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#' The function for hierarchical imputation of variables with count data.
#'
#' The function is called by the wrapper.
#' @param y_imp_multi A Vector with the variable to impute.
#' @param X_imp_multi A data.frame with the fixed effects variables.
#' @param Z_imp_multi A data.frame with the random effects variables.
#' @param clID A vector with the cluster ID.
#' @param M An integer defining the number of imputations that should be made.
#' @param nitt An integer defining number of MCMC iterations (see MCMCglmm).
#' @param thin An integer defining the thinning interval (see MCMCglmm).
#' @param burnin An integer defining the percentage of draws from the gibbs sampler
#' that should be discarded as burn in (see MCMCglmm).
#' @return A n x M matrix. Each column is one of M imputed y-variables.
imp_count_multi <- function(y_imp_multi,
X_imp_multi,
Z_imp_multi,
clID,
M = 10,
nitt = 3000,
thin = 10,
burnin = 1000){
# -----------------------------preparing the data ------------------
# -- standardise the covariates in X (which are numeric and no intercept)
need_stand_X <- apply(X_imp_multi, 2, get_type) %in% c("cont", "count")
X_imp_multi_stand <- X_imp_multi
X_imp_multi_stand[, need_stand_X] <- scale(X_imp_multi[, need_stand_X])
#generate model.matrix (from the class matrix)
n <- nrow(X_imp_multi_stand)
#X_model_matrix <- stats::model.matrix(stats::rnorm(n) ~ 0 + ., data = X_imp_multi_stand)
# Remove ` from the variable names
#colnames(X_model_matrix) <- gsub("`", "", colnames(X_model_matrix))
# -- standardise the covariates in Z (which are numeric and no intercept)
need_stand_Z <- apply(Z_imp_multi, 2, get_type) %in% c("cont", "count")
Z_imp_multi_stand <- Z_imp_multi
Z_imp_multi_stand[, need_stand_Z] <- scale(Z_imp_multi[, need_stand_Z])
# Get the number of random effects variables
n.par.rand <- ncol(Z_imp_multi_stand)
length.alpha <- length(table(clID)) * n.par.rand
# -------------- calling the gibbs sampler to get imputation parameters----
n <- length(y_imp_multi)
lmstart <- stats::lm(stats::rnorm(n) ~ 0 +., data = X_imp_multi_stand)
X_model_matrix_1 <- stats::model.matrix(lmstart)
xnames_1 <- paste("X", 1:ncol(X_model_matrix_1), sep = "")
znames <- paste("Z", 1:ncol(Z_imp_multi_stand), sep = "")
tmp_1 <- data.frame(y = stats::rnorm(n))
tmp_1[, xnames_1] <- X_model_matrix_1
reg_1 <- stats::lm(y ~ 0 + . , data = tmp_1)
blob <- y_imp_multi
tmp_2 <- data.frame(target = blob)
xnames_2 <- xnames_1[!is.na(stats::coefficients(reg_1))]
X_model_matrix_2 <- X_model_matrix_1[, !is.na(stats::coefficients(reg_1)), drop = FALSE]
tmp_2[, xnames_2] <- X_model_matrix_2
tmp_2[, znames] <- Z_imp_multi_stand
tmp_2[, "ClID"] <- clID
fixformula <- stats::formula(paste("target~", paste(xnames_2, collapse = "+"), "- 1", sep = ""))
randformula <- stats::as.formula(paste("~us(", paste(znames, collapse = "+"), "):ClID", sep = ""))
prior <- list(R = list(V = 1e-07, nu = -2),
G = list(G1 = list(V = diag(ncol(Z_imp_multi_stand)), nu = 0.002)))
MCMCglmm_draws <- MCMCglmm::MCMCglmm(fixformula, random = randformula, data = tmp_2,
verbose = FALSE, pr = TRUE, prior = prior,
family = "poisson",
saveX = TRUE, saveZ = TRUE,
nitt = 3000,
thin = 10,
burnin = 1000)
pointdraws <- MCMCglmm_draws$Sol
xdraws <- pointdraws[, 1:ncol(X_model_matrix_2), drop = FALSE]
zdraws <- pointdraws[, ncol(X_model_matrix_2) + 1:length.alpha, drop = FALSE]
variancedraws <- MCMCglmm_draws$VCV
# the last column contains the variance (not standard deviation) of the residuals
number_of_draws <- nrow(pointdraws)
select.record <- sample(1:number_of_draws, M, replace = TRUE)
# -------------------- drawing samples with the parameters from the gibbs sampler --------
y_imp <- array(NA, dim = c(n, M))
###start imputation
for (j in 1:M){
rand.eff.imp <- matrix(zdraws[select.record[j],],
ncol = n.par.rand)
fix.eff.imp <- matrix(xdraws[select.record[j], ], nrow = ncol(X_model_matrix_2))
sigma.y.imp <- sqrt(variancedraws[select.record[j], ncol(variancedraws)])
lambda <- exp(stats::rnorm(n, X_model_matrix_2 %*% fix.eff.imp +
apply(Z_imp_multi_stand * rand.eff.imp[clID,], 1, sum), sigma.y.imp))
y_imp[, j] <- ifelse(is.na(y_imp_multi), stats::rpois(n, lambda), y_imp_multi)
}
# --------- returning the imputed data --------------
return(y_imp)
}
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