traj_j + 1],
"_psi01, ", y_var[traj_i], y_var[traj_j + 1], "_psi0g),",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11, ",
y_var[traj_i], y_var[traj_j + 1], "_psi1g), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psig0, ",
y_var[traj_i], y_var[traj_j + 1], "_psig1, ",
y_var[traj_i], y_var[traj_j + 1], "_psigg))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi",
c("00", "01", "0g", "10", "11", "1g", "g0", "g1", "gg")),
byrow = T, nrow = 3, ncol = 3)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 3 + 1):((traj - 1) * 3 + 3), ((traj - 1) * 3 + 1):((traj - 1) * 3 + 3)] <-
gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 3 + 1):((traj_i - 1) * 3 + 3), (traj_j * 3 + 1):(traj_j * 3 + 3)] <-
gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Change Score Model, Negative Exponential", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents[1:(length(y_var) * 3)], to = latents[1:(length(y_var) * 3)],
arrows = 2, connect = "unique.pairs", free = TRUE,
values = t(starts[[2]])[row(t(starts[[2]])) >= col(t(starts[[2]]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, AddPara, GAMMA, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L,
psi_btw_L, PATH_L_L, PATH_SLP_L, PATH_AUTO_L)
}
else if (!intrinsic){
latents <- c(paste0(rep(c("eta0", "eta1"), length(y_var)), rep(y_var, each = 2)),
unlist(L_list), unlist(D_list))
multi_label <- matrix(NA, nrow = 2 * length(y_var), ncol = 2 * length(y_var))
GF_MEAN <- GF_LOADINGS <- GAMMA <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:2],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1")))
GAMMA[[traj]] <- mxMatrix("Full", 1, 1, free = TRUE, values = starts[[1]][[traj]][3],
labels = paste0(y_var[traj], "_slp_ratio"),
name = paste0(y_var[traj], "_mug"))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj], "_mueta1, ",
y_var[traj], "_slp_ratio)"),
name = paste0(y_var[traj], "_mean0"))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0", y_var[traj]),
to = paste0("l", y_var_L[traj], records[[traj]][1]),
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]),
to = paste0("d", y_var_L[traj], records[[traj]][-1]),
arrows = 1, free = FALSE, values = 0,
labels = paste0(y_var[traj], "L1", records[[traj]][-1], "[1,1]")))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj], "_psi01), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj], "_psi11))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi", c("00", "01", "01", "11")),
byrow = T, nrow = 2, ncol = 2)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ",
y_var[traj_i], y_var[traj_j + 1], "_psi01), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi", c("00", "01", "10", "11")),
byrow = T, nrow = 2, ncol = 2)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 2 + 1):((traj - 1) * 2 + 2), ((traj - 1) * 2 + 1):((traj - 1) * 2 + 2)] <-
gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 2 + 1):((traj_i - 1) * 2 + 2), (traj_j * 2 + 1):(traj_j * 2 + 2)] <-
gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Change Score Model, Negative Exponential", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents[1:(length(y_var) * 2)], to = latents[1:(length(y_var) * 2)],
arrows = 2, connect = "unique.pairs", free = TRUE,
values = t(starts[[2]][c(1:2, 4:5), c(1:2, 4:5)])[row(t(starts[[2]][c(1:2, 4:5), c(1:2, 4:5)])) >=
col(t(starts[[2]][c(1:2, 4:5), c(1:2, 4:5)]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, AddPara, GAMMA, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L,
psi_btw_L, PATH_L_L, PATH_SLP_L, PATH_AUTO_L)
}
}
else if (curveFun %in% c("Jenss-Bayley", "JB")){
if (intrinsic){
latents <- c(paste0(rep(c("eta0", "eta1", "eta2", "deltag"), length(y_var)), rep(y_var, each = 4)),
unlist(L_list), unlist(D_list))
