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I have a longitudinal dataset where I'm building an lmer model using 5 fixed predictors with a random effect for subjects. One of the fixed predictors is Diagnosis ( there are three different diagnosis and I'm interested in seeing the change in outcome for each diagnosis)

I built a full model, but didn't add any interaction terms because I don't know how to go about it. Do I run models with all 16 two way interactions between the fixed predictors and then check for significance by using anova() and comparing to my full model for each interaction? Do I then check for 3-way interactions, 4-way interactions and so on?

N.B- I'm new to all this with no statistical background

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  • $\begingroup$ Much depends on how much data you have. One thing to become aware of as you start to learn statistics is the danger of overfitting: trying to evaluate too many predictors for the amount of data you have leads to trouble. Your 3-level Diagnosis counts as 2 predictors, and each interaction with that would count as at least 2 more. For binary outcome data a rule of thumb is to have about 15 members of the minority outcome class per predictors. So how many cases do you have? And does your knowledge of the subject matter suggest that some interactions might be associated with outcome? $\endgroup$ – EdM Aug 14 '20 at 21:11
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There is no clear answer. If there is a theoretical reason to expect an interaction (or testing for one is important), then try out an interaction. For example: I hope people researching allergy medications test for possible interactions with alcohol since many users of those drugs might take them before going outside and having a drink.

However, adding all 16 possible model terms plus interactions is probably overkill. So I guess I am suggesting that you first think much more about your data and the research problem to determine interactions you would expect (or want to guard against). Typically, when we consider interactions, we first consider two-way interactions, interactions of two variables, before considering three- or four-way interactions.

While you might be a novice at statistics, I cannot promise that even decades of experience would reveal the answer. To some extent, it helps to be familiar with your research area and it helps to have done similar analyses in the past. However, even in these cases we sometimes find surprising or unexpected interactions.

To address some of your newness to statistics, you might benefit from reading a useful introductory text like Box, Hunter, and Hunter's Statistics for Experimenters (2nd Ed.).

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