"sim.congeneric" <- function(N = 1000, loads = c(0.8, 0.7, 0.6, 0.5), err=NULL, short=TRUE) { n <- length(loads) loading <- matrix(loads, nrow = n) error <- diag(1, nrow = n) if (!is.null(err)) {diag(error) <- err} else { diag(error) <- sqrt(1 - loading^2) } pattern <- cbind(loading, error) colnames(pattern) <- c("theta", paste("e", seq(1:n), sep = "")) rownames(pattern) <- c(paste("V", seq(1:n), sep = "")) model <- pattern %*% t(pattern) latent <- matrix(rnorm(N * (n + 1)), ncol = (n + 1)) observed <- latent %*% t(pattern) colnames(latent) <- c("theta", paste("e", seq(1:n), sep = "")) if (short) {return(model)} else {result <- list(model=model,pattern=pattern,observed=observed,latent=latent) return(result)} }