51,872 research outputs found
A generalized linear mixed model for longitudinal binary data with a marginal logit link function
Longitudinal studies of a binary outcome are common in the health, social,
and behavioral sciences. In general, a feature of random effects logistic
regression models for longitudinal binary data is that the marginal functional
form, when integrated over the distribution of the random effects, is no longer
of logistic form. Recently, Wang and Louis [Biometrika 90 (2003) 765--775]
proposed a random intercept model in the clustered binary data setting where
the marginal model has a logistic form. An acknowledged limitation of their
model is that it allows only a single random effect that varies from cluster to
cluster. In this paper we propose a modification of their model to handle
longitudinal data, allowing separate, but correlated, random intercepts at each
measurement occasion. The proposed model allows for a flexible correlation
structure among the random intercepts, where the correlations can be
interpreted in terms of Kendall's . For example, the marginal
correlations among the repeated binary outcomes can decline with increasing
time separation, while the model retains the property of having matching
conditional and marginal logit link functions. Finally, the proposed method is
used to analyze data from a longitudinal study designed to monitor cardiac
abnormalities in children born to HIV-infected women.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS390 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
A review of R-packages for random-intercept probit regression in small clusters
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
Analysing the relationship between ectomycorrhizal infection and forest decline using marginal models
This statistical survey originates from the problem of discovering which relationship exists between root ectomycorrhizal infection and health status of forest plants. The sampling scheme takes observations from roots that come from sectors around the tree resulting in a hierarchical association structure of the observations. Marginal regression models are used to analyze the mean effect of the ectomycorrhizal state on a response variable proxy for the health degree of the plants
Designs for generalized linear models with random block effects via information matrix approximations
The selection of optimal designs for generalized linear mixed models is complicated by the fact that the Fisher information matrix, on which most optimality criteria depend, is computationally expensive to evaluate. Our focus is on the design of experiments for likelihood estimation of parameters in the conditional model. We provide two novel approximations that substantially reduce the computational cost of evaluating the information matrix by complete enumeration of response outcomes, or Monte Carlo approximations thereof: (i) an asymptotic approximation which is accurate when there is strong dependence between observations in the same block; (ii) an approximation via Kriging interpolators. For logistic random intercept models, we show how interpolation can be especially effective for finding pseudo-Bayesian designs that incorporate uncertainty in the values of the model parameters. The new results are used to provide the first evaluation of the efficiency, for estimating conditional models, of optimal designs from closed-form approximations to the information matrix derived from marginal models. It is found that correcting for the marginal attenuation of parameters in binary-response models yields much improved designs, typically with very high efficiencies. However, in some experiments exhibiting strong dependence, designs for marginal models may still be inefficient for conditional modelling. Our asymptotic results provide some theoretical insights into why such inefficiencies occur
Sparse Probit Linear Mixed Model
Linear Mixed Models (LMMs) are important tools in statistical genetics. When
used for feature selection, they allow to find a sparse set of genetic traits
that best predict a continuous phenotype of interest, while simultaneously
correcting for various confounding factors such as age, ethnicity and
population structure. Formulated as models for linear regression, LMMs have
been restricted to continuous phenotypes. We introduce the Sparse Probit Linear
Mixed Model (Probit-LMM), where we generalize the LMM modeling paradigm to
binary phenotypes. As a technical challenge, the model no longer possesses a
closed-form likelihood function. In this paper, we present a scalable
approximate inference algorithm that lets us fit the model to high-dimensional
data sets. We show on three real-world examples from different domains that in
the setup of binary labels, our algorithm leads to better prediction accuracies
and also selects features which show less correlation with the confounding
factors.Comment: Published version, 21 pages, 6 figure
Generalized Functional Additive Mixed Models
We propose a comprehensive framework for additive regression models for
non-Gaussian functional responses, allowing for multiple (partially) nested or
crossed functional random effects with flexible correlation structures for,
e.g., spatial, temporal, or longitudinal functional data as well as linear and
nonlinear effects of functional and scalar covariates that may vary smoothly
over the index of the functional response. Our implementation handles
functional responses from any exponential family distribution as well as many
others like Beta- or scaled non-central -distributions. Development is
motivated by and evaluated on an application to large-scale longitudinal
feeding records of pigs. Results in extensive simulation studies as well as
replications of two previously published simulation studies for generalized
functional mixed models demonstrate the good performance of our proposal. The
approach is implemented in well-documented open source software in the "pffr()"
function in R-package "refund"
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d-QPSO: A Quantum-Behaved Particle Swarm Technique for Finding D-Optimal Designs With Discrete and Continuous Factors and a Binary Response
Identifying optimal designs for generalized linear models with a binary response can be a challengingtask, especially when there are both discrete and continuous independent factors in the model. Theoreticalresults rarely exist for such models, and for the handful that do, they usually come with restrictive assumptions.In this article, we propose the d-QPSO algorithm, a modified version of quantum-behaved particleswarm optimization, to find a variety of D-optimal approximate and exact designs for experiments withdiscrete and continuous factors and a binary response. We show that the d-QPSO algorithm can efficientlyfind locally D-optimal designs even for experiments with a large number of factors and robust pseudo-Bayesian designs when nominal values for the model parameters are not available. Additionally, we investigaterobustness properties of the d-QPSO algorithm-generated designs to variousmodel assumptions andprovide real applications to design a bio-plastics odor removal experiment, an electronic static experiment,and a 10-factor car refueling experiment. Supplementary materials for the article are available online
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