I have a correlated normal data
y <- -1 + 3*x1- 2*x2 + e
where, e is generated from multivariate normal distribution and thus correlated.
To get a correlated binary data I followed these steps
- scale to get a marginally standard Normal distribution.
- transform by their cumulative distribution function to get a uniform distribution
use the inverse transform method to get binomial responses.
st.y <- (y-mean(y))/sd(y) erfc <- function(x) 2 * pnorm(x * sqrt(2), lower = FALSE) #complementary error fuction u <- .5*erfc(-st.y/sqrt(2)) z <- ifelse(u<=.5, 0,1)
But if I fit gee from this data the pre-specified parameter of intercept and slope is changed. Because in glm, logit(z) = $\beta_0$ + $\beta_1$x1 + $\beta_2$x2.
How can I get a correlated binary variable satisfying logit(z) = -1+3x1-2x2?