A General Maximum Likelihood Analysis of Variance Components in Generalized Linear Models

Aitkin, Murray

doi:10.1111/j.0006-341x.1999.00117.x

Cited by 324 publications

(316 citation statements)

References 59 publications

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“…The familiar linear model E[Y it | X i , α i ] = X it β * + α i is also included as a special case of equation (1).…”

Section: A Conditional Mean Model and Linear Estimatorsmentioning

confidence: 99%

“…The two critical assumptions made in equation (1) are that X i is strictly exogenous conditional on α and that m(x, α) does not vary with time. We consider identification without the strict exogeneity assumption below.…”

Section: A Conditional Mean Model and Linear Estimatorsmentioning

confidence: 99%

“…Nonlinear fixed effects estimators are biased toward zero for the unidentified effects, and have probability limits that usually lie outside of the identified set. However, both 1 We consider the version of the linear probability model that allows for individual specific slopes in addition to the fixed effects.…”

Section: Numerical Examplesmentioning

confidence: 99%

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Identification and estimation of marginal effects in nonlinear panel models

Chernozhukov¹,

Fernández‐Val²,

Hahn³

et al. 2009

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This paper gives identification and estimation results for marginal effects in nonlinear panel models. We find that linear fixed effects estimators are not consistent, due in part to marginal effects not being identified. We derive bounds for marginal effects and show that they can tighten rapidly as the number of time series observations grows. We also show in numerical calculations that the bounds may be very tight for small numbers of observations, suggesting they may be useful in practice. We propose two novel inference methods for parameters defined as solutions to linear and nonlinear programs such as marginal effects in multinomial choice models. We show that these methods produce uniformly valid confidence regions in large samples. We give an empirical illustration.

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“…The familiar linear model E[Y it | X i , α i ] = X it β * + α i is also included as a special case of equation (1).…”

Section: A Conditional Mean Model and Linear Estimatorsmentioning

confidence: 99%

Section: A Conditional Mean Model and Linear Estimatorsmentioning

confidence: 99%

See 1 more Smart Citation

Identification and estimation of marginal effects in nonlinear panel models

Chernozhukov¹,

Fernández‐Val²,

Hahn³

et al. 2009

View full text Add to dashboard Cite

show abstract

“…A common strategy for guarding against such misspecification is to build more flexible distributional assumptions for the random effects into the model. For instance, Aitkin (1996Aitkin ( , 1999 proposed estimating this distribution nonparametrically as a finite number of mass points and corresponding probabilities. Magder and Zeger (1996), Verbeke & Lesaffre (1996), and Chen, Zhang & Davidian (2002) constructed alternative nonparametric estimates based on mixtures of Gaussian distributions.…”

Section: Introductionmentioning

confidence: 99%

“…That is, with the exception of the nonparametric approach of Aitkin (1996Aitkin ( , 1999, for which there exist GLIM macros, we are not aware of any commercial software or macros that easily implement these more general models. Before investing time programming one of these more robust approaches, one would like to be able to diagnose whether such methods are required.…”

Section: Introductionmentioning

confidence: 99%

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

Tchetgen

Coull

2006

Biometrika

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We introduce a diagnostic test for the mixing distribution in a generalised linear mixed model. The test is based on the difference between the marginal maximum likelihood and conditional maximum likelihood estimates of a subset of the fixed effects in the model. We derive the asymptotic variance of this difference, and propose a test statistic that has a limiting chi-square distribution under the null hypothesis that the mixing distribution is correctly specified. For the important special case of the logistic regression model with random intercepts, we evaluate via simulation the power of the test in finite samples under several alternative distributional forms for the mixing distribution. We illustrate the method by applying it to data from a clinical trial investigating the effects of hormonal contraceptives in women. A Diagnostic Test for the Mixing Distribution in a GeneralisedLinear Mixed Model conditional maximum likelihood estimates of a subset of the fixed effects in the model. We derive the asymptotic variance of this difference, and propose a test statistic that has a limiting chi-square distribution under the null hypothesis that the mixing distribution is correctly specified. For the important special case of the logistic regression model with random intercepts, we evaluate via simulation the power of the test in finite samples under several alternative distributional forms for the mixing distribution. We illustrate the method by applying it to data from a clinical trial investigating the effects of hormonal contraceptives in women.

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A semi-parametric Bayesian approach to generalized linear mixed models

Kleinman

Ibrahim

1998

Statist. Med.

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The linear mixed effects model with normal errors is a popular model for the analysis of repeated measures and longitudinal data. The generalized linear model is useful for data that have non-normal errors but where the errors are uncorrelated. A descendant of these two models generates a model for correlated data with non-normal errors, called the generalized linear mixed model (GLMM). Frequentist attempts to fit these models generally rely on approximate results and inference relies on asymptotic assumptions. Recent advances in computing technology have made Bayesian approaches to this class of models computationally feasible. Markov chain Monte Carlo methods can be used to obtain 'exact' inference for these models, as demonstrated by Zeger and Karim. In the linear or generalized linear mixed model, the random effects are typically taken to have a fully parametric distribution, such as the normal distribution. In this paper, we extend the GLMM by allowing the random effects to have a non-parametric prior distribution. We do this using a Dirichlet process prior for the general distribution of the random effects. The approach easily extends to more general population models. We perform computations for the models using the Gibbs sampler.

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A General Maximum Likelihood Analysis of Variance Components in Generalized Linear Models

Cited by 324 publications

References 59 publications

Identification and estimation of marginal effects in nonlinear panel models

Identification and estimation of marginal effects in nonlinear panel models

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

A semi-parametric Bayesian approach to generalized linear mixed models

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