I'm confused about the difference between log-linear model and poisson regression and I am not sure which one to use to answer my research question.
In the experiment, participants were grouped into young/old, treatment/no treatment, white/non-white. Researchers were to collect questionnaires every 2 weeks. It turned out the number of questionnaire collected were less than the original goal. I would like to know if the missingness has something to do with ethnicity, treatment, changes in protocol or interaction between these factors.
My instinct would be to use a Poisson regression with number of questionnaire as the outcome, and ethnicity, treatment and protocol change as the predictors. However, my mentor told me to use a log-linear model to examine the association between these factors. My understanding is that log-linear model examines expected cell counts in n-way contingency table. Can log-linear model answer this question? If yes, does that mean I have to look at the interaction between number of questionnaire and ethnicity, treatment or protocol change in a 4-way table?
When searching online, some people also used log-linear model and poisson regression interchangeably. Are they actually the same thing under certain circumstances?