multi_label <- matrix(NA, nrow = 4 * length(y_var), ncol = 4 * length(y_var))
GF_MEAN <- GF_LOADINGS <- GAMMA <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1", "eta2"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:3],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1", "_mueta2")))
GAMMA[[traj]] <- mxMatrix("Full", 1, 1, free = TRUE, values = starts[[1]][[traj]][4],
labels = paste0(y_var[traj], "_acc_ratio"),
name = paste0(y_var[traj], "_mug"))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj], "_mueta1, ",
y_var[traj], "_mueta2, ", y_var[traj], "_acc_ratio)"),
name = paste0(y_var[traj], "_mean0"))
GF_LOADINGS[[traj]] <- list(mxPath(from = paste0("eta0", y_var[traj]),
to = paste0("l", y_var_L[traj], records[[traj]][1]),
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]),
to = paste0("d", y_var_L[traj], records[[traj]][-1]),
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta2", y_var[traj]),
to = paste0("d", y_var_L[traj], records[[traj]][-1]),
arrows = 1, free = FALSE, values = 0,
labels = paste0(y_var[traj], "L2", records[[traj]][-1], "[1,1]")),
mxPath(from = paste0("deltag", y_var[traj]),
to = paste0("d", y_var_L[traj], records[[traj]][-1]), arrows = 1, free = FALSE, values = 0,
labels = paste0(y_var[traj], "L3", records[[traj]][-1], "[1,1]")))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj], "_psi01, ",
y_var[traj], "_psi02, ", y_var[traj], "_psi0g), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj], "_psi11, ",
y_var[traj], "_psi12, ", y_var[traj], "_psi1g), ",
"cbind(", y_var[traj], "_psi02, ", y_var[traj], "_psi12, ",
y_var[traj], "_psi22, ", y_var[traj], "_psi2g), ",
"cbind(", y_var[traj], "_psi0g, ", y_var[traj], "_psi1g, ",
y_var[traj], "_psi2g, ", y_var[traj], "_psigg))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi", c("00", "01", "02", "0g", "01", "11", "12", "1g",
"02", "12", "22", "2g", "0g", "1g", "2g", "gg")),
byrow = T, nrow = 4, ncol = 4)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ",
y_var[traj_i], y_var[traj_j + 1], "_psi01, ",
y_var[traj_i], y_var[traj_j + 1], "_psi02, ",
y_var[traj_i], y_var[traj_j + 1], "_psi0g), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11, ",
y_var[traj_i], y_var[traj_j + 1], "_psi12, ",
y_var[traj_i], y_var[traj_j + 1], "_psi1g), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi20, ",
y_var[traj_i], y_var[traj_j + 1], "_psi21, ",
y_var[traj_i], y_var[traj_j + 1], "_psi22, ",
y_var[traj_i], y_var[traj_j + 1], "_psi2g), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psig0, ",
y_var[traj_i], y_var[traj_j + 1], "_psig1, ",
y_var[traj_i], y_var[traj_j + 1], "_psig2, ",
y_var[traj_i], y_var[traj_j + 1], "_psigg))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi",
c("00", "01", "02", "0g", "10", "11", "12", "1g",
"20", "21", "22", "2g", "g0", "g1", "g2", "gg")),
byrow = T, nrow = 4, ncol = 4)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 4 + 1):((traj - 1) * 4 + 4), ((traj - 1) * 4 + 1):((traj - 1) * 4 + 4)] <-
gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 4 + 1):((traj_i - 1) * 4 + 4), (traj_j * 4 + 1):(traj_j * 4 + 4)] <-
gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Change Score Model, Jenss Bayley (random ratio)", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents[1:(length(y_var) * 4)], to = latents[1:(length(y_var) * 4)],
arrows = 2, connect = "unique.pairs",
free = TRUE, values = t(starts[[2]])[row(t(starts[[2]])) >= col(t(starts[[2]]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, AddPara, GAMMA, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L,
psi_btw_L, PATH_L_L, PATH_SLP_L, PATH_AUTO_L)
}
else if (!intrinsic){
latents <- c(paste0(rep(c("eta0", "eta1", "eta2"), length(y_var)), rep(y_var, each = 3)),
unlist(L_list), unlist(D_list))
