(Following the private request from a more senior CV member, I am editing this question to make it more readable and comply with CV standards).
I am looking for a method to simulate multivariate, non-normal data with a pre-specified pattern of missingness while making sure that the missingness on does not invalidate my non-normality.
I thought about doing this as a two-step process: (1) Generate multivariate, non-normal data following the method described in Vale & Maurelli 1983 (the multivariate extension of Fleishman 1978). The Vale & Maurelli process allows me to specify the population values of skewness/kurtosis in all 1-dimensional marginals. (2) Once a sample is taken from said distribution with given population values of skewness/kurtosis on the one-dimensional marginals , generate some missing data pattern on the sample data.
I immediatley recognized that by inducing missingness, my non-normality could disappear (e.g. if I sample from a skewed distribution and then have missing data on the higher values, the skewness could be severely diminished or disappear all togehter). My attempt at a solution was to introduce a 3rd step where (3) Once the data were sampled and the missingness introduced, I would calculate the sample estimates of skewness/kurtosis and only retain those datasets for further analysis that fell within certain "acceptable" (<--- this would be set by me) range of skewness/kurtosis.
A professor commented on the fact that my step (3) would be invalid because #1 the definitions of skewness/kurtosis we have only exist for complete datasets and #2 if I only kept certain datasets and threw away others I could no longer claim I was sampling randomly from my distribution and I could only do this under MCAR (Missing Compeletely at Random) but not under MAR (Missing At Random) and NMAR (Not Missing At Random).
So I am stuck now and would very much appreciate any insights on anyone who could have some idea about how to implement said algorithm. I believe maybe going about with a different sampling scheme than the one I suggested?