Misspecified maximum likelihood estimates and generalised linear mixed models

Heagerty, Patrick J.; Kurland, Brenda F.

doi:10.1093/biomet/88.4.973

Cited by 256 publications

(318 citation statements)

References 16 publications

Supporting

Mentioning

297

Contrasting

Unclassified

Order By: Relevance

“…For a detailed description of the psychotherapy treatment and the drugs used in these studies, we refer the reader to Thase et al [1]. The sample means in Table I supported a quadratic trend for the HRSD trajectory over time.…”

Section: Depression Datamentioning

confidence: 76%

“…We assume the Y i follow a random effects model (1) where β is a p × 1 vector of fixed effects, X i , b i is a q × 1 dimensional vector of random effects with corresponding design matrix Z i , and the random effects covariance matrix Σ i is indexed by subject, i. The b i represent subject-specific deviations from an overall curve.…”

Section: Modelmentioning

confidence: 99%

“…In particular, examining whether this matrix is the same for all subjects or whether it differs depending on subjectspecific characteristics is often neglected in the modelling. For discrete longitudinal data modelled using generalized linear mixed models, ignoring this heterogeneity can result in biased estimates of the fixed effects [1]. For continuous longitudinal data, which will be our focus here, the standard errors for the fixed and random effects, and consequently, inferences, will be incorrect, the random effects will not be shrunk correctly, and prediction of subjectspecific trajectories can be poor.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Modelling the random effects covariance matrix in longitudinal data

Daniels

Zhao

2003

Statistics in Medicine

View full text Add to dashboard Cite

SUMMARYA common class of models for longitudinal data are random effects (mixed) models. In these models, the random effects covariance matrix is typically assumed constant across subject. However, in many situations this matrix may differ by measured covariates. In this paper, we propose an approach to model the random effects covariance matrix by using a special Cholesky decomposition of the matrix. In particular, we will allow the parameters that result from this decomposition to depend on subjectspecific covariates and also explore ways to parsimoniously model these parameters. An advantage of this parameterization is that there is no concern about the positive definiteness of the resulting estimator of the covariance matrix. In addition, the parameters resulting from this decomposition have a sensible interpretation. We propose fully Bayesian modelling for which a simple Gibbs sampler can be implemented to sample from the posterior distribution of the parameters. We illustrate these models on data from depression studies and examine the impact of heterogeneity in the covariance matrix on estimation of both fixed and random effects.

show abstract

Section: Depression Datamentioning

confidence: 76%

Section: Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Modelling the random effects covariance matrix in longitudinal data

Daniels

Zhao

2003

Statistics in Medicine

View full text Add to dashboard Cite

show abstract

“…Agresti, Caffo & Ohman-Strickland (2002) showed that severe misspecification of this distribution, such as assuming normality when the true distribution is a two-point mixture, can arise in a considerable loss of efficiency. Moreover, Heagerty & Kurland (2001) showed that substantial bias in the regression coefficient estimates can result in simple random intercept models when either the variance of the random effects depends on a between-cluster covariate or when the random effects follow an autoregressive structure. A common strategy for guarding against such misspecification is to build more flexible distributional assumptions for the random effects into the model.…”

Section: Introductionmentioning

confidence: 99%

“…These authors showed that such strategies can model a wide variety of shapes, including skewed and multimodal forms, for the distribution of the random effects. Heagerty (1999) and Heagerty & Zeger (2000) proposed estimating effects in a marginally specified model, and Heagerty & Kurland (2001) showed that such an approach yields fixed effect estimates that are more robust to misspecification of the random effect distribution.…”

Section: Introductionmentioning

confidence: 99%

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

Tchetgen

Coull

2006

Biometrika

View full text Add to dashboard Cite

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.

show abstract

Correlated Binary Data

Pendergast

Gange

Lindstrom

2005

Encyclopedia of Biostatistics

View full text Add to dashboard Cite

Correlated binary data may arise in longitudinal or spatial studies or through some other form of clustering of sampling units. The simplest setting, with clusters of size two and no covariates, leads to familiar methods of analysis. Models with covariates include response feature models, conditionally specified models, transitional models, marginal models, and cluster‐specific models. These may lead to different interpretations of the regression parameters.

show abstract

Misspecified maximum likelihood estimates and generalised linear mixed models

Cited by 256 publications

References 16 publications

Modelling the random effects covariance matrix in longitudinal data

Modelling the random effects covariance matrix in longitudinal data

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

Correlated Binary Data

Contact Info

Product

Resources

About