R/fit_pspat.R
In rominsal/pspatreg: Spatial and Spatio-Temporal Semiparametric Regression Models with Spatial Lags
Defines functions
fit_pspat
fit_pspat <- function(env, con) {
y <- env$y
nfull <- length(y)
if (!is.null(env$Xfull)) {
X <- Matrix(env$Xfull)
} else X <- matrix(0, nrow = length(y), ncol = 1)
if (!is.null(env$Zfull)) {
Z <- Matrix(env$Zfull)
} else Z <- matrix(0, nrow = length(y), ncol = 1)
Wsp <- env$Wsp
sp1 <- env$sp1
sp2 <- env$sp2
time <- env$time
nfull <- env$nfull
nsp <- env$nsp
nt <- env$nt
Ifull <- Diagonal(nfull)
Isp <- Diagonal(nsp)
It <- Diagonal(nt)
if (is.null(con$vary_init)) {
la <- var(as.numeric(y))
} else la <- con$vary_init
namesla <- c("sig2u")
# Build vector and matrices for variance components in mixed model
if (is.null(time))
var_comp <- par_var_comp2d(la = la, env)
else var_comp <- par_var_comp3d(la = la, env)
# Number of parameters
np <- var_comp$np
np_eff <- var_comp$np_eff
assign("np", np, envir = env)
assign("np_eff", np_eff, envir = env)
# Vector of parameters
la <- var_comp$la
if (env$nvarspt > 0) {
if (is.null(time)) {
if (!env$psanova) {
namestauspt <- paste("tausp", 1:2, sep = "")
} else {
namestauspt <- c("tauf1_main", "tauf2_main",
"tauf12.1", "tauf12.2")
}
} else { # nt > 1
if (!env$psanova) {
namestauspt <- c(paste("tausp", 1:2, sep = ""),
"tautime")
} else {
namestauspt <- c("tauf1_main",
"tauf2_main",
"tauft_main",
"tauf12.1", "tauf12.2",
"tauf1t.1", "tauf1t.2",
"tauf2t.1", "tauf2t.2",
"tauf12t.1", "tauf12t.2",
"tauf12t.3")
}
}
namesla <- c(namesla, namestauspt)
}
if (env$nvarnopar > 0) {
namestaunopar <- paste("taunopar", 1:env$nvarnopar,
sep = "")
namesla <- c(namesla, namestaunopar)
}
names(la) <- namesla
## initialize rho, delta and phi
if (env$type %in% c("sar", "sdm", "sarar"))
rho <- con$rho_init
else rho <- NULL
if (env$type %in% c("sem", "sdem", "sarar"))
delta <- con$delta_init
else delta <- NULL
if (env$cor == "ar1" )
phi <- con$phi_init
else phi <- NULL
# Initialise the parameters
if (is.null(con$bold)) bold = rep(0, sum(np_eff))
if (length(np_eff) > 1) {
eta <- X %*% bold[1:np_eff[1]] +
Z %*% bold[-(1:np_eff[1])] #+ offset
} else eta <- X %*% bold[1:np_eff[1]] # Only fixed effects
# Do not remove var_comp, it is used in the next loop...
# 0 0
# 0 I
D <- Matrix(diag(c(rep(0, np_eff[1]),
rep(1, sum(np_eff[-1])))))
assign("D", D, envir = env)
env$D <- D
start <- proc.time()[3]
for (iq in 1:con$maxit) {
# Nested loops for spatial parameters and SAP
if (!is.null(rho)) {
A1 <- Isp - rho*Wsp } else if (nsp > 1) {
A1 <- Isp } else A1 <- Ifull
if (!is.null(delta)) {
A2 <- Isp - delta*Wsp } else if (nsp > 1) {
A2 <- Isp } else A2 <- Ifull
if (!is.null(time) || nt > 1) {
if (!is.null(phi)) {
call_Omega <- build_Omega_ar1(phi, nt)
Omega <- call_Omega$Omega
Omegainv <- call_Omega$Omegainv
LcholOmegainv <- chol(Omegainv)
} else { # phi <- NULL
Omega <- Omegainv <- LcholOmegainv <- It
}
# fast index nt, slow index nsp
ystar <- matrix(RH(A2 %*% A1,
RH(LcholOmegainv,
array(y, dim = c(ncol(LcholOmegainv),
ncol(A1))))),
ncol = 1)
# ystar_check <- matrix(kronecker(A2 %*% A1,
# LcholOmegainv) %*% y,
# ncol = 1)
#range(ystar - ystar_check)
Xstar <- kronecker(A2, LcholOmegainv) %*% X
Zstar <- kronecker(A2, LcholOmegainv) %*% Z
} else {
Omega <- Omegainv <- LcholOmegainv <- It
ystar <- A2 %*% (A1 %*% y)
Xstar <- A2 %*% X
Zstar <- A2 %*% Z
}
edftot_old <- 0
for (it in 1:con$maxit) {
if (length(np_eff) > 1) {
# Model includes random effects
# Builds covariance G matrix for random effects
if (is.null(time)) {
lG <- build_G2d(la = la, lg = var_comp, env)
} else {
lG <- build_G3d(la = la, lg = var_comp, env)
}
G <- lG$G
Ginv <- lG$Ginv
G_eff <- lG$G_eff
Ginv_eff <- lG$Ginv_eff
assign("G", G, envir = env)
assign("Ginv", Ginv, envir = env)
assign("G_eff", G_eff, envir = env)
assign("Ginv_eff", Ginv_eff, envir = env)
sig2u <- la["sig2u"]
assign("sig2u", sig2u, envir = env)
#if (is.null(weights)) {
# w <- as.vector(matrix(1,nrow=length(y))) } else { w <- weights }
mat <- construct_matrices(Xstar, Zstar, ystar)
# MATRIX C IN (12). PAPER SAP
C <- Matrix(
construct_block(mat$XtX,
t(mat$ZtX*G_eff),
mat$ZtX,
t(mat$ZtZ*G_eff)))
H <- (1/sig2u)*C + D
Hinv <- try(solve(H))
if (inherits(Hinv, "try-error"))
Hinv <- ginv(as.matrix(H))
b <- as.vector((1/sig2u)*Hinv %*% mat$u)
bfixed <- b[1:np_eff[1]]
names(bfixed) <- gsub("X_", "", colnames(X))
names(bfixed) <- paste("fixed_",
names(bfixed), sep = "")
assign("bfixed", bfixed, envir = env)
brandom <- G_eff*b[-(1:np_eff[1])]
names(brandom) <- gsub("Z_", "", colnames(Z))
names(brandom) <- paste("random_",
names(brandom), sep = "")
