Mixed model with panel data when some cases have constant responses (zero) over time

I have a panel data with about 300 units observed over a period of 4 weeks. In each week, I recorded a response that is a binary variable, y, for each unit of that week. For about 50% of the units, the response y is zero in all four weeks.

I want to fit a mixed model with time trends and individual random effects for the unit (using Stan). But it seems odd to assume normal individual random effects given most of the units have only zeros. Do you have any suggestions on how to proceed? Should I instead use a compound model (fitting the non-zeros separately)? Any help would be greatly appreciated.

• Can you give some context? Maybe some units have a very low binomial $p$, but that could still vary between units (in principle). For modeling ideas we would need some context, what are the units? what does the binary response represent? ... – kjetil b halvorsen Dec 6 '19 at 15:42
• One way to think about the response is to imagine an event that can or cannot occur. Although it is possible that some of the nonoccurrences are driven by units having dropped out. – mrb Dec 6 '19 at 16:21
• It seems related: stats.stackexchange.com/questions/439621/… – mrb Dec 6 '19 at 17:34
• Have you tried a zero-inflated model ? – Robert Long Dec 12 '19 at 18:47