Type I and Type II Error Under Random‐Effects Misspecification in Generalized Linear Mixed Models

Litière, Saskia; Alonso, Ariel; Molenberghs, Geert

doi:10.1111/j.1541-0420.2007.00782.x

Cited by 110 publications

(127 citation statements)

References 21 publications

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“…Note that this theory can also be regarded as the underpinning of such commonly used methods as generalized estimating equations. This methodology has been applied by Litiére et al [37,38] in the context of miss-specification arising from the random-effects distribution in generalized linear mixed models. Moreover, we did not address the effect of ignoring the correlated frailty structure by using a shared frailty distribution on the estimation of covariate effects.…”

Section: Discussionmentioning

confidence: 99%

The correlated and shared gamma frailty model for bivariate current status data: An illustration for cross‐sectional serological data

Hens

Wienke

Aerts

et al. 2009

Statistics in Medicine

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SUMMARYFrailty models are often used to study the individual heterogeneity in multivariate survival analysis. Whereas the shared frailty model is widely applied, the correlated frailty model has gained attention because it elevates the restriction of unobserved factors to act similar within clusters. Estimating frailty models is not straightforward due to various types of censoring. In this paper, we study the behavior of the bivariate-correlated gamma frailty model for type I interval-censored data, better known as current status data. We show that applying a shared rather than a correlated frailty model to cross-sectionally collected serological data on hepatitis A and B leads to biased estimates for the baseline hazard and variance parameters.

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Section: Discussionmentioning

confidence: 99%

The correlated and shared gamma frailty model for bivariate current status data: An illustration for cross‐sectional serological data

Hens

Wienke

Aerts

et al. 2009

Statistics in Medicine

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show abstract

“…In the case of mixed models for binary responses, Agresti, Caffo, and OhmanStrickland (2004) have found that inferences tend to be unbiased under general departures from normality and only found a drop in efficiency when the random effects' true distribution is discrete with large variance. As a matter of fact, for this type of model Litière, Alonso, and Molenberghs (2007) formally showed (see their theorem 1 and corollary 1) that a significant finding (i.e., β significantly different from zero) is a reliable result even under a misspecified distribution of the random effects. We make this normality assumption because (i) it allows us to use two-step estimation methods instead of direct maximum likelihood and (ii) it yields closed-form E-and M-steps in the EM-algorithm that we propose for the second step of the two-step estimation procedure.…”

Section: Two-step Estimationmentioning

confidence: 90%

Conditional Logistic Regression With Longitudinal Follow-up and Individual-Level Random Coefficients: A Stable and Efficient Two-Step Estimation Method

Craiu

Duchesne

Fortin

et al. 2011

Journal of Computational and Graphical Statistics

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The analysis of data generated by animal habitat selection studies, by family studies of genetic diseases, or by longitudinal follow-up of households often involves fitting a mixed conditional logistic regression model to longitudinal data composed of clusters of matched case-control strata. The estimation of model parameters by maximum likelihood is especially difficult when the number of cases per stratum is greater than one. In this case, the denominator of each cluster contribution to the conditional likelihood involves a complex integral in high dimension, which leads to convergence problems in the numerical maximization. In this article we show how these computational complexities can be bypassed using a global two-step analysis for nonlinear mixed effects models. The first step estimates the cluster-specific parameters and can be achieved with standard statistical methods and software based on maximum likelihood for independent data. The second step uses the EM-algorithm in conjunction with conditional restricted maximum likelihood to estimate the population parameters. We use simulations to demonstrate that the method works well when the analysis is based on a large number of strata per cluster, as in many ecological studies. We apply the proposed twostep approach to evaluate habitat selection by pairs of bison roaming freely in their natural environment. This article has supplementary material online.

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“…Very often such random effects are assumed to be normally distributed. The normality assumption for the random effects has been both criticised and supported by several authors [25,26,27].…”

Section: Discussionmentioning

confidence: 99%

A More Robust Random Effects Model for Disease Mapping

Cheruiyot¹

2018

AJTAS

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Disease mapping studies have found wide applications within geographical epidemiology and public health and are typically analysed within a Bayesian hierarchical model formulation. The most popular disease mapping model is the Besag-York-Molli´e model. A distinguishing feature of this model is the use of two sets of random effects: one spatially structured to model spatial autocorrelation and the other spatially unstructured to describe residual unstructured heterogeneity. Very often the spatially unstructured random effect is assumed to be normally distributed. Under practical situations, this normality assumption is found to be over restrictive. In this study, we investigate a more robust spatially unstructured random effect distribution by considering the Inverse Gaussian (IG) distribution in the disease mapping problem. The distribution has the normal distribution as special case. The inferences under this model are carried out within a bayesian hierarchical model formulation implemented in WinBUGS. The IG distribution is introduced in WinBUGS using zero tricks. The usefulness of the proposed model is investigated with a simulation study and applied in real data; mapping HIV in Kenya. In this work we showed that the IG distribution can produce better results when the normality assumption is violated due to the skewness of the data. For the case of data in which the random effects are truly normal, the IG distribution adjusts to a normal distribution as dictated by the data itself. On the other hand, the spatially structured random effect is normally modelled using the intrinsic conditional autoregressive (iCAR) prior. This prior is improper and has the undesirable large scale property of leading to a negative pairwise correlation for regions located further apart. In addition, the BYM model presents some identifiability problems of the spatial and non-spatial effects. In this work, we consider Leroux CAR (named lCAR hereafter) prior, a less widely used prior in disease mapping, as the prior distribution for the spatially structured random effects.

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Type I and Type II Error Under Random‐Effects Misspecification in Generalized Linear Mixed Models

Cited by 110 publications

References 21 publications

The correlated and shared gamma frailty model for bivariate current status data: An illustration for cross‐sectional serological data

The correlated and shared gamma frailty model for bivariate current status data: An illustration for cross‐sectional serological data

Conditional Logistic Regression With Longitudinal Follow-up and Individual-Level Random Coefficients: A Stable and Efficient Two-Step Estimation Method

A More Robust Random Effects Model for Disease Mapping

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