assign("brandom", brandom, envir = env)
# Compute effective dimensions and variances
# Only the diagonal of ZtPZ
dZtPZ <- 1/la[1] * apply((t(Hinv[-(1:np_eff[1]), ]) *
mat$ZtXtZ), 2, sum)
## Check (8). Paper SAP
# n1 <- ncol(env$Zfull)
# n2 <- ncol(env$Xfull)
# pr <- cbind(
# matrix(0, nrow = n1,
# ncol = n2),
# Diagonal(n1)
# )
# dZtPZ2 <- (1/la[1]*pr %*%
# Hinv %*% mat$ZtXtZ)
# diag_dZtPZ2 <- diag(as.matrix(dZtPZ2))
# range(dZtPZ - diag_dZtPZ2)
index.zeros.G <- G == 0
brandom_wide <- dZtPZ_wide <- rep(0, length(G))
brandom_wide[!index.zeros.G] <- brandom
dZtPZ_wide[!index.zeros.G] <- dZtPZ
if (is.null(time)) {
ltau_edf <- update_tau2d(la = la,
lg = var_comp,
G = G,
dZtPZ_wide = dZtPZ_wide,
brandom_wide = brandom_wide,
env = env)
} else {
ltau_edf <- update_tau3d(la = la,
lg = var_comp,
G = G,
dZtPZ_wide = dZtPZ_wide,
brandom_wide = brandom_wide,
env = env)
}
if (env$nvarspt > 0) {
if (is.null(time)) {
tau1 <- ltau_edf$tau1
tau2 <- ltau_edf$tau2
ed1 <- ltau_edf$ed1
ed2 <- ltau_edf$ed2
tauspt <- c(tau1, tau2)
edfspt <- c(ed1, ed2)
if (env$psanova) {
tau3 <- ltau_edf$tau4
tau4 <- ltau_edf$tau4
ed3 <- ltau_edf$ed3
ed4 <- ltau_edf$ed4
tauspt <- c(tauspt, tau3, tau4)
edfspt <- c(edfspt, ed3, ed4)
}
} else {
tau1 <- ltau_edf$tau1
tau2 <- ltau_edf$tau2
tau3 <- ltau_edf$tau3
ed1 <- ltau_edf$ed1
ed2 <- ltau_edf$ed2
ed3 <- ltau_edf$ed3
tauspt <- c(tau1, tau2, tau3)
edfspt <- c(ed1, ed2, ed3)
if (env$psanova) {
tau4 <- ltau_edf$tau4
tau5 <- ltau_edf$tau5
tau6 <- ltau_edf$tau6
tau7 <- ltau_edf$tau7
tau8 <- ltau_edf$tau8
tau9 <- ltau_edf$tau9
tau10 <- ltau_edf$tau10
tau11 <- ltau_edf$tau11
tau12 <- ltau_edf$tau12
ed4 <- ltau_edf$ed4
ed5 <- ltau_edf$ed5
ed6 <- ltau_edf$ed6
ed7 <- ltau_edf$ed7
ed8 <- ltau_edf$ed8
ed9 <- ltau_edf$ed9
ed10 <- ltau_edf$ed10
ed11 <- ltau_edf$ed11
ed12 <- ltau_edf$ed12
tauspt <- c(tauspt, tau4, tau5, tau6, tau7,
tau8, tau9, tau10, tau11, tau12)
edfspt <- c(edfspt, ed4, ed5, ed6, ed7, ed8,
ed9, ed10, ed11, ed12)
}
}
names(tauspt) <- namestauspt
names(edfspt) <- gsub("tau", "", namestauspt)
} else {
tauspt <- NULL
edfspt <- NULL
}
if (env$nvarnopar > 0) {
taunopar <- ltau_edf$taunopar
# Add 1 for fixed effects of each nonparametric variable
# edfnopar <- ltau_edf$edfnopar + 1
edfnopar <- ltau_edf$edfnopar
} else {
taunopar <- NULL
edfnopar <- NULL
}
# Regression (Fahrmeir et al.) pp. 180
ssr <- as.numeric(mat$yty - t(c(bfixed, brandom)) %*%
(2*mat$u - C %*% b))
## Checking ssr
# resids <- y - Xfull %*% bfixed - Zfull %*% brandom
# ssr2 <- sum(resids^2)
# New variance
lanew <- c(sig2u)
namesX <- colnames(X)
namesX.nopar <- namesX[grepl("pspl", namesX)]
# Fixed effects of X.nopar has been added to edfnopar.
#edftot <- length(namesX) - length(namesX.nopar)
edftot <- length(namesX)
if (env$nvarspt > 0) {
lanew <- c(lanew, tauspt)
edftot <- edftot + sum(edfspt)
}
if (env$nvarnopar > 0) {
lanew <- c(lanew, taunopar)
edftot <- edftot + sum(edfnopar)
}
} else { # Model without random effects
tauspt <- taunopar <- NULL
edfspt <- edfnopar <- NULL
sig2u <- la["sig2u"]
assign("sig2u", sig2u, envir = env)
mat <- construct_matrices(Xstar, Zstar, ystar)
# MATRIX C IN (12). PAPER SAP
C <- Matrix(mat$XtX)
H <- (1/sig2u)*C
Hinv <- try(solve(H))
if (inherits(Hinv, "try-error"))
Hinv <- ginv(as.matrix(H))
b <- as.vector((1/sig2u)*Hinv %*% mat$u[1:np_eff[1]])
bfixed <- b[1:np_eff[1]]
names(bfixed) <- gsub("X_", "", colnames(X))
names(bfixed) <- paste("fixed_",
names(bfixed), sep = "")
assign("bfixed", bfixed, envir = env)
brandom <- 0
assign("brandom", brandom, envir = env)
ssr <- as.numeric(mat$yty - t(c(bfixed)) %*%
(2*mat$u[1:np_eff[1]] - C %*% b))
lanew <- c(sig2u)
edftot <- ncol(X)
} # end Model without random effects
if (!is.null(rho)) edftot <- edftot + 1
if (!is.null(delta)) edftot <- edftot + 1
sig2u <- as.numeric((ssr/(length(y) - edftot)))
# Update first component of la with new sig2u
lanew["sig2u"] <- sig2u
assign("sig2u", sig2u, envir = env)
# Update rho and delta
dla <- mean(abs(la - lanew))
la <- lanew
dedftot <- edftot - edftot_old
edftot_old <- edftot
if (con$trace) {
message(paste('\n Iteration SAP: ', it))
message(paste('\n mean change in penalization param.: ', dla))
message(paste('\n change in edftot: ', dedftot))
message(paste('\n sig2u ', la[1]))
if (env$nvarspt > 0)
message(paste('\n edfspt:', round(edfspt, 2)))
if (env$nvarnopar > 0)
message(paste('\n edfnopar: ',
round(edfnopar, 2))) }
# convergence check
if (nfull > 500) {
if (dedftot < con$tol2) break
} else {
if (dla < con$tol1) break
}
} # end for (it in 1:maxit)
if (!(env$type %in% c("sim", "slx")) || env$cor == "ar1") {
