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A scalable and efficient covariate selection criterion for mixed effects regression models with unknown random effects structure

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2018年 117卷 154-161页

作者： Craiu, Radu V. Duchesne, Thierry Univ Toronto Dept Stat Sci Toronto ON M5S 3G3 Canada Univ Laval Dept Math & Stat Quebec City PQ G1V 0A6 Canada

A new model selection criterion for mixed effects regression models is introduced. The criterion is computable even when the model is fitted with a two-step method or when the structure and the distribution of the random effects are unknown. The criterion is especially useful in the early stage of the model building process when one needs to decide which covariates should be included in a mixed effects regression model, but has no knowledge of the random effect structure. This is particularly relevant in substantive fields where variable selection is guided by information criteria rather than regularization. The calculation of the criterion requires only the evaluation of cluster-level log-likelihoods and does not rely on heavy numerical integration. Theoretical and numerical arguments are used to justify the method and its usefulness is illustrated by analysing data from a youth behaviour study. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Akaike information criterion generalized linear mixed model h-likelihood Random coefficient model Two-stage estimation Variable selection

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Parameterization of multivariate random effects models for categorical data

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BIOMETRICS 2001年第4期57卷 1256-1263页

作者： Rabe-Hesketh, S Skrondal, A Inst Psychiat Dept Biostat & Comp London SE5 8AF England Natl Inst Publ Hlth Dept Epidemiol N-0403 Oslo Norway

Alternative parameterizations and problems of identification and estimation of multivariate random effects models fur categorical responses are investigated. The issues are illustrated in the context of the multivariate binomial logit-normal (BLN) model introduced by Coull and Agresti (2000, Biometrics 56, 73-80). We demonstrate that the BLN model is poorly identified unless proper restrictions are imposed on the parameters. Moreover, estimation of BLN models is unduly computationally complex. In the first application considered by Coull and Agresti, an identification problem results in highly unstable, highly correlated parameter estimates and large standard errors. A probit-normal version of the specified BLN model is demonstrated to be underidentified, whereas the BLN model is empirically underidentified. Identification can be achieved by constraining one of the parameters. We show that a one-factor probit model is equivalent to the probit version of the specified BLN model and that a one-factor logit model is empirically equivalent to the BLN model. Estimation is greatly simplified by using a factor model.

关键词： equivalence factor model generalized linear mixed model identification multivariate binomial logit-normal model numerical integration

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From mixed effects modeling to spike and slab variable selection: A Bayesian regression model for group testing data

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BIOMETRICS 2020年第3期76卷 913-923页

作者： Joyner, Chase N. McMahan, Christopher S. Tebbs, Joshua M. Bilder, Christopher R. Clemson Univ Sch Math & Stat Sci Clemson SC 29634 USA Univ South Carolina Dept Stat Columbia SC 29208 USA Univ Nebraska Dept Stat Lincoln NE USA

Due to reductions in both time and cost, group testing is a popular alternative to individual-level testing for disease screening. These reductions are obtained by testing pooled biospecimens (eg, blood, urine, swabs, etc.) for the presence of an infectious agent. However, these reductions come at the expense of data complexity, making the task of conducting disease surveillance more tenuous when compared to using individual-level data. This is because an individual's disease status may be obscured by a group testing protocol and the effect of imperfect testing. Furthermore, unlike individual-level testing, a given participant could be involved in multiple testing outcomes and/or may never be tested individually. To circumvent these complexities and to incorporate all available information, we propose a Bayesian generalized linear mixed model that accommodates data arising from any group testing protocol, estimates unknown assay accuracy probabilities and accounts for potential heterogeneity in the covariate effects across population subgroups (eg, clinic sites, etc.);this latter feature is of key interest to practitioners tasked with conducting disease surveillance. To achieve model selection, our proposal uses spike and slab priors for both fixed and random effects. The methodology is illustrated through numerical studies and is applied to chlamydia surveillance data collected in Iowa.

关键词： binary regression generalized linear mixed model latent variable modeling pooled testing random effects spike and slab prior

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Multiple Determinants of Anuran Richness and Occurrence in an Agricultural Region in South-Eastern Brazil

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ENVIRONMENTAL MANAGEMENT 2014年第4期53卷 823-837页

作者： Prado, Vitor H. M. Rossa-Feres, Denise de C. Univ Estadual Paulista UNESP Inst Biociencias Letras & Ciencias Exatas IBILCE BR-15054000 Sao Paulo Brazil Univ Estadual Paulista UNESP Inst Biociencias Letras & Ciencias Exatas IBILCE Dept Zool & Bot BR-15054000 Sao Paulo Brazil

