I'm looking to generate a set of 5 random variables and enforce a dependence structure between them and onto a dependent variable $Y$. I understand how to generate correlated random variables for multivariate normal, but not when mixing different types. Below is a little more than I need, but I'm hoping someone can give me a general way of solving this problem...
- $X_1$ and $X_2$ need to be highly correlated Bernoulli variables.
- $X_3$ needs to take one of 5 categorical values, call them "A"..."E".
- $X_4$ needs to be normal, and negatively correlated with $X_1$, $X_2$.
- $X_5$ needs to approximate test scores from $0$ to $100$ with a high skew, so gamma probably. $X_5$ needs to be positively correlated with $X_1$, $X_2$, $X_4$.
Each of these variables must impact a "success/occurrence" Bernoulli distributed variable $Y$.
How would I begin? I would like to enforce correlation both between the values of $X$, and also between each $X$ and $Y$. (The categorical correlations seem particularly confusing to me.)