# Optimize using spatial and/or correlation parameters
param <- namesparam <- NULL
lower_par <- upper_par <- NULL
if (!is.null(rho)) {
param <- c(param, rho)
namesparam <- c(namesparam, "rho")
lower_par <- c(lower_par, env$interval[1])
upper_par <- c(upper_par, env$interval[2])
}
if (!is.null(delta)) {
param <- c(param, delta)
namesparam <- c(namesparam, "delta")
lower_par <- c(lower_par, env$interval[1])
upper_par <- c(upper_par, env$interval[2])
}
if (!is.null(phi)) {
param <- c(param, phi)
namesparam <- c(namesparam, "phi")
lower_par <- c(lower_par, -0.99)
upper_par <- c(upper_par, 0.99)
}
names(param) <- namesparam
if (con$optim == "llik_reml") {
par_optim <- bobyqa(par = param,
fn = llikc_reml,
lower = lower_par,
upper = upper_par,
control = list(rhobeg = 0.5,
iprint = 0),
env = env)
param_new <- par_optim$par
}
if (con$optim == "llik") {
par_optim <- bobyqa(par = param,
fn = llikc,
lower = lower_par,
upper = upper_par,
control = list(rhobeg = 0.5,
iprint = 0),
env = env)
param_new <- par_optim$par
}
names(param_new) <- namesparam
dparam <- mean(abs(param - param_new))
param <- param_new
if (!is.null(rho)) rho <- param["rho"]
if (!is.null(delta)) delta <- param["delta"]
if (!is.null(phi)) phi <- param["phi"]
} else {
rho <- delta <- phi <- NULL
param <- c(rho, delta, phi)
param_optim <- param
dparam <- 0
}
if (con$trace) {
message(paste("\n Iteration Spatials and/or
Correlation Parameters: ", iq))
if (!is.null(rho))
message(paste("\n rho: ", rho))
if (!is.null(delta))
message(paste("\n delta: ", delta))
if (!is.null(phi))
message(paste("\n phi: ", phi))
}
# Check Convergence
if (dparam < con$tol3) break
} # End loop
end <- proc.time()[3]
message(paste("\n Time to fit the model: ", round(end - start, 2),
"seconds \n"))
# FINAL ESTIMATES OF PARAMETERS
assign("sig2u", sig2u, envir = env)
assign("tauspt", tauspt, envir = env)
assign("taunopar", taunopar, envir = env)
assign("edfspt", edfspt, envir = env)
assign("edfnopar", edfnopar, envir = env)
assign("edftot", edftot, envir = env)
# Update matrices in the optimum
if (!is.null(rho)) {
A1 <- Isp - rho*Wsp } else { A1 <- Isp }
if (!is.null(delta)) {
A2 <- Isp - delta*Wsp } else { A2 <- Isp }
if (!is.null(time) || nt > 1) {
if (!is.null(phi)) {
call_Omega <- build_Omega_ar1(phi, nt)
Omega <- call_Omega$Omega
Omegainv <- call_Omega$Omegainv
LcholOmegainv <- chol(Omegainv)
} else { # phi <- NULL
Omega <- Omegainv <- LcholOmegainv <- It
}
# fast index nt, slow index nsp
ystar <- matrix(RH(A2 %*% A1,
RH(LcholOmegainv,
array(y, dim = c(ncol(LcholOmegainv),
ncol(A1))))),
ncol = 1)
Xstar <- kronecker(A2, LcholOmegainv) %*% X
Zstar <- kronecker(A2, LcholOmegainv) %*% Z
} else {
Omega <- Omegainv <- LcholOmegainv <- It
ystar <- Matrix(A2 %*% (A1 %*% y))
Xstar <- Matrix(A2 %*% X)
Zstar <- Matrix(A2 %*% Z)
}
if (length(np_eff) > 1) { # Random Effects
if (is.null(time)) {
lG <- build_G2d(la = la, lg = var_comp, env)
} else {
lG <- build_G3d(la = la, lg = var_comp, env)
}
G <- lG$G
Ginv <- lG$Ginv
G_eff <- lG$G_eff
Ginv_eff <- lG$Ginv_eff
assign("G", G, envir = env)
assign("Ginv", Ginv, envir = env)
assign("G_eff", G_eff, envir = env)
assign("Ginv_eff", Ginv_eff, envir = env)
mat <- construct_matrices(Xstar, Zstar, ystar)
C <- construct_block(mat$XtX,
t(mat$ZtX*G_eff),
mat$ZtX,
t(mat$ZtZ*G_eff))
H <- (1/sig2u)*C + D
Hinv <- try(solve(H))
if (inherits(Hinv, "try-error"))
Hinv <- ginv(as.matrix(H))
bfixed <- b[1:np_eff[1]]
names(bfixed) <- gsub("X_", "", colnames(X))
names(bfixed) <- paste("fixed_",
names(bfixed), sep = "")
assign("bfixed", bfixed, envir = env)
brandom <- G_eff*b[-(1:np_eff[1])]
names(brandom) <- gsub("Z_", "", colnames(Z))
names(brandom) <- paste("random_",
names(brandom), sep = "")
assign("brandom", brandom, envir = env)
eta <- X %*% bfixed + Z %*% brandom
} else { # Only fixed effects
mat <- construct_matrices(Xstar, Zstar, ystar)
# MATRIX C IN (12). PAPER SAP
C <- mat$XtX
H <- (1/sig2u)*C
Hinv <- try(solve(H))
if (inherits(Hinv, "try-error"))
Hinv <- ginv(as.matrix(H))
b <- as.vector((1/sig2u)*Hinv %*% mat$u[1:np_eff[1]])
bfixed <- b[1:np_eff[1]]
names(bfixed) <- gsub("X_", "", colnames(X))
names(bfixed) <- paste("fixed_",
names(bfixed), sep = "")
assign("bfixed", bfixed, envir = env)
brandom <- 0
assign("brandom", brandom, envir = env)
eta <- X %*% bfixed
}
param_optim <- param
# Valor de log.lik y log.lik.reml en el óptimo
llikc_reml_optim <- -llikc_reml(param_optim, env)
llikc_optim <- -llikc(param_optim, env)
if (!(env$type %in% c("sim", "slx")) || env$cor == "ar1") {
hessian_optim <- hessian(llikc_reml,
param_optim, env = env)
var_num <- solve(hessian_optim)
se_num <- sqrt(diag(var_num))
