According to the literature and past discussion board, it seems that in SEM, FIML is highly advised over LISTWISE deletion. One of my independent variables, participation hours in extra-curricular activities is coded as missing if the response was zero. (It is done so, as 50% of the cases are zero, and if I code it as zero, it would not be a normal distribution, and would pull down the mean immensely.) In this case, the missing is dependent on the value of hours in extra-curricular activities (zero), so it is not missing at random. I am tempted to use LISTWISE, with a caution that I am only looking at a relationship among those who participate (i.e. it is a biased sample). Or should I still use FIML? What would be the rationale? If FIML is used, is it correct to understand that the missing values are imputed based on other variables in the model (such as parent's income, education) to a very low value, but not zero?