In a future project, I plan to not use listwise deletion, but include some missings as parameters to be estimated.
I'll figure the code out when the time comes, but I'm curious how to handle computing the log_lik statements needed for looic or other model fit metrics.
Generally, you just throw vector[N] log_lik into gen quantities, and compute the log-likelihood of each observation, throw it back into that vector.
But what do you do if you model missing data? Do you only compute log_lik for observed data, or do you include log_lik for missings as well?
Context: The model will be an SEM type of model, where inevitably, some people will not answer all scales' responses. Generally, this number has been small enough that I can just dump the 2-3 cases that didn't fully answer the scales, but I plan on including all /available/ responses into the model, then model missing responses by just constructing a full data matrix from observed and unobserved data, and running the model on that data matrix. I'll want to compute some model fit stats using the joint likelihood of the data, but I have no clue whether to include missing, estimated observations into the log-likelihood estimates. Thoughts?