names(var_num) <- names(se_num) <- namesparam
} else var_num <- se_num <- NULL
# se_an <- NULL
# CHANGE WHEN IT IS READY anhess_llikc_reml FUNCTION...
# if (env$type == "sar" && !(con$fdHess)) {
# se_an <- sqrt(-(1/anhess_llikc_reml_2d(param_optim,
# env)))
# names(se_an) <- namesparam
# } else se_an <- NULL
se_rho <- se_num["rho"]
se_delta <- se_num["delta"]
se_phi <- se_num["phi"]
########## COVARIANCE MATRICES FIXED AND RANDOM EFFECTS
## pp.375 Fahrmeir et al.
## Bayesian Covariance Matrix using matrices equal than SOP
## (see sop.fit code, lines 121-132 )
mat <- construct_matrices(Xstar, Zstar, ystar)
if (length(np_eff) > 1) {
if (is.null(time)) {
lG <- build_G2d(la = la, lg = var_comp, env)
} else {
lG <- build_G3d(la = la, lg = var_comp, env)
}
Ginv_eff <- lG$Ginv_eff
V2 <- construct_block(mat$XtX, mat$XtZ, mat$ZtX, mat$ZtZ)
D2 <- diag(c(rep(0, np_eff[1]), Ginv_eff))
H2 <- (1/sig2u) * V2 + D2
Hinv2 <- try(solve(H2))
if (inherits(Hinv2, "try-error")) {
message("Problems to compute covariance matrix. Near singular matrix")
Hinv2 <- ginv(as.matrix(H2))
}
} else {
V2 <- mat$XtX
H2 <- (1/sig2u)*V2
Hinv2 <- try(solve(H2))
if (inherits(Hinv2, "try-error"))
Hinv2 <- ginv(as.matrix(H2))
}
Var_By <- Hinv2
rownames(Var_By) <- colnames(Var_By) <- c(names(bfixed),
names(brandom))
seby_bfixed <- sqrt(diag(as.matrix(Var_By[names(bfixed),
names(bfixed)])))
names(seby_bfixed) <- names(bfixed)
if (length(np_eff) > 1) {
seby_brandom <- sqrt(diag(as.matrix(Var_By[names(brandom),
names(brandom)])))
names(seby_brandom) <- names(brandom)
} else seby_brandom <- NULL
## Frequentist Covariance Matrix
if (length(np_eff) > 1) {
XZstar <- cbind(Xstar, Zstar)
XZt_Rinv_XZ <- (1/sig2u)*crossprod(XZstar)
} else XZt_Rinv_XZ <- (1/sig2u)*crossprod(Xstar)
Var_Fr <- Var_By %*% XZt_Rinv_XZ %*% Var_By
rownames(Var_Fr) <- colnames(Var_Fr) <- c(names(bfixed),
names(brandom))
sefr_bfixed <- sqrt(diag(as.matrix(Var_Fr[names(bfixed),
names(bfixed)])))
names(sefr_bfixed) <- names(bfixed)
if (length(np_eff) > 1) {
sefr_brandom <- sqrt(diag(as.matrix(Var_Fr[names(brandom),
names(brandom)])))
names(sefr_brandom) <- names(brandom)
} else sefr_brandom <- NULL
if (con$trace) {
end <- proc.time()[3]
message(paste("\n Time to compute covariances: ",
(end-start), "seconds")) }
# Fits and Resids
if (length(np_eff) > 1) {
fit_A1y <- X %*% bfixed + Z %*% brandom # + offset
XZ <- cbind(X, Z)
} else {
fit_A1y <- X %*% bfixed
XZ <- X # Only fixed effects
}
if (is.null(time) && nt == 1) {
fit <- solve(A1, fit_A1y)
seby_fit_A1y <- rowSums((XZ %*% Var_By) * XZ)^0.5
seby_fit <- rowSums((solve(A1, XZ) %*% Var_By) *
solve(A1, XZ))^0.5
sefr_fit_A1y <- rowSums((XZ %*% Var_Fr) * XZ)^0.5
sefr_fit <- rowSums((solve(A1, XZ) %*% Var_Fr) *
solve(A1, XZ))^0.5
#residuals <- as.vector((A1 %*% y) - fit_A1y)
} else {
fit <- solve( kronecker(A1, It), fit_A1y)
seby_fit_A1y <- rowSums((XZ %*% Var_By) * XZ)^0.5
seby_fit <- rowSums((
solve( kronecker(A1, It), XZ) %*% Var_By) *
solve( kronecker(A1, It), XZ))^0.5
sefr_fit_A1y <- rowSums((XZ %*% Var_Fr) * XZ)^0.5
sefr_fit <- rowSums((
solve( kronecker(A1, It), XZ) %*% Var_Fr) *
solve( kronecker(A1, It), XZ))^0.5
# residuals <- as.vector((
# kronecker(A1, It) %*% y) - fit_A1y)
}
residuals <- as.vector(y - fit)
# Compute AIC y BIC based on loglik functions
# (Fahrmeir, pp. 664 and 677)
aic <- -2*llikc_optim + 2*edftot
bic <- -2*llikc_optim + log(length(y))*edftot
res <- list(edfspt = edfspt,
edfnopar = edfnopar,
edftot = edftot,
tauspt = tauspt,
taunopar = taunopar,
fitted.values = as.vector(fit),
fit_A1y = as.vector(fit_A1y),
seby_fitted.values = as.vector(seby_fit),
seby_fit_A1y = as.vector(seby_fit_A1y),
sefr_fitted.values = as.vector(sefr_fit),
sefr_fit_A1y = as.vector(sefr_fit_A1y),
residuals = as.vector(residuals),
sig2 = sig2u,
rho = rho,
se_rho = se_rho,
delta = delta,
se_delta = se_delta,
phi = phi,
se_phi = se_phi,
bfixed = bfixed,
brandom = brandom,
seby_bfixed = seby_bfixed,
seby_brandom = seby_brandom,
sefr_bfixed = sefr_bfixed,
sefr_brandom = sefr_brandom,
llik = llikc_optim,
llik_reml = llikc_reml_optim,
aic = aic,
bic = bic,
vcov_by = Var_By,
vcov_fr = Var_Fr,
sp1 = env$sp1,
sp2 = env$sp2,
time = env$time,
psanova = env$psanova)
} # end of function
rominsal/pspatreg documentation built on July 8, 2022, 9:28 p.m.
