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I have fit a linear mixed-effects model using lmer. The model includes 1 categorical predictor variable, 2 continuous predictor variable, all interactions, and a categorical random effect. To test for significance of each main and interaction effect, I am using car::Anova. But I am having trouble figuring out whether to specify Type II or Type III. The model does include interaction terms- does this mean I should use type III, even if those interaction terms are non-significant? Or should I use type II if the interaction terms are significant? Using type II indicates that one of the continuous predictor variables is significant, but none of the others are. Using type III tells me that none of the predictor variables are significant.

Mark Calhoun
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  • One thing to add- when running car::Anova as Type II, one continuous predictor variable has a P-value of 0.01 and all other variables have P > 0.05. When running car::Anova as Type III, all p-values are >0.8. – Mark Calhoun May 18 '22 at 20:52
  • Type II makes more sense, because it does not test the effect of ommitting one variable while it is still present in an interaction term. Actually, this is the whole point of Type II ANOVA: it does not make meaningless tests. Note that Type II ANOVA can also be done with several calls of the base R function drop1(..., test="F"), but it requires using different formulas in each call. – cdalitz May 19 '22 at 06:10

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