topic How to compare 2 mixed models with different Fixed Effects? in Statistical Procedures

How to compare 2 mixed models with different Fixed Effects?

Daisy2 — Fri, 14 Aug 2020 21:41:51 GMT

How do I compare 2 mixed models with different fixed Effects (here "B"). I understand I cannot use REML but want to know if model B fits the data better than model A. On the internet I saw something about using ANOVA for a Chi-square analysis in R, but don't know how to do it in SAS. I'm a SAS newbie. Thanks.

proc mixed data=ttnc_subsetsort PLOTS=RESIDUALPANEL(UNPACK) RATIO;
  class hyb ntrt pd loc pass rep;
  model tnc =hyb ntrt pd ntrt*hyb pd*hyb ntrt*pd / residual;
  random loc rep(loc) loc*ntrt loc*hyb ;
  lsmeans hyb ntrt pd hyb*ntrt / pdiff=all cl adjust=tukey alpha=0.10;
  title1 'Fit Model A with Factors';
  store modA;
  run;

proc mixed data=ttnc_subsetsort PLOTS=RESIDUALPANEL(UNPACK) RATIO;
  class hyb ntrt pd loc pass rep;
  model tnc =hyb ntrt pd ntrt*hyb pd*hyb ntrt*pd B / residual;
  random loc rep(loc) loc*ntrt loc*hyb ;
  lsmeans hyb ntrt pd hyb*ntrt / pdiff=all cl adjust=tukey alpha=0.10;
  title1 'Fit Model B with Factors';
  store modB;
  run;

Re: How to compare 2 mixed models with different Fixed Effects?

SteveDenham — Mon, 17 Aug 2020 12:02:09 GMT

Since the base model is nested within model B, you can get a likelihood ratio test for the significance of adding the B parameter by subtracting the -2 log likelihood for the base model from the same factor of model B. This should give the same probability as the F test for B in the B model.

But somehow, I don't think this is quite what you are looking for. I suspect you want to know something about the adequacy of the full models. This is where information criteria are helpful. In this case, as there are a fairly substantial number of parameters, I would suggest looking at the corrected AIC values for the two models, and selecting the one with the smaller value. See Burnham, K. P.; Anderson, D. R. (2002), Model Selection and Multimodel Inference: A practical information-theoretic approach (2nd ed.), Springer-Verlag., or for a quick overview, look at the Wikipedia article here.

SteveDenham