#' Pseudo-Random Number Generation of Correlated Binary (Bernoulli-Beta) or Count (Binomial-Beta) Outcomes
#'
#' This function produces pseudo-random numbers for responses for correlated (longitudinal) data. The responses are generated as either binary (Bernoulli) data or count (Binomial), using a transformed Beta random effect to induce autocorrelation. Once the Beta-distributed random effects are generated, the values are transformed according to a logit transformation to ensure they interact with the response similarly to otherpredictors. The predictors must be provided as a vector. The function returns a response vector, labeled "Outcomes".
#' @param M The number of groups in the resulting data.
#' @param mvec A vector indicating the length of each group in the data.
#' @param D A vector of denominators for each response; a vector of 1's indicates Bernoulli data.
#' @param beta0 The true intercept in the systematic component of the model.
#' @param beta1 The true slope in the systematic component of the model.
#' @param x A vector of predictor values.
#' @param seed The seed for data generation.
#' @keywords Data Generation Simulation Correlated
#' @export
#' @examples
#' PRNGBinBeta()
PRNGBinBeta=function(M,mvec,D,beta0,beta1,x,seed){
set.seed(seed)
seeds = rpois(M,125)
y = rep(0,length(D))
for(j in 1:M)
{
set.seed(seeds[j])
uj = rbeta(1,2,3)
vj = log(uj/(1-uj))
for(k in 1:mvec[j])
{
set.seed(k*seeds[j])
index = sum(mvec[0:(j-1)])+k
pk = (exp(beta0+beta1*x[index]+vj))/(1+exp(beta0+beta1*x[index]+vj))
y[index] = rbinom(1,D[index],pk)
}
}
list(Outcomes=y)
} # END PRNGBinBeta
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