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Defines functions fit_pspat
fit_pspat <- function(env, con) {
y <- env$y
nfull <- length(y)
if (!is.null(env$Xfull)) {
X <- Matrix(env$Xfull)
} else X <- matrix(0, nrow = length(y), ncol = 1)
if (!is.null(env$Zfull)) {
Z <- Matrix(env$Zfull)
} else Z <- matrix(0, nrow = length(y), ncol = 1)
Wsp <- env$Wsp
sp1 <- env$sp1
sp2 <- env$sp2
time <- env$time
nfull <- env$nfull
nsp <- env$nsp
nt <- env$nt
Ifull <- Diagonal(nfull)
Isp <- Diagonal(nsp)
It <- Diagonal(nt)
if (is.null(con$vary_init)) {
la <- var(as.numeric(y))
} else la <- con$vary_init
namesla <- c("sig2u")
# Build vector and matrices for variance components in mixed model
if (is.null(time))
var_comp <- par_var_comp2d(la = la, env)
else var_comp <- par_var_comp3d(la = la, env)
# Number of parameters
np <- var_comp$np
np_eff <- var_comp$np_eff
assign("np", np, envir = env)
assign("np_eff", np_eff, envir = env)
# Vector of parameters
la <- var_comp$la
if (env$nvarspt > 0) {
if (is.null(time)) {
if (!env$psanova) {
namestauspt <- paste("tausp", 1:2, sep = "")
} else {
namestauspt <- c("tauf1_main", "tauf2_main",
"tauf12.1", "tauf12.2")
}
} else { # nt > 1
if (!env$psanova) {
namestauspt <- c(paste("tausp", 1:2, sep = ""),
"tautime")
} else {
namestauspt <- c("tauf1_main",
"tauf2_main",
"tauft_main",
"tauf12.1", "tauf12.2",
"tauf1t.1", "tauf1t.2",
"tauf2t.1", "tauf2t.2",
"tauf12t.1", "tauf12t.2",
"tauf12t.3")
}
}
namesla <- c(namesla, namestauspt)
}
if (env$nvarnopar > 0) {
namestaunopar <- paste("taunopar", 1:env$nvarnopar,
sep = "")
namesla <- c(namesla, namestaunopar)
}
names(la) <- namesla
## initialize rho, delta and phi
if (env$type %in% c("sar", "sdm", "sarar"))
rho <- con$rho_init
else rho <- NULL
if (env$type %in% c("sem", "sdem", "sarar"))
delta <- con$delta_init
else delta <- NULL
if (env$cor == "ar1" )
phi <- con$phi_init
else phi <- NULL
# Initialise the parameters
if (is.null(con$bold)) bold = rep(0, sum(np_eff))
if (length(np_eff) > 1) {
eta <- X %*% bold[1:np_eff[1]] +
Z %*% bold[-(1:np_eff[1])] #+ offset
} else eta <- X %*% bold[1:np_eff[1]] # Only fixed effects
# Do not remove var_comp, it is used in the next loop...
# 0 0
# 0 I
D <- Matrix(diag(c(rep(0, np_eff[1]),
rep(1, sum(np_eff[-1])))))
assign("D", D, envir = env)
env$D <- D
start <- proc.time()[3]
for (iq in 1:con$maxit) {
# Nested loops for spatial parameters and SAP
if (!is.null(rho)) {
A1 <- Isp - rho*Wsp } else if (nsp > 1) {
A1 <- Isp } else A1 <- Ifull
if (!is.null(delta)) {
A2 <- Isp - delta*Wsp } else if (nsp > 1) {
A2 <- Isp } else A2 <- Ifull
if (!is.null(time) || nt > 1) {
if (!is.null(phi)) {
call_Omega <- build_Omega_ar1(phi, nt)
Omega <- call_Omega$Omega
Omegainv <- call_Omega$Omegainv
LcholOmegainv <- chol(Omegainv)
} else { # phi <- NULL
Omega <- Omegainv <- LcholOmegainv <- It
}
# fast index nt, slow index nsp
ystar <- matrix(RH(A2 %*% A1,
RH(LcholOmegainv,
array(y, dim = c(ncol(LcholOmegainv),
ncol(A1))))),
ncol = 1)
# ystar_check <- matrix(kronecker(A2 %*% A1,
# LcholOmegainv) %*% y,
# ncol = 1)
#range(ystar - ystar_check)
Xstar <- kronecker(A2, LcholOmegainv) %*% X
Zstar <- kronecker(A2, LcholOmegainv) %*% Z
} else {
Omega <- Omegainv <- LcholOmegainv <- It
ystar <- A2 %*% (A1 %*% y)
Xstar <- A2 %*% X
Zstar <- A2 %*% Z
}
edftot_old <- 0
for (it in 1:con$maxit) {
if (length(np_eff) > 1) {
# Model includes random effects
# Builds covariance G matrix for random effects
if (is.null(time)) {
lG <- build_G2d(la = la, lg = var_comp, env)
} else {
lG <- build_G3d(la = la, lg = var_comp, env)
}
G <- lG$G
Ginv <- lG$Ginv
G_eff <- lG$G_eff
Ginv_eff <- lG$Ginv_eff
assign("G", G, envir = env)
assign("Ginv", Ginv, envir = env)
assign("G_eff", G_eff, envir = env)
assign("Ginv_eff", Ginv_eff, envir = env)
sig2u <- la["sig2u"]
assign("sig2u", sig2u, envir = env)
#if (is.null(weights)) {
# w <- as.vector(matrix(1,nrow=length(y))) } else { w <- weights }
mat <- construct_matrices(Xstar, Zstar, ystar)
# MATRIX C IN (12). PAPER SAP
C <- Matrix(
construct_block(mat$XtX,
t(mat$ZtX*G_eff),
mat$ZtX,
t(mat$ZtZ*G_eff)))
H <- (1/sig2u)*C + D
Hinv <- try(solve(H))
if (inherits(Hinv, "try-error"))
Hinv <- ginv(as.matrix(H))
b <- as.vector((1/sig2u)*Hinv %*% mat$u)
bfixed <- b[1:np_eff[1]]
names(bfixed) <- gsub("X_", "", colnames(X))
names(bfixed) <- paste("fixed_",
names(bfixed), sep = "")
assign("bfixed", bfixed, envir = env)
brandom <- G_eff*b[-(1:np_eff[1])]
names(brandom) <- gsub("Z_", "", colnames(Z))
names(brandom) <- paste("random_",
names(brandom), sep = "")
assign("brandom", brandom, envir = env)