In agricultural landscapes, studies that identify factors driving species richness and occupancy are important because they can guide farmers to use conservation practices that minimize species loss. In this context, anurans are threatened by habitat loss because they depend on the characteristics of both local water bodies and adjacent landscapes. We used a model selection approach to evaluate the influence of local and landscape variables in determining anuran species richness and occurrence in 40 freshwater bodies in a heavily deforested region of semideciduous Atlantic Forest in southeastern Brazil. Our aim was to develop recommendations for conservation of anuran communities in rural areas. Pond hydroperiod and area were the most important variables for explaining anuran species richness and occupancy, with greatest species richness being found in water bodies with intermediate hydroperiod and area. Other important variables that reflected individual species occupancies were the number of vegetation types and pond isolation. In addition, recent studies evidenced that water bodies near forest fragments have higher anuran abundance or diversity. In conclusion, we suggest the maintenance of semi-permanent ponds, isolated from large rivers or reservoirs and near forest fragments, as an effective strategy to conserve anuran fauna in agricultural landscapes of southeastern Brazil. Brazilian government requires the maintenance of forests as legal reserve in each farm, and farmers need to maintain ponds as drinking water for cattle or crop irrigation. For this reason, the guidelines suggested in the present study can be easily adopted, without additional costs to rural productivity.

关键词： Amphibian generalized linear mixed model Community ecology Landscape Wildlife management Environmental quality

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Alternating imputation posterior estimation of models with crossed random effects

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COMPUTATIONAL STATISTICS & DATA ANALYSIS 2011年第1期55卷 12-25页

作者： Cho, S. -J. Rabe-Hesketh, S. Vanderbilt Univ Peabody Coll Nashville TN 37203 USA Univ Calif Berkeley Grad Sch Educ Berkeley CA 94720 USA Univ London Inst Educ London WC1E 7HU England

generalized 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. (C) 2010 Elsevier B.V. All rights reserved.

关键词： Adaptive quadrature Crossed random effects generalized linear mixed model Item response theory Laplace approximation Random cross-classification Salamander mating data Two-way error components

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Measuring intrarater association between correlated ordinal ratings

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BIOMETRICAL JOURNAL 2020年第7期62卷 1687-1701页

作者： Nelson, Kerrie P. Zhou, Thomas J. Edwards, Don Boston Univ Dept Biostat 801 Massachusetts Ave Boston MA 02118 USA Univ South Carolina Dept Stat Columbia SC 29208 USA

Variability between raters' ordinal scores is commonly observed in imaging tests, leading to uncertainty in the diagnostic process. In breast cancer screening, a radiologist visually interprets mammograms and MRIs, while skin diseases, Alzheimer's disease, and psychiatric conditions are graded based on clinical judgment. Consequently, studies are often conducted in clinical settings to investigate whether a new training tool can improve the interpretive performance of raters. In such studies, a large group of experts each classify a set of patients' test results on two separate occasions, before and after some form of training with the goal of assessing the impact of training on experts' paired ratings. However, due to the correlated nature of the ordinal ratings, few statistical approaches are available to measure association between raters' paired scores. Existing measures are restricted to assessing association at just one time point for a single screening test. We propose here a novel paired kappa to provide a summary measure of association between many raters' paired ordinal assessments of patients' test results before versus after rater training. Intrarater association also provides valuable insight into the consistency of ratings when raters view a patient's test results on two occasions with no intervention undertaken between viewings. In contrast to existing correlated measures, the proposed kappa is a measure that provides an overall evaluation of the association among multiple raters' scores from two time points and is robust to the underlying disease prevalence. We implement our proposed approach in two recent breast-imaging studies and conduct extensive simulation studies to evaluate properties and performance of our summary measure of association.

关键词： association generalized linear mixed model model-based kappa ordinal classifications screening test

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Bayesian modeling of retrospective time-to-pregnancy data with digit preference bias

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MATHEMATICAL AND COMPUTER modelLING 2006年第11-12期43卷 1424-1433页

作者： Price, Karen L. Seaman, John W. Baylor Univ Inst Stat Dept Stat Sci Waco TX 76798 USA Eli Lilly & Co Indianapolis IN 46285 USA

The study of factors affecting human fertility is an important problem affording interesting statistical and computational challenges. Analyses of human fertility rates must cope with extra variability in fecundability parameters as well as a host of covariates ranging from the obvious, such as coital frequency, to the subtle, like the smoking habits of the female's mother. In retrospective human fecundity studies, researchers ask couples the time required to conceive. This time-to-pregnancy data often exhibits digit preference bias, among other problems. We introduce computationally intensive models with sufficient flexibility to represent such bias and other causes yielding a similar lack of monotonicity in conception probabilities. (c) 2006 Elsevier Ltd. All rights reserved.

