A diagnostic test for the mixing distribution in a generalised linear mixed model

Tchetgen, Eric J. Tchetgen; Coull, Brent A.

doi:10.1093/biomet/93.4.1003

Cited by 36 publications

(37 citation statements)

References 27 publications

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“…Several approaches have been proposed for assessing whether CBC or ICS is present. McCulloch et al recommended testing whether the ML and conditional ML estimators of β va are estimating the same quantity . This is a test for ICS or CBC.…”

Section: Considerations In Choosing a Methodsmentioning

confidence: 99%

“…As mentioned in Section 5, the fact that this estimate is closer to zero than the population‐average estimate of 0.600 is suggestive of CBC . The Tchetgen and Coull test for CBC or ICS mentioned in Section 5 , which compares the estimates 0.546 and 0.460 from ML and conditional ML, respectively, yielded a p ‐value of 0.07. So, evidence for CBC is not significant but is suggestive.…”

Section: Examplementioning

confidence: 99%

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Review of methods for handling confounding by cluster and informative cluster size in clustered data

Seaman

Pavlou

Copas

2014

Statistics in Medicine

111

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Clustered data are common in medical research. Typically, one is interested in a regression model for the association between an outcome and covariates. Two complications that can arise when analysing clustered data are informative cluster size (ICS) and confounding by cluster (CBC). ICS and CBC mean that the outcome of a member given its covariates is associated with, respectively, the number of members in the cluster and the covariate values of other members in the cluster. Standard generalised linear mixed models for cluster-specific inference and standard generalised estimating equations for population-average inference assume, in general, the absence of ICS and CBC. Modifications of these approaches have been proposed to account for CBC or ICS. This article is a review of these methods. We express their assumptions in a common format, thus providing greater clarity about the assumptions that methods proposed for handling CBC make about ICS and vice versa, and about when different methods can be used in practice. We report relative efficiencies of methods where available, describe how methods are related, identify a previously unreported equivalence between two key methods, and propose some simple additional methods. Unnecessarily using a method that allows for ICS/CBC has an efficiency cost when ICS and CBC are absent. We review tools for identifying ICS/CBC. A strategy for analysis when CBC and ICS are suspected is demonstrated by examining the association between socio-economic deprivation and preterm neonatal death in Scotland.

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Section: Considerations In Choosing a Methodsmentioning

confidence: 99%

Section: Examplementioning

confidence: 99%

Review of methods for handling confounding by cluster and informative cluster size in clustered data

Seaman

Pavlou

Copas

2014

Statistics in Medicine

111

View full text Add to dashboard Cite

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“…Diagnostic tests have been developed to examine the adequacy of the assumed random-effects distribution specifically, or more generally to identify misspecification in the structure of either the random effects or the model. Tchetgen and Coull (2006) proposed a diagnostic test based on the difference between marginal and conditional maximum likelihood estimation of time varying explanatory variables to examine the assumed distribution of the random effects. Similarly, misspecification of the random-effects structure can be detected by a simulation-based test (Waagepetersen, 2006) by generating random effects conditional on the observations, or by two-step parametric diagnostic tests (Huang, 2011) based on comparing parameter estimates when using the observed data and reconstructed data.…”

Section: Diagnosing Misspecification Of the Random-effects Distributionmentioning

confidence: 99%

“…As the random effects are unmeasurable, the validity of assumptions relating to the randomeffects distribution can be difficult to check (Alonso et al, 2010). However, diagnostic tests can be used to assess the adequacy of the fit of the model under different distributional assumptions for the random effects (Tchetgen and Coull, 2006;Waagepetersen, 2006;Alonso et al, 2008;Huang, 2011). Recently, Verbeke and Molenberghs (2013) proposed a graphical exploratory diagnostic tool based on the average of likelihood ratios for the random effect (gradient function) to investigate the adequacy of the assumed random-effects distribution.…”

