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I have various potential fixed effect predictors for a linear mixed effect model. Some are control variables and some are predictors of interest (on their own and interactions). I am interested in testing the inclusion of certain predictors of interest using LRTs.

In what order should I test the predictors? Should I start with the ones I am most interested in? Should I start with main effects and then test interactions?

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It doesn't really matter in what order you test them. However I would just make a few points:

  • avoid stepwise procedures. There are many resources on this site and elsewhere that go into detail about why.
  • you should adjust your p values for multiple testing.
  • it is better to let clinical/expert knowledge determine which variables to include and not be guided by statistical significance, due to the arbitrariness of significance levels. See the first part of my answer to this question.
  • regarding interactions, in particular, you should include the relevant main effects when you include an interaction. That is, don't include an interaction without the main effects.
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    $\begingroup$ @Dave if this answers your question please consider marking it as the accepted answer $\endgroup$ – Robert Long Jul 6 at 5:00

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