multi_label <- matrix(NA, nrow = 3 * length(y_var), ncol = 3 * length(y_var))
GF_MEAN <- GF_LOADINGS <- GAMMA <- list()
mean_L <- psi_L <- list()
gf_var_label <- gf_cov_label <- list()
psi_btw_L <- list()
for (traj in 1:length(y_var)){
GF_MEAN[[traj]] <- mxPath(from = "one", to = paste0(c("eta0", "eta1", "eta2"), y_var[traj]),
arrows = 1, free = TRUE, values = starts[[1]][[traj]][1:3],
labels = paste0(y_var[traj], c("_mueta0", "_mueta1", "_mueta2")))
GAMMA[[traj]] <- mxMatrix("Full", 1, 1, free = TRUE, values = starts[[1]][[traj]][4],
labels = paste0(y_var[traj], "_acc_ratio"),
name = paste0(y_var[traj], "_mug"))
mean_L[[traj]] <- mxAlgebraFromString(paste0("rbind(", y_var[traj], "_mueta0, ", y_var[traj], "_mueta1, ",
y_var[traj], "_mueta2, ", y_var[traj], "_acc_ratio)"),
name = paste0(y_var[traj], "_mean0"))
GF_LOADINGS[[length(GF_LOADINGS) + 1]] <- list(mxPath(from = paste0("eta0", y_var[traj]),
to = paste0("l", y_var_L[traj], records[[traj]][1]),
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta1", y_var[traj]),
to = paste0("d", y_var_L[traj], records[[traj]][-1]),
arrows = 1, free = FALSE, values = 1),
mxPath(from = paste0("eta2", y_var[traj]),
to = paste0("d", y_var_L[traj], records[[traj]][-1]),
arrows = 1, free = FALSE, values = 0,
labels = paste0(y_var[traj], "L2", records[[traj]][-1], "[1,1]")))
psi_L[[traj]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj], "_psi00, ", y_var[traj], "_psi01, ",
y_var[traj], "_psi02), ",
"cbind(", y_var[traj], "_psi01, ", y_var[traj], "_psi11, ",
y_var[traj], "_psi12), ",
"cbind(", y_var[traj], "_psi02, ", y_var[traj], "_psi12, ",
y_var[traj], "_psi22))"),
name = paste0(y_var[traj], "_psi0"))
gf_var_label[[traj]] <- matrix(paste0(y_var[traj], "_psi", c("00", "01", "02", "01", "11", "12",
"02", "12", "22")),
byrow = T, nrow = 3, ncol = 3)
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
psi_btw_L[[traj_i + traj_j - 1]] <- mxAlgebraFromString(paste0("rbind(cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi00, ",
y_var[traj_i], y_var[traj_j + 1], "_psi01, ",
y_var[traj_i], y_var[traj_j + 1], "_psi02), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi10, ",
y_var[traj_i], y_var[traj_j + 1], "_psi11, ",
y_var[traj_i], y_var[traj_j + 1], "_psi12), ",
"cbind(", y_var[traj_i], y_var[traj_j + 1], "_psi20, ",
y_var[traj_i], y_var[traj_j + 1], "_psi21, ",
y_var[traj_i], y_var[traj_j + 1], "_psi22))"),
name = paste0(y_var[traj_i], y_var[traj_j + 1], "_psi"))
gf_cov_label[[traj_i + traj_j - 1]] <- matrix(paste0(y_var[traj_i], y_var[traj_j + 1], "_psi",
c("00", "01", "02", "10", "11", "12",
"20", "21", "22")),
byrow = T, nrow = 3, ncol = 3)
}
}
for (traj in 1:length(y_var)){
multi_label[((traj - 1) * 3 + 1):((traj - 1) * 3 + 3), ((traj - 1) * 3 + 1):((traj - 1) * 3 + 3)] <-
gf_var_label[[traj]]
}
for (traj_i in 1:(length(y_var) - 1)){
for (traj_j in traj_i:(length(y_var) - 1)){
multi_label[((traj_i - 1) * 3 + 1):((traj_i - 1) * 3 + 3), (traj_j * 3 + 1):(traj_j * 3 + 3)] <-
gf_cov_label[[traj_i + traj_j - 1]]
}
}
model_mx <- mxModel("Multivariate Latent Change Score Model, Jenss Bayley (fixed ratio)", type = "RAM",
manifestVars = manifests, latentVars = latents,
mxData(observed = dat, type = "raw"),
mxPath(from = latents[1:(length(y_var) * 3)], to = latents[1:(length(y_var) * 3)],
arrows = 2, connect = "unique.pairs", free = TRUE,
values = t(starts[[2]][c(1:3, 5:7), c(1:3, 5:7)])[row(t(starts[[2]][c(1:3, 5:7), c(1:3, 5:7)])) >=
col(t(starts[[2]][c(1:3, 5:7), c(1:3, 5:7)]))],
labels = t(multi_label)[row(t(multi_label)) >= col(t(multi_label))]),
GF_loadings, AddPara, GAMMA, GF_MEAN, GF_LOADINGS, RES, COV, mean_L, psi_L,
psi_btw_L, PATH_L_L, PATH_SLP_L, PATH_AUTO_L)
}
}
}
return(model_mx)
}
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