I set up a mix-logit model with random coefficients in PROC IML. Each random coefficient equation is a function of observed characteristics and unobserved heterogeneity. The unobserved components (error terms) are coming from a multivariate normal distribution with zero means and a variance-covariance matrix and they are added to the observed characteristics. I need to estimate the variance-covariance matrix parameters (variances and correlation coefficients) of the MVN along with the other parameters of the model using simulated maximum likelihood estimator.
I tried to estimate the parameters using Cholesky decomposition by simply adding standard normal errors that are generated outside the optimization procedure, to these coefficient equations. The coefficients of these error terms are then, the lower triangular matrix. However, I’m wondering if there is another way that does not require Cholesky decomposition of the error terms so that I can draw the errors from a MVN and estimate the error variances and correlation parameters directly (along with the other model parameters). I appreciate any suggestions.