grad_alpha <- function(y, x, alpha, theta, var.type){
#internal function to compute gradient of main effects coefficients
d <- dim(y)
n <- d[1]
p <- d[2]
m <- sum(!is.na(y))
Omega <- !is.na(y)
q <- ncol(x)
grad <- rep(0, n+p+q)
par <- matrix(x%*% alpha, nrow=n) + theta
YY <- y
YY[is.na(y)] <- 0
mat <- par
mat[, var.type=="binomial"] <- exp(mat[, var.type=="binomial"])/(1+exp(mat[, var.type=="binomial"]))
mat[, var.type=="poisson"] <- exp(mat[, var.type=="poisson"])
mat[is.na(y)] <- 0
grad[(n+p+1):(n+p+q)] <- t(x)%*%(-c(YY)+c(mat))/m
return(grad)
}
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