# Compute effective dimensions and variances
# Only the diagonal of ZtPZ
dZtPZ <- 1/la[1] * apply((t(Hinv[-(1:np_eff[1]), ]) *
mat$ZtXtZ), 2, sum)
## Check (8). Paper SAP
# n1 <- ncol(env$Zfull)
# n2 <- ncol(env$Xfull)
# pr <- cbind(
# matrix(0, nrow = n1,
# ncol = n2),
# Diagonal(n1)
# )
# dZtPZ2 <- (1/la[1]*pr %*%
# Hinv %*% mat$ZtXtZ)
# diag_dZtPZ2 <- diag(as.matrix(dZtPZ2))
# range(dZtPZ - diag_dZtPZ2)
index.zeros.G <- G == 0
brandom_wide <- dZtPZ_wide <- rep(0, length(G))
brandom_wide[!index.zeros.G] <- brandom
dZtPZ_wide[!index.zeros.G] <- dZtPZ
if (is.null(time)) {
ltau_edf <- update_tau2d(la = la,
lg = var_comp,
G = G,
dZtPZ_wide = dZtPZ_wide,
brandom_wide = brandom_wide,
env = env)
} else {
ltau_edf <- update_tau3d(la = la,
lg = var_comp,
G = G,
dZtPZ_wide = dZtPZ_wide,
brandom_wide = brandom_wide,
env = env)
}
if (env$nvarspt > 0) {
if (is.null(time)) {
tau1 <- ltau_edf$tau1
tau2 <- ltau_edf$tau2
ed1 <- ltau_edf$ed1
ed2 <- ltau_edf$ed2
tauspt <- c(tau1, tau2)
edfspt <- c(ed1, ed2)
if (env$psanova) {
tau3 <- ltau_edf$tau4
tau4 <- ltau_edf$tau4
ed3 <- ltau_edf$ed3
ed4 <- ltau_edf$ed4
tauspt <- c(tauspt, tau3, tau4)
edfspt <- c(edfspt, ed3, ed4)
}
} else {
tau1 <- ltau_edf$tau1
tau2 <- ltau_edf$tau2
tau3 <- ltau_edf$tau3
ed1 <- ltau_edf$ed1
ed2 <- ltau_edf$ed2
ed3 <- ltau_edf$ed3
tauspt <- c(tau1, tau2, tau3)
edfspt <- c(ed1, ed2, ed3)
if (env$psanova) {
tau4 <- ltau_edf$tau4
tau5 <- ltau_edf$tau5
tau6 <- ltau_edf$tau6
tau7 <- ltau_edf$tau7
tau8 <- ltau_edf$tau8
tau9 <- ltau_edf$tau9
tau10 <- ltau_edf$tau10
tau11 <- ltau_edf$tau11
tau12 <- ltau_edf$tau12
ed4 <- ltau_edf$ed4
ed5 <- ltau_edf$ed5
ed6 <- ltau_edf$ed6
ed7 <- ltau_edf$ed7
ed8 <- ltau_edf$ed8
ed9 <- ltau_edf$ed9
ed10 <- ltau_edf$ed10
ed11 <- ltau_edf$ed11
ed12 <- ltau_edf$ed12
tauspt <- c(tauspt, tau4, tau5, tau6, tau7,
tau8, tau9, tau10, tau11, tau12)
edfspt <- c(edfspt, ed4, ed5, ed6, ed7, ed8,
ed9, ed10, ed11, ed12)
}
}
names(tauspt) <- namestauspt
names(edfspt) <- gsub("tau", "", namestauspt)
} else {
tauspt <- NULL
edfspt <- NULL
}
if (env$nvarnopar > 0) {
taunopar <- ltau_edf$taunopar
# Add 1 for fixed effects of each nonparametric variable
# edfnopar <- ltau_edf$edfnopar + 1
edfnopar <- ltau_edf$edfnopar
} else {
taunopar <- NULL
edfnopar <- NULL
}
# Regression (Fahrmeir et al.) pp. 180
ssr <- as.numeric(mat$yty - t(c(bfixed, brandom)) %*%
(2*mat$u - C %*% b))
## Checking ssr
# resids <- y - Xfull %*% bfixed - Zfull %*% brandom
# ssr2 <- sum(resids^2)
# New variance
lanew <- c(sig2u)
namesX <- colnames(X)
namesX.nopar <- namesX[grepl("pspl", namesX)]
# Fixed effects of X.nopar has been added to edfnopar.
#edftot <- length(namesX) - length(namesX.nopar)
edftot <- length(namesX)
if (env$nvarspt > 0) {
lanew <- c(lanew, tauspt)
edftot <- edftot + sum(edfspt)
}
if (env$nvarnopar > 0) {
lanew <- c(lanew, taunopar)
edftot <- edftot + sum(edfnopar)
}
} else { # Model without random effects
tauspt <- taunopar <- NULL
edfspt <- edfnopar <- NULL
sig2u <- la["sig2u"]
assign("sig2u", sig2u, envir = env)
mat <- construct_matrices(Xstar, Zstar, ystar)
# MATRIX C IN (12). PAPER SAP
C <- Matrix(mat$XtX)
H <- (1/sig2u)*C
Hinv <- try(solve(H))
if (inherits(Hinv, "try-error"))
Hinv <- ginv(as.matrix(H))
b <- as.vector((1/sig2u)*Hinv %*% mat$u[1:np_eff[1]])
bfixed <- b[1:np_eff[1]]
names(bfixed) <- gsub("X_", "", colnames(X))
names(bfixed) <- paste("fixed_",
names(bfixed), sep = "")
assign("bfixed", bfixed, envir = env)
brandom <- 0
assign("brandom", brandom, envir = env)
ssr <- as.numeric(mat$yty - t(c(bfixed)) %*%
(2*mat$u[1:np_eff[1]] - C %*% b))
lanew <- c(sig2u)
edftot <- ncol(X)
} # end Model without random effects
if (!is.null(rho)) edftot <- edftot + 1
if (!is.null(delta)) edftot <- edftot + 1
sig2u <- as.numeric((ssr/(length(y) - edftot)))
# Update first component of la with new sig2u
lanew["sig2u"] <- sig2u
assign("sig2u", sig2u, envir = env)
# Update rho and delta
dla <- mean(abs(la - lanew))
la <- lanew
dedftot <- edftot - edftot_old
edftot_old <- edftot
if (con$trace) {
message(paste('\n Iteration SAP: ', it))
message(paste('\n mean change in penalization param.: ', dla))
message(paste('\n change in edftot: ', dedftot))
message(paste('\n sig2u ', la[1]))
if (env$nvarspt > 0)
message(paste('\n edfspt:', round(edfspt, 2)))
if (env$nvarnopar > 0)
message(paste('\n edfnopar: ',
round(edfnopar, 2))) }
# convergence check
if (nfull > 500) {
if (dedftot < con$tol2) break
} else {
if (dla < con$tol1) break
}
} # end for (it in 1:maxit)
if (!(env$type %in% c("sim", "slx")) || env$cor == "ar1") {
# Optimize using spatial and/or correlation parameters
param <- namesparam <- NULL
