Bayesian density regression for discrete outcomes

We develop Bayesian models for density regression with emphasis on discrete outcomes. The problem of density regression is approached by considering methods for multivariate density estimation of mixed scale variables, and obtaining conditional densities from the multivariate ones. The approach to multivariate mixed scale outcome density estimation that we describe represents discrete variables, either responses or covariates, as discretised versions of continuous latent variables. We present and compare several models for obtaining these thresholds in the challenging context of count data analysis where the response may be over‐ and/or under‐dispersed in some of the regions of the covariate space. We utilise a nonparametric mixture of multivariate Gaussians to model the directly observed and the latent continuous variables. The paper presents a Markov chain Monte Carlo algorithm for posterior sampling, sufficient conditions for weak consistency, and illustrations on density, mean and quantile regression utilising simulated and real datasets.     

Bivariate short distributions

The method of MML estimation for a univariate normal (Tiku 1967, 1973) is extended to a bivariate normal population. Thus, a theoretical foundation is given to the robust correlation coefficient proposed by Tiku and Balakrishnan (1986).     

Multivariate mixtures of normals with unknown number of components

We present full Bayesian analysis of finite mixtures of multivariate normals with unknown number of components. We adopt reversible jump Markov chain Monte Carlo and we construct, in a manner similar to that of Richardson and Green (1997), split and merge moves that produce good mixing of the Markov chains. The split moves are constructed on the space of eigenvectors and eigenvalues of the current covariance matrix so that the proposed covariance matrices are positive definite. Our proposed methodology has applications in classification and discrimination as well as heterogeneity modelling. We test our algorithm with real and simulated data.     

Restricted maximum likelihood estimation of joint mean‐covariance models

The class of joint mean‐covariance models uses the modified Cholesky decomposition of the within subject covariance matrix in order to arrive to an unconstrained, statistically meaningful reparameterisation. The new parameterisation of the covariance matrix has two sets of parameters that separately describe the variances and correlations. Thus, with the mean or regression parameters, these models have three sets of distinct parameters. In order to alleviate the problem of inefficient estimation and downward bias in the variance estimates, inherent in the maximum likelihood estimation procedure, the usual REML estimation procedure adjusts for the degrees of freedom lost due to the estimation of the mean parameters. Because of the parameterisation of the joint mean covariance models, it is possible to adapt the usual REML procedure in order to estimate the variance (correlation) parameters by taking into account the degrees of freedom lost by the estimation of both the mean and correlation (variance) parameters. To this end, here we propose adjustments to the estimation procedures based on the modified and adjusted profile likelihoods. The methods are illustrated by an application to a real data set and simulation studies. The Canadian Journal of Statistics 40: 225–242; 2012 © 2012 Statistical Society of Canada     

Multiobjective optimisation of production,distribution and capacity planning of global supply chains in the process industry

The performance of a supply chain should usually be measured by multiple criteria. We address production, distribution and capacity planning of global supply chains considering cost, responsiveness and customer service level simultaneously. A multiobjective mixed-integer linear programming (MILP) approach is developed with total cost, total flow time and total lost sales as key objectives. Also, two strategies to expand the formulation plants’ capacities are considered in the model. The ε-constraint method and lexicographic minimax method are used as solution approaches to tackle the multiobjective problem. Finally, a numerical example is investigated to demonstrate the applicability of the proposed model and solution approaches.     

Characterization of hypergeometric type distributions by regression

The conditional distribution of Y given X is proved to be of the positive or the negative hypergeometric law when X follows a positive or a negative hypergeometric distribution, respectively and the regression function of X on Y is of a known linear form     

CHARACTERIZATIONS OF MULTINOMIAL AND NEGATIVE MULTINOMIAL MIXTURES BY REGRESSION

Characterizations are given for mixtures of multinomial and negative multinomial distributions with respect to their index parameter. Several well known multivariate discrete distributions are used as illustrative examples.     

Estimation of small area event rates and of the associated standard errors

We develop empirical best estimators for small area event rates based on the hierarchical Poisson model with log-normal mixing distribution, when the basic data consists of area level measurements. We derive an approximate expression to the mean squared error of the estimators and we provide a method for estimating this expression.     

What’s in a Topic? Exploring the Interaction Between Test-taker Age and Item Content in High-Stakes Testing

The research reported in this article investigates differential item functioning (DIF) in a listening comprehension test. The study explores the relationship between test-taker age and the items’ language domains across multiple test forms. The data comprise test-taker responses (N = 2861) to a total of 133 unique items, 46 items of which were shared across two or more forms. Twenty-one items demonstrated DIF. However, there was no pattern by language domain. Eleven items showing DIF appeared in more than one test form but DIF for these items occurred only once.