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Is it possible that GEE and mixed effect GLM give contradictive answers in significance of covariates? I assume both GEE and GLM selects same covariates. If so, which one should be trusted? From asymptotic viewpoint, GEE and GLM should give same answer. However, I am always in finite sample case. The same answer is not guaranteed.

AdamO
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user45765
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1 Answers1

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Do you mean inference rather than "answer", in terms of the supposed contradictions? Then yes for a number of reasons. A non-comprehensive list:

  1. There is not a perfect 1-1 correspondence between the types of models GEE and LME fit. Consider variance structures versus random effects. For instance, a single random intercept cannot induce a negative correlation within subjects in the same cluster, but the WLS estimator with exchangeable correlation can. Even when positive intraclass correlation is met, the estimates induced by random effect variance may not be the same as those from WLS.
  2. The GEE is not a maximum likelihood procedure, and so handles missing and unbalanced data differently. LME places relatively more weight on subjects with sparser data.
  3. GEE is, in general, more robust to model specification whereas LME is, in general, more efficient with smaller sample sizes.
  4. When considering marginal models for response, such as the famous example of educational attainment versus age in a sample with a strong cohort effect, the LME is powered to detect individual level effects, or conditional effects, whereas the GEE is powered to detect population-average effects.
AdamO
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  • GEE has weighted GEE as well to account MAR missing patterns. I would assume weight GEE exists as well. How small is "small" sample here? – user45765 Jun 09 '22 at 18:33
  • What does LME stand for? – Richard Hardy Jun 09 '22 at 19:23
  • @RichardHardy LME should mean mixed effect but I am not sure about L here. I guess AdamO means generalized linear mixed effect. – user45765 Jun 09 '22 at 19:29
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    Also mixed-effects GLMs (GLMMs) and GEEs estimate different estimands! GLMMs estimate relationships conditional on the random effects whereas GEEs estimate relationships that marginalize over the clustering variables. This can create huge attenuating effects for GEEs and changes the interpretation of all the coefficients. – Noah Jun 09 '22 at 21:22
  • @user45765 yes, you can read the paper from Zhao on IPWEE - inverse probability weighted estimating equations. – AdamO Nov 02 '22 at 16:32