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Prediction in multilevel generalized linear models
 Journal of the Royal Statistical Society. Series A (Statistics in Society
"... Summary. We discuss prediction of random effects and of expected responses in multilevel generalized linear models. Prediction of random effects is useful for instance in small area estimation and disease mapping, effectiveness studies and model diagnostics. Prediction of expected responses is usefu ..."
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Summary. We discuss prediction of random effects and of expected responses in multilevel generalized linear models. Prediction of random effects is useful for instance in small area estimation and disease mapping, effectiveness studies and model diagnostics. Prediction of expected responses is useful for planning, model interpretation and diagnostics. For prediction of random effects, we concentrate on empirical Bayes prediction and discuss three different kinds of standard errors; the posterior standard deviation and the marginal prediction error standard deviation (comparative standard errors) and the marginal sampling standard deviation (diagnostic standard error). Analytical expressions are available only for linear models and are provided in an appendix. For other multilevel generalized linear models we present approximations and suggest using parametric bootstrapping to obtain standard errors. We also discuss prediction of expectations of responses or probabilities for a new unit in a hypothetical cluster, or in a new (randomly sampled) cluster or in an existing cluster. The methods are implemented in gllamm and illustrated by applying them to survey data on reading proficiency of children nested in schools. Simulations are used to assess the performance of various predictions and associated standard errors for logistic randomintercept models under a range of conditions.
Correspondence
"... Assessing construct structural validity of epidemiological measurement tools: a sevenstep roadmap Acessando a validade de construto estrutural de ferramentas de medidas epidemiológicas: um roteiro em sete passos Acceso a la validez de un constructo estructural de herramientas de medidas epidemiológ ..."
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Assessing construct structural validity of epidemiological measurement tools: a sevenstep roadmap Acessando a validade de construto estrutural de ferramentas de medidas epidemiológicas: um roteiro em sete passos Acceso a la validez de un constructo estructural de herramientas de medidas epidemiológicas: un guión en siete pasos
ProfileLikelihood Approach for Estimating Generalized Linear Mixed Models With Factor Structures
"... In this article, the authors suggest a profilelikelihood approach for estimating complex models by maximum likelihood (ML) using standard software and minimal programming. The method works whenever setting some of the parameters of the model to known constants turns the model into a standard model ..."
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In this article, the authors suggest a profilelikelihood approach for estimating complex models by maximum likelihood (ML) using standard software and minimal programming. The method works whenever setting some of the parameters of the model to known constants turns the model into a standard model. An important class of models that can be estimated this way is generalized linear mixed models with factor structures. Such models are useful in educational research, for example, for estimation of valueadded teacher or school effects with persistence parameters and for analysis of largescale assessment data using multilevel item response models with discrimination parameters. The authors describe the profilelikelihood approach, implement it in the R software, and apply the method to longitudinal data and binary item response data. Simulation studies and comparison with gllamm show that the profilelikelihood method performs well in both types of applications. The authors also briefly discuss other types of models that can be estimated using the profilelikelihood idea.
High Dimensional Semiparametric Latent Graphical Model for Mixed Data
"... Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete variables or a combination of both continuous and discrete var ..."
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Graphical models are commonly used tools for modeling multivariate random variables. While there exist many convenient multivariate distributions such as Gaussian distribution for continuous data, mixed data with the presence of discrete variables or a combination of both continuous and discrete variables poses new challenges in statistical modeling. In this paper, we propose a semiparametric model named latent Gaussian copula model for binary and mixed data. The observed binary data are assumed to be obtained by dichotomizing a latent variable satisfying the Gaussian copula distribution or the nonparanormal distribution. The latent Gaussian model with the assumption that the latent variables are multivariate Gaussian is a special case of the proposed model. A novel rankbased approach is proposed for both latent graph estimation and latent principal component analysis. Theoretically, the proposed methods achieve the same rates of convergence for both precision matrix estimation and eigenvector estimation, as if the latent variables were observed. Under similar conditions, the consistency of graph structure recovery and feature selection for leading eigenvectors is established. The performance of the proposed methods is numerically assessed through simulation studies, and the usage of our methods is illustrated by a genetic dataset.
RESEARCH ARTICLE Open Access
"... Decomposing the heterogeneity of depression at the person, symptom, and timelevel: latent variable models versus multimode principal component analysis ..."
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Decomposing the heterogeneity of depression at the person, symptom, and timelevel: latent variable models versus multimode principal component analysis
A joint latent class model for classifying
"... severely hemorrhaging trauma patients ..."
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