lower_par <- upper_par <- NULL
if (!is.null(rho)) {
param <- c(param, rho)
namesparam <- c(namesparam, "rho")
lower_par <- c(lower_par, env$interval[1])
upper_par <- c(upper_par, env$interval[2])
}
if (!is.null(delta)) {
param <- c(param, delta)
namesparam <- c(namesparam, "delta")
lower_par <- c(lower_par, env$interval[1])
upper_par <- c(upper_par, env$interval[2])
}
if (!is.null(phi)) {
param <- c(param, phi)
namesparam <- c(namesparam, "phi")
lower_par <- c(lower_par, -0.99)
upper_par <- c(upper_par, 0.99)
}
names(param) <- namesparam
if (con$optim == "llik_reml") {
par_optim <- bobyqa(par = param,
fn = llikc_reml,
lower = lower_par,
upper = upper_par,
control = list(rhobeg = 0.5,
iprint = 0),
env = env)
param_new <- par_optim$par
}
if (con$optim == "llik") {
par_optim <- bobyqa(par = param,
fn = llikc,
lower = lower_par,
upper = upper_par,
control = list(rhobeg = 0.5,
iprint = 0),
env = env)
param_new <- par_optim$par
}
names(param_new) <- namesparam
dparam <- mean(abs(param - param_new))
param <- param_new
if (!is.null(rho)) rho <- param["rho"]
if (!is.null(delta)) delta <- param["delta"]
if (!is.null(phi)) phi <- param["phi"]
} else {
rho <- delta <- phi <- NULL
param <- c(rho, delta, phi)
param_optim <- param
dparam <- 0
}
if (con$trace) {
message(paste("\n Iteration Spatials and/or
Correlation Parameters: ", iq))
if (!is.null(rho))
message(paste("\n rho: ", rho))
if (!is.null(delta))
message(paste("\n delta: ", delta))
if (!is.null(phi))
message(paste("\n phi: ", phi))
}
# Check Convergence
if (dparam < con$tol3) break
} # End loop
end <- proc.time()[3]
message(paste("\n Time to fit the model: ", round(end - start, 2),
"seconds \n"))
# FINAL ESTIMATES OF PARAMETERS
assign("sig2u", sig2u, envir = env)
assign("tauspt", tauspt, envir = env)
assign("taunopar", taunopar, envir = env)
assign("edfspt", edfspt, envir = env)
assign("edfnopar", edfnopar, envir = env)
assign("edftot", edftot, envir = env)
# Update matrices in the optimum
if (!is.null(rho)) {
A1 <- Isp - rho*Wsp } else { A1 <- Isp }
if (!is.null(delta)) {
A2 <- Isp - delta*Wsp } else { A2 <- Isp }
if (!is.null(time) || nt > 1) {
if (!is.null(phi)) {
call_Omega <- build_Omega_ar1(phi, nt)
Omega <- call_Omega$Omega
Omegainv <- call_Omega$Omegainv
LcholOmegainv <- chol(Omegainv)
} else { # phi <- NULL
Omega <- Omegainv <- LcholOmegainv <- It
}
# fast index nt, slow index nsp
ystar <- matrix(RH(A2 %*% A1,
RH(LcholOmegainv,
array(y, dim = c(ncol(LcholOmegainv),
ncol(A1))))),
ncol = 1)
Xstar <- kronecker(A2, LcholOmegainv) %*% X
Zstar <- kronecker(A2, LcholOmegainv) %*% Z
} else {
Omega <- Omegainv <- LcholOmegainv <- It
ystar <- Matrix(A2 %*% (A1 %*% y))
Xstar <- Matrix(A2 %*% X)
Zstar <- Matrix(A2 %*% Z)
}
if (length(np_eff) > 1) { # Random Effects
if (is.null(time)) {
lG <- build_G2d(la = la, lg = var_comp, env)
} else {
lG <- build_G3d(la = la, lg = var_comp, env)
}
G <- lG$G
Ginv <- lG$Ginv
G_eff <- lG$G_eff
Ginv_eff <- lG$Ginv_eff
assign("G", G, envir = env)
assign("Ginv", Ginv, envir = env)
assign("G_eff", G_eff, envir = env)
assign("Ginv_eff", Ginv_eff, envir = env)
mat <- construct_matrices(Xstar, Zstar, ystar)
C <- construct_block(mat$XtX,
t(mat$ZtX*G_eff),
mat$ZtX,
t(mat$ZtZ*G_eff))
H <- (1/sig2u)*C + D
Hinv <- try(solve(H))
if (inherits(Hinv, "try-error"))
Hinv <- ginv(as.matrix(H))
bfixed <- b[1:np_eff[1]]
names(bfixed) <- gsub("X_", "", colnames(X))
names(bfixed) <- paste("fixed_",
names(bfixed), sep = "")
assign("bfixed", bfixed, envir = env)
brandom <- G_eff*b[-(1:np_eff[1])]
names(brandom) <- gsub("Z_", "", colnames(Z))
names(brandom) <- paste("random_",
names(brandom), sep = "")
assign("brandom", brandom, envir = env)
eta <- X %*% bfixed + Z %*% brandom
} else { # Only fixed effects
mat <- construct_matrices(Xstar, Zstar, ystar)
# MATRIX C IN (12). PAPER SAP
C <- mat$XtX
H <- (1/sig2u)*C
Hinv <- try(solve(H))
if (inherits(Hinv, "try-error"))
Hinv <- ginv(as.matrix(H))
b <- as.vector((1/sig2u)*Hinv %*% mat$u[1:np_eff[1]])
bfixed <- b[1:np_eff[1]]
names(bfixed) <- gsub("X_", "", colnames(X))
names(bfixed) <- paste("fixed_",
names(bfixed), sep = "")
assign("bfixed", bfixed, envir = env)
brandom <- 0
assign("brandom", brandom, envir = env)
eta <- X %*% bfixed
}
param_optim <- param
# Valor de log.lik y log.lik.reml en el óptimo
llikc_reml_optim <- -llikc_reml(param_optim, env)
llikc_optim <- -llikc(param_optim, env)
if (!(env$type %in% c("sim", "slx")) || env$cor == "ar1") {
hessian_optim <- hessian(llikc_reml,
param_optim, env = env)
var_num <- solve(hessian_optim)
se_num <- sqrt(diag(var_num))