Section: Introductionmentioning

confidence: 99%

Misspecification of Multimodal Random-Effect Distributions in Logistic Mixed Models for Panel Survey Data

Marquart

Haynes

2018

Journal of the Royal Statistical Society Series A: Statistics in Society

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Summary Logistic mixed models for longitudinal binary data typically assume normally distributed random effects, which may be too restrictive if an underlying subpopulation structure exists. The paper illustrates the ease of implementing diagnostic tests and fitting random effects as a mixture of normal distributions to detect and address distributional misspecification of the random effects in a potential mover–stayer scenario. Methods are illustrated by using data from the Household, Income and Labour Dynamics in Australia panel survey. The robustness of the normality assumption to violations characterized by a three‐component mixture of normal distributions was assessed via a simulation study. Adverse inferential impact of incorrectly assuming normality was identified for parameters directly related to the random effects, resulting in biased estimates and poor coverage rates for confidence intervals. The results support the general robustness of fixed effect parameters to non‐extreme distributional violations of the random effects.

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“…To examine the adequacy of the assumed random effects distribution in GLMMs with canonical links, Tchetgen and Coull (2006) proposed a diagnostic test based on the difference between marginal and conditional ML estimation of time-varying explanatory variables. In a similar context, diagnostic tests have been proposed that compare estimates between two approaches.…”

Section: Formal Diagnostic Testsmentioning

confidence: 99%

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

Marquart-Wilson¹

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Logistic mixed models for binary longitudinal panel data typically assume normal distributed random effects, and appropriately account for correlated data, unobserved heterogeneity and missing data due to attrition. However, this normality assumption may be too restrictive to capture unobserved heterogeneity. The motivating case study is a longitudinal analysis of women's employment participation using data from the Household Income and Labour Force Dynamics in Australia (HILDA) survey. Multimodality of the random effects was identified, potentially due to an underlying mover-stayer scenario.This study focuses on logistic mixed models applied to the HILDA case study and simulation studies motivated by the case study, and aims to investigate:1. robustness of random intercept logistic models to the assumed normal random effects distribution when the true distribution is multimodal 2. whether relaxing the parametric assumption of the random effects distribution can provide a practical solution to reduce the impact of distributional misspecification 3. impact of misspecification and performance of logistic mixed models in the presence of missing data due to attrition.Random intercept logistic models applied to the case study demonstrate that the assumed normal distribution may not adequately capture the underlying heterogeneity due to a potential moverstayer scenario. An asymmetric three component mixture of normal distributions provided a more appropriate fit, potentially representing three sub-populations: those with an extremely low, moderate, or extremely high propensity to be constantly employed.Two simulation studies motivated by the HILDA study considered a three component mixture of normal distributions for the random intercept. The inferential impact of incorrectly assuming a normal distribution was dependent on the severity of departure of the true distribution from normality. In the first study, simulating a potential mover-stayer scenario, misspecification produced biased estimates of the intercept constant and random effect variance. More severely asymmetric and skewed multimodal distributions produced larger bias. The second study considered a range of true symmetric multimodal distributions, with increasing severity in departures from normality. The random intercept logistic model assuming normality was robust to minor deviations. However, for larger departures characterised by three distinct modes, ii misspecification produced biased parameter estimates and poor coverage rates for the intercept constant, time-invariant explanatory variables and those time-varying explanatory variables exhibiting minimal within-individual variability. For both simulation studies, estimates of the random effect variance were extremely sensitive to distributional misspecification, resulting in biased parameter estimates, poor coverage rates and inaccurate standard errors.Non-parametric estimation techniques, which leave the distribution completely unspecified, reduced the risks associated with misspecification o...

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A diagnostic test for the mixing distribution in a generalised linear mixed model

Cited by 36 publications

References 27 publications

Review of methods for handling confounding by cluster and informative cluster size in clustered data

Review of methods for handling confounding by cluster and informative cluster size in clustered data

Misspecification of Multimodal Random-Effect Distributions in Logistic Mixed Models for Panel Survey Data

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

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