We did an analysis recently with time varying covariates but there is missing data due to the exogenous time varying covariates. A reviewer suggested that we can have the covariates included in the model in Mplus by freeing their variances so that we wouldn't have so much missing data. This didn't work; the model won't solve. Is there a way to include the time varying covariates in the mode so that we don't have so much missing data?
Just score the missingness on the xt's as something like 888 while your missing data flag is say 999. This means that people with missing on xt won't be eliminated, but at the same time xt won't have an influence on the model because the corresponding yt is missing so there is no contribution to the likelihood.