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

Alternative approaches to multilevel modelling of survey noncontact and refusal

We review three alternative approaches to modelling survey noncontact and refusal: multinomial, sequential and sample selection (bivariate probit) models. We then propose a multilevel extension of the sample selection model to allow for both interviewer effects and dependency between noncontact and refusal rates at the household and interviewer level. All methods are applied and compared in an analysis of household nonresponse in the UK, using a dataset with unusually rich information on both respondents and nonrespondents from six major surveys. After controlling for household characteristics, there is little evidence of residual correlation between the unobserved characteristics affecting noncontact and refusal propensities at either the household or the interviewer level. We also find that the estimated coefficients of the multinomial and sequential models are surprisingly similar, which further investigation via a simulation study suggests is due to there being little overlap between the predictors of noncontact and refusal

Multiple Comparisons using Composite Likelihood in Clustered Data

We study the problem of multiple hypothesis testing for multidimensional data when inter-correlations are present. The problem of multiple comparisons is common in many applications. When the data is multivariate and correlated, existing multiple comparisons procedures based on maximum likelihood estimation could be prohibitively computationally intensive. We propose to construct multiple comparisons procedures based on composite likelihood statistics. We focus on data arising in three ubiquitous cases: multivariate Gaussian, probit, and quadratic exponential models. To help practitioners assess the quality of our proposed methods, we assess their empirical performance via Monte Carlo simulations. It is shown that composite likelihood based procedures maintain good control of the familywise type I error rate in the presence of intra-cluster correlation, whereas ignoring the correlation leads to erratic performance. Using data arising from a diabetic nephropathy study, we show how our composite likelihood approach makes an otherwise intractable analysis possible

Models for Paired Comparison Data: A Review with Emphasis on Dependent Data

Thurstonian and Bradley-Terry models are the most commonly applied models in the analysis of paired comparison data. Since their introduction, numerous developments have been proposed in different areas. This paper provides an updated overview of these extensions, including how to account for object- and subject-specific covariates and how to deal with ordinal paired comparison data. Special emphasis is given to models for dependent comparisons. Although these models are more realistic, their use is complicated by numerical difficulties. We therefore concentrate on implementation issues. In particular, a pairwise likelihood approach is explored for models for dependent paired comparison data, and a simulation study is carried out to compare the performance of maximum pairwise likelihood with other limited information estimation methods. The methodology is illustrated throughout using a real data set about university paired comparisons performed by students.Comment: Published in at http://dx.doi.org/10.1214/12-STS396 the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

Efficient pairwise composite likelihood estimation for spatial‐clustered data

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/108642/1/biom12199-sm-0001-SuppData.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/108642/2/biom12199.pd