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The laplace approximation and inference in generalized linear models with two or more random effects

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dc.contributor.advisor Schafer, Daniel
dc.creator Pratt, James L.
dc.date.accessioned 2012-11-15T16:50:49Z
dc.date.available 2012-11-15T16:50:49Z
dc.date.copyright 1994-11-29
dc.date.issued 1994-11-29
dc.identifier.uri http://hdl.handle.net/1957/35078
dc.description Graduation date: 1995 en_US
dc.description.abstract This thesis proposes an approximate maximum likelihood estimator and likelihood ratio test for parameters in a generalized linear model when two or more random effects are present. Substantial progress in parameter estimation for such models has been made with methods involving generalized least squares based on the approximate marginal mean and covariance matrix. However, tests and confidence intervals based on this approach have been limited to what is provided through asymptotic normality of estimates. The proposed solution is based on maximizing a Laplace approximation to the log-likelihood function. This approximation is remarkably accurate and has previously been demonstrated to work well for obtaining likelihood based estimates and inferences in generalized linear models with a single random effect. This thesis concentrates on extensions to the case of several random effects and the comparison of the likelihood ratio inference from this approximate likelihood analysis to the Wald-like inferences for existing estimators. The shapes of the Laplace approximate and true log-likelihood functions are practically identical, implying that maximum likelihood estimates and likelihood ratio inferences are obtained from the Laplace approximation to the log-likelihood. Use of the Laplace approximation circumvents the need for numerical integration, which can be practically impossible to compute when there are two random effects. However, both the Laplace and exact (via numerical integration) methods require numerical optimization, a sometimes slow process, for obtaining estimates and inferences. The proposed Laplace method for estimation and inference is demonstrated for three real (and some simulated) data sets, along with results from alternative methods which involve use of marginal means and covariances. The Laplace approximate method and another denoted as Restricted Maximum Likelihood (REML) performed rather similarly for estimation and hypothesis testing. The REML approach produced faster analyses and was much easier to implement while the Laplace implementation provided likelihood ratio based inferences rather than those relying on asymptotic normality. en_US
dc.language.iso en_US en_US
dc.subject.lcsh Linear models (Statistics) en_US
dc.title The laplace approximation and inference in generalized linear models with two or more random effects en_US
dc.type Thesis/Dissertation en_US
dc.degree.name Doctor of Philosophy (Ph. D.) in Statistics en_US
dc.degree.level Doctoral en_US
dc.degree.discipline Science en_US
dc.degree.grantor Oregon State University en_US
dc.description.digitization File scanned at 300 ppi (Monochrome) using ScandAll PRO 1.8.1 on a Fi-6770A in PDF format. CVista PdfCompressor 4.0 was used for pdf compression and textual OCR. en_US
dc.description.peerreview no en_us

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