A goodness-of-fit test for the random-effects distribution in mixed models

Efendi, Achmad; Drikvandi, Reza; Verbeke, Geert; Molenberghs, Geert

doi:10.1177/0962280214564721

Cited by 21 publications

(29 citation statements)

References 24 publications

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“…Additionally, the variance components τ 2 1 and τ 2 2 were also affected by the misspecification. For these reasons, in practice, we recommend checking the random effect distribution using diagnostic tests as proposed by Drikvandi et al [37] and Efendi et al [38]. Then, if the random effect distribution is not normal, use flexible procedures by considering non-normal distributions for the random effects to estimate the model parameters.…”

Section: Discussionmentioning

confidence: 99%

The Impact of Misspecified Random Effect Distribution in a Weibull Regression Mixed Model

Hernández

Giampaoli

2018

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Mixed models are useful tools for analyzing clustered and longitudinal data. These models assume that random effects are normally distributed. However, this may be unrealistic or restrictive when representing information of the data. Several papers have been published to quantify the impacts of misspecification of the shape of the random effects in mixed models. Notably, these studies primarily concentrated their efforts on models with response variables that have normal, logistic and Poisson distributions, and the results were not conclusive. As such, we investigated the misspecification of the shape of the random effects in a Weibull regression mixed model with random intercepts in the two parameters of the Weibull distribution. Through an extensive simulation study considering six random effect distributions and assuming normality for the random effects in the estimation procedure, we found an impact of misspecification on the estimations of the fixed effects associated with the second parameter σ of the Weibull distribution. Additionally, the variance components of the model were also affected by the misspecification.

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Section: Discussionmentioning

confidence: 99%

The Impact of Misspecified Random Effect Distribution in a Weibull Regression Mixed Model

Hernández

Giampaoli

2018

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“…Detecting misspecification of the distributional assumptions of the random effects is far from straightforward (Efendi et al, 2014). This is an area of research that has recently attracted considerable attention in the literature, with several informal and formal diagnostic tools developed to assess the validity of the assumed random effects distribution in GLMMs.…”

Section: Diagnosing Misspecification Of the Assumed Random Effects DImentioning

confidence: 99%

“…More recently, tests based on the gradient function have been proposed by Efendi et al (2014) and Drikvandi et al (2016) to diagnose misspecification of the parametric assumption of the random effects distribution. Both methods have been proposed to complement the informal graphical approach developed by Verbeke and Molenberghs (2013) (Section 2.7.2.1), and test whether the fluctuations observed in the gradient function graphical tool are due to distributional misspecification of the random effects and not just random variability.…”

Section: Formal Diagnostic Testsmentioning

confidence: 99%

“…Both methods have been proposed to complement the informal graphical approach developed by Verbeke and Molenberghs (2013) (Section 2.7.2.1), and test whether the fluctuations observed in the gradient function graphical tool are due to distributional misspecification of the random effects and not just random variability. Efendi et al (2014) propose a bootstrap test based on the gradient function, however it is restricted to evaluating the gradient within an interval. Therefore, for binary response data, the diagnostic test of Efendi et al (2014) is restricted to those subjects with non-constant response profiles.…”

Section: Formal Diagnostic Testsmentioning

confidence: 99%

“…Efendi et al (2014) propose a bootstrap test based on the gradient function, however it is restricted to evaluating the gradient within an interval. Therefore, for binary response data, the diagnostic test of Efendi et al (2014) is restricted to those subjects with non-constant response profiles. To provide a formal diagnostic test based on the gradient function across the whole support of the random effects distribution, Drikvandi et al (2016) propose and derive the asymptotic properties of a test statistic that utilises the Cramer-von Mises measure.…”

Section: Formal Diagnostic Testsmentioning

confidence: 99%

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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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Nonlinear mixed‐effects models with misspecified random‐effects distribution

Drikvandi

2019

Pharmaceutical Statistics

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Nonlinear mixed-effects models are being widely used for the analysis of longitudinal data, especially from pharmaceutical research. They use random effects which are latent and unobservable variables so the random-effects distribution is subject to misspecification in practice. In this paper, we first study the consequences of misspecifying the random-effects distribution in nonlinear mixed-effects models. Our study is focused on Gauss-Hermite quadrature, which is now the routine method for calculation of the marginal likelihood in mixed models. We then present a formal diagnostic test to check the appropriateness of the assumed random-effects distribution in nonlinear mixed-effects models, which is very useful for real data analysis. Our findings show that the estimates of fixed-effects parameters in nonlinear mixed-effects models are generally robust to deviations from normality of the random-effects distribution, but the estimates of variance components are very sensitive to the distributional assumption of random effects. Furthermore, a misspecified random-effects distribution will either overestimate or underestimate the predictions of random effects. We illustrate the results using a real data application from an intensive pharmacokinetic study.

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A goodness-of-fit test for the random-effects distribution in mixed models

Cited by 21 publications

References 24 publications

The Impact of Misspecified Random Effect Distribution in a Weibull Regression Mixed Model

The Impact of Misspecified Random Effect Distribution in a Weibull Regression Mixed Model

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

Nonlinear mixed‐effects models with misspecified random‐effects distribution

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