关键词： iterative simulation methods Markov chain Monte Carlo slice sampling generalized linear mixed model hierarchical centering

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Confronting uncertainty in model-based geostatistics using Markov Chain Monte Carlo simulation

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GEODERMA 2011年第3-4期163卷 150-162页

作者： Minasny, Budiman Vrugt, Jasper A. McBratney, Alex B. Univ Sydney Fac Agr Food & Nat Resources Sydney NSW 2006 Australia Univ Calif Irvine Dept Civil & Environm Engn Irvine CA 92697 USA Univ Amsterdam IBED NL-1018 WV Amsterdam Netherlands Los Alamos Natl Lab Div Earth & Environm Sci Los Alamos NM 87545 USA

This paper demonstrates for the first time the use of Markov Chain Monte Carlo (MCMC) simulation for parameter inference in model-based soil geostatistics. We implemented the recently developed DiffeRential Evolution Adaptive Metropolis (DREAM) algorithm to jointly summarize the posterior distribution of variogram parameters and the coefficients of a linear spatial model, and derive estimates of predictive uncertainty. The DREAM method runs multiple different Markov chains in parallel and jumps in each chain are generated from a discrete proposal distribution containing a fixed multiple of the difference of the states of randomly chosen pairs of other chains. This approach automatically scales the orientation and scale of the proposal distribution, and is especially designed to maintain detailed balance and ergodicity, thereby generating an exact approximation of the posterior probability density function (pdf) of the parameters of the linear model and variogram. This approach is tested using three different data sets from Australia involving variogram estimation of soil thickness, kriging of soil pH, and spatial prediction of soil organic carbon content. The results showed some advantages of MCMC over the conventional method of moments and residual maximum likelihood (REML) estimation. The posterior pdf derived with MCMC conveys important information about parameter uncertainty, multi-dimensional parameter correlation, and thus how many significant parameters are warranted by the calibration data. Parameter uncertainty constitutes only a small part of total prediction uncertainty for the case studies considered here. The prediction accuracies using MCMC and REML are similar. The variogram estimated using conventional approaches (method of moments, and without simulation) lies within the 95% prediction uncertainty interval of the posterior distribution derived with DREAM. Altogether our results show that conventional kriging and regression-kriging still remain a via

关键词： generalized linear mixed model Bayesian inference Bayesian kriging Regression-kriging Best linear unbiased predictor Pedometrics

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The use of mixed logit models to reflect heterogeneity in capture-recapture studies

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BIOMETRICS 1999年第1期55卷 294-301页

作者： Coull, BA Agresti, A Harvard Univ Sch Publ Hlth Dept Biostat Boston MA 02115 USA Univ Florida Dept Stat Gainesville FL 32611 USA

We examine issues in estimating population size N with capture-recapture models when there is variable catchability among subjects. We focus on a logistic-normal mixed model, for which the logit of the probability of capture is an additive function of a random subject and a fixed sampling occasion parameter. When the probability of capture is small or the degree of heterogeneity is large,the log-Likelihood surface is relatively flat and it is difficult;to obtain much information about N. We also discuss a latent class model and a log-linear model that account for heterogeneity and show that the log-linear model has greater scope. models assuming homogeneity provide much narrower intervals for N but are usually highly overly optimistic, the: actual coverage probability being much lower than the nominal level.

关键词： generalized linear mixed model latent class model log-linear model profile likelihood quasi symmetry Rasch model

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Group sequential methods for an ordinal logistic random-effects model under misspecification

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BIOMETRICS 2002年第3期58卷 569-575页

作者： Spiessens, B Lesaffre, E Verbeke, G Kim, KM Catholic Univ Louvain Ctr Biostat B-3000 Louvain Belgium Univ Wisconsin Dept Biostat & Med Informat Madison WI 53792 USA

Interim analyses in clinical trials are planned for ethical as well as economic reasons. General results have been published in the literature that allow the use of standard group sequential methodology if one uses an efficient test statistic, e.g., when Wald-type statistics are used in random-effects models for ordinal longitudinal data. These models often assume that the random effects are normally distributed. However;this is not always the case. We will show that, when the random-effects distribution is misspecified in ordinal regression models;the joint distribution of the test statistics over the different interim analyses is still a multivariate normal distribution, but a sandwich-type correction to the covariance matrix is needed in order to obtain the correct covariance matrix. The independent increment structure is also investigated. A bias in estimation will occur due to the misspecification. However, we will also show that the treatment effect estimate will be unbiased under the null hypothesis, thus maintaining the type I error. Extensive simulations based on a toenail dermatophyte onychomycosis trial are used to illustrate our results.

关键词： clinical trials generalized linear mixed model interim analyses ordinal data repeated measurements

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