Correction or ajdust of alpha level when multiple comparision using contrast coding was employed in Linear Mixed model?

Hi there,

Sorry to bother you. I encountered a problem with multiple comparison in LME in R (Package LME4) and I hope you could help me solve the problem. Basically I am fitting a mixed effect model with two categorical factors: Y~A+B+A:B+(1+A||Subject) + (1+A||Item) in which factor A had two levels and factor B had three levels. In the model I used simple contrast coding in which the predictors that entered the model were the contrast between the reference level and one of the rest of the level(s) in the categorical factors. I used A1 and B1 as the reference level

So I got the final model after model selection: Model1 = Y~A1vs.A2+B1vs.B2+B1vs.B3+A1vs.A2:B1vs.B2+A1vs.A2:B1vs.B3+(1+A1vsA2||Subject) + (1+A1vsA2||Item).

The contrast between B2 and B3 was also theoretically interesting. So what I did now was to fit a model that treat B2 in factor B as the reference level but everything else was the same. So I got a new mixed model:

Model2 = Y~A1vs.A2+B2vs.B1+B2vs.B3+A1vs.A2:B2vs.B1+A1vs.A2:B2vs.B3‚Äč+random model

.

I have two questions around the multiple comparison by fitting two models using different reference level.

  1. Should I go through the model selection again for Model 2 or keep using the model structure of Model 1?

  2. Should use any kind of correction or simply adjust the alpha level to avoid type I error? If I should use correction, how can I do it with LME models (packages such as phia or lsmeans might not be so appropriate in this case)?

Thank you so much!

Best,

Chi

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