Diagnosing Misspecification of the Random-Effects Distribution in Mixed Models

Drikvandi, Reza; Verbeke, Geert; Molenberghs, Geert

doi:10.1111/biom.12551

Cited by 37 publications

(62 citation statements)

References 37 publications

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“…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%

“…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. Further details about the diagnostic test of Drikvandi et al (2016) are presented in Section 3.3.2.…”

Section: Formal Diagnostic Testsmentioning

confidence: 99%

“…Section 3.3.1 describes the gradient function exploratory diagnostic tool of Verbeke and Molenberghs (2013), a graphical tool to assess whether the assumed random effects, G, adequately fits the data, or if there exists any other random effects distribution that improves the fit. However, as the exploratory tool is an informal diagnostic tool, Drikvandi et al (2016) have recently proposed a powerful diagnostic test to supplement the graphical diagnostic function tool. The diagnostic test of Drikvandi et al (2016) is also based on the gradient function, and formally tests for misspecification of the random effects distribution, as described in Section 3.3.2.…”

Section: Misspecification Diagnostic Toolsmentioning

confidence: 99%

“…However, as the exploratory tool is an informal diagnostic tool, Drikvandi et al (2016) have recently proposed a powerful diagnostic test to supplement the graphical diagnostic function tool. The diagnostic test of Drikvandi et al (2016) is also based on the gradient function, and formally tests for misspecification of the random effects distribution, as described in Section 3.3.2.…”

Section: Misspecification Diagnostic Toolsmentioning

confidence: 99%

“…A powerful diagnostic test based on the gradient function has been developed by Drikvandi et al (2016) to formally test for misspecification of the random effects distribution for a general class of mixed models. The diagnostic test of Drikvandi et al (2016) supplements the graphical diagnostic gradient function tool proposed by Verbeke and Molenberghs (2013), providing a formal way to determine whether the fluctuations observed in the gradient plot (detailed in Section 3.3.1) are due to distributional misspecification of the random effects, not just random variability (Drikvandi et al, 2016).…”

Section: Asymptotic Diagnostic Test Based On the Gradient Functionmentioning

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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Section: Formal Diagnostic Testsmentioning

confidence: 99%

Section: Formal Diagnostic Testsmentioning

confidence: 99%

Section: Misspecification Diagnostic Toolsmentioning

confidence: 99%

Section: Misspecification Diagnostic Toolsmentioning

confidence: 99%

Section: Asymptotic Diagnostic Test Based On the Gradient Functionmentioning

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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Testing random effects in linear mixed‐effects models with serially correlated errors

Drikvandi

Noorian

2019

Biometrical J

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In linear mixed‐effects models, random effects are used to capture the heterogeneity and variability between individuals due to unmeasured covariates or unknown biological differences. Testing for the need of random effects is a nonstandard problem because it requires testing on the boundary of parameter space where the asymptotic chi‐squared distribution of the classical tests such as likelihood ratio and score tests is incorrect. In the literature several tests have been proposed to overcome this difficulty, however all of these tests rely on the restrictive assumption of i.i.d. measurement errors. The presence of correlated errors, which often happens in practice, makes testing random effects much more difficult. In this paper, we propose a permutation test for random effects in the presence of serially correlated errors. The proposed test not only avoids issues with the boundary of parameter space, but also can be used for testing multiple random effects and any subset of them. Our permutation procedure includes the permutation procedure in Drikvandi, Verbeke, Khodadadi, and Partovi Nia (2013) as a special case when errors are i.i.d., though the test statistics are different. We use simulations and a real data analysis to evaluate the performance of the proposed permutation test. We have found that random slopes for linear and quadratic time effects may not be significant when measurement errors are serially correlated.

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A statistical model for the dynamics of COVID‐19 infections and their case detection ratio in 2020

et al. 2021

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The case detection ratio of coronavirus disease 2019 (COVID‐19) infections varies over time due to changing testing capacities, different testing strategies, and the evolving underlying number of infections itself. This note shows a way of quantifying these dynamics by jointly modeling the reported number of detected COVID‐19 infections with nonfatal and fatal outcomes. The proposed methodology also allows to explore the temporal development of the actual number of infections, both detected and undetected, thereby shedding light on the infection dynamics. We exemplify our approach by analyzing German data from 2020, making only use of data available since the beginning of the pandemic. Our modeling approach can be used to quantify the effect of different testing strategies, visualize the dynamics in the case detection ratio over time, and obtain information about the underlying true infection numbers, thus enabling us to get a clearer picture of the course of the COVID‐19 pandemic in 2020.

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Diagnosing Misspecification of the Random-Effects Distribution in Mixed Models

Cited by 37 publications

References 37 publications

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

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

Testing random effects in linear mixed‐effects models with serially correlated errors

A statistical model for the dynamics of COVID‐19 infections and their case detection ratio in 2020

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