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A standard assumption is that of normality of the random effects, but this assumption may not always be realistic, and, because the random effects are not observed, it may be difficult to verify.
However, this result should be taken with caution because the random effects model is more conservative than the fixed effects one.
These authors mention the fact that, because the random effects are unobservable latent model components, no straightforward diagnostic is available to check the validity of the normality assumption.
This is necessary because the random effects are on the individual level and therefore they are integrated out before the individual log-likelihoods are weighted with the a posteriori probabilities in the M-step.
They proposed a measure for the fixed effect called median odds ratio (MOR) in order to take into account the fact that, in practice, the procedure of conditioning in the random effects is unrealistic because the random effects are unobservable.
Hence the exactness of the confidence intervals for both examples below is brought into question, because the random effects model only provides an approximation for real data such as these.
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The magnitude of this tree-to-tree variation is apparent in this study because when the random effects of site and tree were considered, the total amount of variation in SGA explained by the models almost doubled.
Because the random effect has only one level, the covariance structure is scaled identity.
Functional and cosmetic outcomes were assessed using a fixed-effects meta-analysis model with the meta statistical package in STATA v. 10.0 (Stata Corp., College Station, TX) because heterogeneity was not significant in the random effects model (P value > 0.05 in all cases).
We chose the random effects model because we expected heterogeneity across study participants and settings.
39 By default we used the random effects model because adjusted indirect comparisons that used the fixed effects model tend to underestimate the standard errors of pooled estimates.
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