names(var_num) <- names(se_num) <- namesparam
} else var_num <- se_num <- NULL
# se_an <- NULL
# CHANGE WHEN IT IS READY anhess_llikc_reml FUNCTION...
# if (env$type == "sar" && !(con$fdHess)) {
# se_an <- sqrt(-(1/anhess_llikc_reml_2d(param_optim,
# env)))
# names(se_an) <- namesparam
# } else se_an <- NULL
se_rho <- se_num["rho"]
se_delta <- se_num["delta"]
se_phi <- se_num["phi"]
########## COVARIANCE MATRICES FIXED AND RANDOM EFFECTS
## pp.375 Fahrmeir et al.
## Bayesian Covariance Matrix using matrices equal than SOP
## (see sop.fit code, lines 121-132 )
mat <- construct_matrices(Xstar, Zstar, ystar)
if (length(np_eff) > 1) {
if (is.null(time)) {
lG <- build_G2d(la = la, lg = var_comp, env)
} else {
lG <- build_G3d(la = la, lg = var_comp, env)
}
Ginv_eff <- lG$Ginv_eff
V2 <- construct_block(mat$XtX, mat$XtZ, mat$ZtX, mat$ZtZ)
D2 <- diag(c(rep(0, np_eff[1]), Ginv_eff))
H2 <- (1/sig2u) * V2 + D2
Hinv2 <- try(solve(H2))
if (inherits(Hinv2, "try-error")) {
message("Problems to compute covariance matrix. Near singular matrix")
Hinv2 <- ginv(as.matrix(H2))
}
} else {
V2 <- mat$XtX
H2 <- (1/sig2u)*V2
Hinv2 <- try(solve(H2))
if (inherits(Hinv2, "try-error"))
Hinv2 <- ginv(as.matrix(H2))
}
Var_By <- Hinv2
rownames(Var_By) <- colnames(Var_By) <- c(names(bfixed),
names(brandom))
seby_bfixed <- sqrt(diag(as.matrix(Var_By[names(bfixed),
names(bfixed)])))
names(seby_bfixed) <- names(bfixed)
if (length(np_eff) > 1) {
seby_brandom <- sqrt(diag(as.matrix(Var_By[names(brandom),
names(brandom)])))
names(seby_brandom) <- names(brandom)
} else seby_brandom <- NULL
## Frequentist Covariance Matrix
if (length(np_eff) > 1) {
XZstar <- cbind(Xstar, Zstar)
XZt_Rinv_XZ <- (1/sig2u)*crossprod(XZstar)
} else XZt_Rinv_XZ <- (1/sig2u)*crossprod(Xstar)
Var_Fr <- Var_By %*% XZt_Rinv_XZ %*% Var_By
rownames(Var_Fr) <- colnames(Var_Fr) <- c(names(bfixed),
names(brandom))
sefr_bfixed <- sqrt(diag(as.matrix(Var_Fr[names(bfixed),
names(bfixed)])))
names(sefr_bfixed) <- names(bfixed)
if (length(np_eff) > 1) {
sefr_brandom <- sqrt(diag(as.matrix(Var_Fr[names(brandom),
names(brandom)])))
names(sefr_brandom) <- names(brandom)
} else sefr_brandom <- NULL
if (con$trace) {
end <- proc.time()[3]
message(paste("\n Time to compute covariances: ",
(end-start), "seconds")) }
# Fits and Resids
if (length(np_eff) > 1) {
fit_A1y <- X %*% bfixed + Z %*% brandom # + offset
XZ <- cbind(X, Z)
} else {
fit_A1y <- X %*% bfixed
XZ <- X # Only fixed effects
}
if (is.null(time) && nt == 1) {
fit <- solve(A1, fit_A1y)
seby_fit_A1y <- rowSums((XZ %*% Var_By) * XZ)^0.5
seby_fit <- rowSums((solve(A1, XZ) %*% Var_By) *
solve(A1, XZ))^0.5
sefr_fit_A1y <- rowSums((XZ %*% Var_Fr) * XZ)^0.5
sefr_fit <- rowSums((solve(A1, XZ) %*% Var_Fr) *
solve(A1, XZ))^0.5
#residuals <- as.vector((A1 %*% y) - fit_A1y)
} else {
fit <- solve( kronecker(A1, It), fit_A1y)
seby_fit_A1y <- rowSums((XZ %*% Var_By) * XZ)^0.5
seby_fit <- rowSums((
solve( kronecker(A1, It), XZ) %*% Var_By) *
solve( kronecker(A1, It), XZ))^0.5
sefr_fit_A1y <- rowSums((XZ %*% Var_Fr) * XZ)^0.5
sefr_fit <- rowSums((
solve( kronecker(A1, It), XZ) %*% Var_Fr) *
solve( kronecker(A1, It), XZ))^0.5
# residuals <- as.vector((
# kronecker(A1, It) %*% y) - fit_A1y)
}
residuals <- as.vector(y - fit)
# Compute AIC y BIC based on loglik functions
# (Fahrmeir, pp. 664 and 677)
aic <- -2*llikc_optim + 2*edftot
bic <- -2*llikc_optim + log(length(y))*edftot
res <- list(edfspt = edfspt,
edfnopar = edfnopar,
edftot = edftot,
tauspt = tauspt,
taunopar = taunopar,
fitted.values = as.vector(fit),
fit_A1y = as.vector(fit_A1y),
seby_fitted.values = as.vector(seby_fit),
seby_fit_A1y = as.vector(seby_fit_A1y),
sefr_fitted.values = as.vector(sefr_fit),
sefr_fit_A1y = as.vector(sefr_fit_A1y),
residuals = as.vector(residuals),
sig2 = sig2u,
rho = rho,
se_rho = se_rho,
delta = delta,
se_delta = se_delta,
phi = phi,
se_phi = se_phi,
bfixed = bfixed,
brandom = brandom,
seby_bfixed = seby_bfixed,
seby_brandom = seby_brandom,
sefr_bfixed = sefr_bfixed,
sefr_brandom = sefr_brandom,
llik = llikc_optim,
llik_reml = llikc_reml_optim,
aic = aic,
bic = bic,
vcov_by = Var_By,
vcov_fr = Var_Fr,
sp1 = env$sp1,
sp2 = env$sp2,
time = env$time,
psanova = env$psanova)
} # end of function
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