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Generalised linear models with clustered data
Umeå University, Faculty of Social Sciences, Department of Statistics.
2010 (English)Licentiate thesis, comprehensive summary (Other academic)
Abstract [en]

In situations where a large data set is partitioned into many relativelysmall clusters, and where the members within a cluster have some common unmeasured characteristics, the number of parameters requiring estimation tends to increase with sample size if a fixed effects model is applied. This fact causes the assumptions underlying asymptotic results to be violated. The first paper in this thesis considers two possible solutions to this problem, a random intercepts model and a fixed effects model, where asymptoticsare replaced by a simple form of bootstrapping. A profiling approach is introduced in the fixed effects case, which makes it computationally efficient even with a huge number of clusters. The grouping effect is mainly seen as a nuisance in this paper.

In the second paper the effect of misspecifying the distribution of the random effects in a generalised linear mixed model for binary data is studied. One problem with mixed effects models is that the distributional assumptions about the random effects are not easily checked from real data. Models with Gaussian, logistic and Cauchy distributional assumptions are used for parameter estimation on data simulated using the same three distributions. The effect of these assumptions on parameter estimation is presented. Two criteria for model selection are investigated, the Akaike information criterion and a criterion based on a chi-square statistic. The estimators for fixed effects parameters are quite robust against misspecification of the random effects distribution, at least with the distributions used in this paper. Even when the true random effects distribution is Cauchy, models assuming a Gaussian or a logistic distribution regularly produce estimates with less bias.

Place, publisher, year, edition, pages
Umeå: Statistiska institutionen, Umeå Universitet , 2010. , 21 p.
Series
Statistical studies, ISSN 1100-8989 ; 43
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
URN: urn:nbn:se:umu:diva-39972ISBN: 978-91-7459-039-5 (print)OAI: oai:DiVA.org:umu-39972DiVA: diva2:396958
Presentation
2009-09-01, Umeå universitet, Umeå, 10:00 (English)
Opponent
Supervisors
Available from: 2011-02-17 Created: 2011-02-11 Last updated: 2011-02-17Bibliographically approved
List of papers
1. Generalized linear models with clustered data: fixed and random effects models
Open this publication in new window or tab >>Generalized linear models with clustered data: fixed and random effects models
2011 (English)In: Computational Statistics & Data Analysis, ISSN 0167-9473, E-ISSN 1872-7352, Vol. 55, no 12, 3123-3134 p.Article in journal (Refereed) Published
Abstract [en]

The statistical analysis of mixed effects models for binary and count data is investigated. In the statistical computing environment R, there are a few packages that estimate models of this kind. The packagelme4 is a de facto standard for mixed effects models. The packageglmmML allows non-normal distributions in the specification of random intercepts. It also allows for the estimation of a fixed effects model, assuming that all cluster intercepts are distinct fixed parameters; moreover, a bootstrapping technique is implemented to replace asymptotic analysis. The random intercepts model is fitted using a maximum likelihood estimator with adaptive Gauss–Hermite and Laplace quadrature approximations of the likelihood function. The fixed effects model is fitted through a profiling approach, which is necessary when the number of clusters is large. In a simulation study, the two approaches are compared. The fixed effects model has severe bias when the mixed effects variance is positive and the number of clusters is large.

Keyword
Bernoulli distribution, Gauss-Hermite quadrature, Laplace approximation, Implicit derivation, Profiling, Poisson distribution
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:umu:diva-40018 (URN)10.1016/j.csda.2011.06.011 (DOI)
Funder
Riksbankens Jubileumsfond, 2005-0488
Available from: 2011-02-14 Created: 2011-02-14 Last updated: 2017-12-11Bibliographically approved
2. Generalised linear models with clustered data: robustness against a misspecified random effects distribution
Open this publication in new window or tab >>Generalised linear models with clustered data: robustness against a misspecified random effects distribution
(English)Manuscript (preprint) (Other academic)
National Category
Probability Theory and Statistics
Research subject
Statistics
Identifiers
urn:nbn:se:umu:diva-40019 (URN)
Available from: 2011-02-14 Created: 2011-02-14 Last updated: 2012-03-05Bibliographically approved

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