Estimation of covariate effects in generalized linear mixed models with a misspecified distribution of random intercepts and slopes

Abstract

Generalized linear mixed models with random intercepts and slopes provide useful analyses of clustered and longitudinal data and typically require the specification of the distribution of the random effects. Previous work for models with only random intercepts has shown that misspecifying the shape of this distribution may bias estimates of the intercept, but typically leads to little bias in estimates of covariate effects. Very few papers have examined the effects of misspecifying the joint distribution of random intercepts and slopes. However, simulation results in a recent paper suggest that misspecifying the shape of the random slope distribution can yield severely biased estimates of all model parameters. Using analytic results, simulation studies and fits to example data, this paper examines the bias in parameter estimates due to misspecification of the shape of the joint distribution of random intercepts and slopes. Consistent with results for models with only random intercepts, and contrary to the claims of severe bias in a recent paper, we show that misspecification of the joint distribution typically yields little bias in estimates of covariate effects and is restricted to covariates associated with the misspecified random effects distributions. We also show that misspecification of the distribution of random effects has little effect on confidence interval performance. Coverage rates based on the model-based standard errors from fitted likelihoods were generally quite close to nominal.

Are corpus-based predictions mirrored in the preferential choices and ratings of native speakers? Predicting the alternation between the Estonian adessive case and the adposition <i>peal</i> ‘on’

“…The ShapiroWilk test indicates that the normality assumption of the random lemmaspecific intercepts is slightly violated (W = 0.98894, p-value = 0.0189). However, the misspecification of the distribution of random effects has little effect on estimates of covariate effects (McCulloch and Neuhaus 2011;Neuhaus et al 2013). It is therefore concluded that the slight violation of the normality assumption of the random lemma-specific intercepts does not pose problems for interpreting the main effects of the model.…”

Detecting treatment-subgroup interactions in clustered data with generalized linear mixed-effects model trees

“…Previous research on GLMMs has shown that misspecifying the shape of the random-effects distribution reduces the accuracy of random-effects predictions, but has little effects on the fixed-effects parameter estimates (e.g., Neuhaus, McCulloch, & Boylan, 2013). This indicates that for GLMM trees, misspecification of the shape of the randomeffects distribution will affect random-effects predictions, but will have little effect on the estimated tree.…”

Misspecification and flexible random effect distributions in logistic mixed effects models applied to panel survey data

“…Maximum likelihood estimates for fixed effects and variance components obtained under the assumption of Gaussian distributed random effects have been shown to be consistent and asymptotically normally distributed under broad regularity conditions, even when the random effects distribution is misspecified Lesaffre, 1996, 1997;Neuhaus et al, 2013). Although the estimates are consistent, sandwich-type corrections are required to obtain the correct asymp-totic standard errors (Butler and Louis, 1992;Verbeke and Lesaffre, 1997).…”

“…Heagerty and Kurland 2001;Neuhaus and McCulloch 2006;Huang 2009;Neuhaus and McCulloch 2014), incorrectly assuming independence to the cluster size , and incorrectly specifying the distribution (e.g. Heagerty and Kurland 2001;McCulloch and Neuhaus 2011a;Neuhaus et al 2013). …”

“…Recent research has investigated the impact of misspecifying the random effects distribution in logistic mixed models (e.g. Neuhaus et al 1992;Heagerty and Kurland 2001;Litiére et al 2008;McCulloch and Neuhaus 2011a;Neuhaus et al 2013), generally reporting biased estimation of parameters associated with the misspecified random effects, such as the intercept constant and variance estimates of the random effects. However there has been no general consensus about the impact on estimating fixed effects parameters, usually the parameters of primary interest.…”