Random-Effects Models for Serial Observations with Binary Response

Stiratelli, Robert G.; Laird, Nan M.; Ware, James H.

doi:10.2307/2531147

Cited by 667 publications

(325 citation statements)

References 19 publications

Supporting

Mentioning

315

Contrasting

Unclassified

Order By: Relevance

“…In our context, and for fixed values of the variance components, estimation of the model's fixed and random effects presents no problem. These can be obtained using Penalized Quasi-likelihood (PQL) methods (Stiratelli et al 1984, Schall 1991, Breslow and Clayton 1993. PQL is a very simple method for estimation of GLMMs, and can be easily implemented by iterative fitting a working linear mixed model to a working dependent variable z, on the basis of a Fisher scoring algorithm which involves a weight matrix W that is updated at each iteration (we describe this point in detail in Appendix A).…”

Section: Mixed Model Representationmentioning

confidence: 99%

Fast smoothing parameter separation in multidimensional generalized P-splines: the SAP algorithm

et al. 2014

View full text Add to dashboard Cite

Abstract:A new computational algorithm for estimating the smoothing parameters of a multidimensional penalized spline generalized model with anisotropic penalty is presented. This new proposal is based on the mixed model representation of a multidimensional P-spline, in which the smoothing parameter for each covariate is expressed in terms of variance components. On the basis of penalized quasi-likelihood methods (PQL), closed-form expressions for the estimates of the variance components are obtained. This formulation leads to an efficient implementation that can considerably reduce the computational load. The proposed algorithm can be seen as a generalization of the algorithm by Schall (1991) -for variance components estimation -to deal with non-standard structures of the covariance matrix of the random effects. The practical performance of the proposed computational algorithm is evaluated by means of simulations, and comparisons with alternative methods are made on the basis of the mean square error criterion and the computing time. Finally, we illustrate our proposal with the analysis of two real datasets: a two dimensional example of historical records of monthly precipitation data in USA and a three dimensional one of mortality data from respiratory disease according to the age at death, the year of death and the month of death.Keywords: Smoothing; P-splines; Tensor product; Anisotropic penalty; Mixed Models. July 29, 2013Abstract A new computational algorithm for estimating the smoothing parameters of a multidimensional penalized spline generalized model with anisotropic penalty is presented. This new proposal is based on the mixed model representation of a multidimensional P-spline, in which the smoothing parameter for each covariate is expressed in terms of variance components. On the basis of penalized quasi-likelihood methods (PQL), closed-form expressions for the estimates of the variance components are obtained. This formulation leads to an efficient implementation that can considerably reduce the computational load. The proposed algorithm can be seen as a generalization of the algorithm by Schall (1991) -for variance components estimation -to deal with non-standard structures of the covariance matrix of the random effects. The practical performance of the proposed computational algorithm is evaluated by means of simulations, and comparisons with alternative methods are made on the basis of the mean square error criterion and the computing time. Finally, we illustrate our proposal with the analysis of two real datasets: a two dimensional example of historical records of monthly precipitation data in USA and a three dimensional one of mortality data from respiratory disease according to the age at death, the year of death and the month of death.1

show abstract

Section: Mixed Model Representationmentioning

confidence: 99%

Fast smoothing parameter separation in multidimensional generalized P-splines: the SAP algorithm

et al. 2014

View full text Add to dashboard Cite

show abstract

“…In linear models, this problem is addressed by using restricted maximum likelihood (REML) estimation (Patterson and Thompson, 1971). Unfortunately, the REML concept cannot be directly applied to generalized linear mixed models, although there are some ad-hoc approaches (Schall, 1991;Breslow and Clayton, 1993;McGilchrist, 1994;Stiratelli et al, 1984;Noh and Lee, 2007). The assumption that downward bias is due to the small number of clusters was confirmed by eliminating the person random effect, simulating data for 10 and 100 items (with J = 100 and ψ 2 = 3.290) and finding that there is a significant downward bias for the item variance with 10 items but not with 100 items, estimated, respectively, as −0.25 (SE = 0.05) and −0.01 (SE = 0.02) using 1000 replications.…”

Section: Tablementioning

confidence: 99%

Alternating imputation posterior estimation of models with crossed random effects

Cho

Rabe‐Hesketh

2011

Computational Statistics & Data Analysis

View full text Add to dashboard Cite

a b s t r a c tGeneralized linear mixed models or latent variable models for categorical data are difficult to estimate if the random effects or latent variables vary at non-nested levels, such as persons and test items. Clayton and Rasbash (1999) suggested an Alternating Imputation Posterior (AIP) algorithm for approximate maximum likelihood estimation. For item response models with random item effects, the algorithm iterates between an item wing in which the item mean and variance are estimated for given person effects and a person wing in which the person mean and variance are estimated for given item effects. The person effects used for the item wing are sampled from the conditional posterior distribution estimated in the person wing and vice versa. Clayton and Rasbash (1999) used marginal quasi-likelihood (MQL) and penalized quasi-likelihood (PQL) estimation within the AIP algorithm, but this method has been shown to produce biased estimates in many situations, so we use maximum likelihood estimation with adaptive quadrature. We apply the proposed algorithm to the famous salamander mating data, comparing the estimates with many other methods, and to an educational testing dataset. We also present a simulation study to assess performance of the AIP algorithm and the Laplace approximation with different numbers of items and persons and a range of item and person variances.

show abstract

“…The Penalized Quasi-Likelihood method (PQL) [11,33,34] also approximates the integrand; more intuitively put, PQL approximates the GLMM with a linear mixed model. This is achieved by considering a Taylor expansion of the response function and by subsequently rewriting this expression in terms of an adjusted dependent variable on which estimation procedures for LMM can be implemented.…”

Section: Estimation Through Likelihood-based Approximation Methodsmentioning

confidence: 99%

A Review of R-packages for Random-Intercept Probit Regression in Small Clusters

Josephy

Loeys

Rosseel

2016

Front. Appl. Math. Stat.

View full text Add to dashboard Cite

Generalized Linear Mixed Models (GLMMs) are widely used to model clustered categorical outcomes. To tackle the intractable integration over the random effects distributions, several approximation approaches have been developed for likelihood-based inference. As these seldom yield satisfactory results when analyzing binary outcomes from small clusters, estimation within the Structural Equation Modeling (SEM) framework is proposed as an alternative. We compare the performance of R-packages for random-intercept probit regression relying on: the Laplace approximation, adaptive Gaussian quadrature (AGQ), Penalized Quasi-Likelihood (PQL), an MCMC-implementation, and integrated nested Laplace approximation within the GLMM-framework, and a robust diagonally weighted least squares estimation within the SEM-framework. In terms of bias for the fixed and random effect estimators, SEM usually performs best for cluster size two, while AGQ prevails in terms of precision (mainly because of SEM's robust standard errors). As the cluster size increases, however, AGQ becomes the best choice for both bias and precision.

show abstract

Random-Effects Models for Serial Observations with Binary Response

Cited by 667 publications

References 19 publications

Fast smoothing parameter separation in multidimensional generalized P-splines: the SAP algorithm

Fast smoothing parameter separation in multidimensional generalized P-splines: the SAP algorithm

Alternating imputation posterior estimation of models with crossed random effects

A Review of R-packages for Random-Intercept Probit Regression in Small Clusters

Contact Info

Product

Resources

About