Bayesian reconstruction of contingency tables with partially categorized data

This paper suggests a Bayesian approach to the reconstruction of a 2 × 2 contingency table where some of the observations are only partially categorized and others are fully categorized. In contrast, most previous Bayesian and non-Bayesian analyses of the partially categorized data problem have been concerned with estimation of the parameters that generated the data. We show in an example that estimates may not be extremely sensitive to the weight placed on prior information relative to the sample data.     

Book Reviews

The diagnostic tools examined in this article are applicable to regressions estimated with panel data or cross-sectional data drawn from a population with grouped structure. The diagnostic tools considered include (a) tests for the existence of group effects under both fixed and random effects models, (b) checks for outlying groups, and (c) specification tests for comparing the fixed and random effects models. A group-specific counterpart to the studentized residual is introduced. The methods are illustrated using a hedonic housing price regression.     

Parsimonious Estimation of the Covariance Matrix in Multinomial Probit Models

This article presents a Bayesian analysis of a multinomial probit model by building on previous work that specified priors on identified parameters. The main contribution of our article is to propose a prior on the covariance matrix of the latent utilities that permits elements of the inverse of the covariance matrix to be identically zero. This allows a parsimonious representation of the covariance matrix when such parsimony exists. The methodology is applied to both simulated and real data, and its ability to obtain more efficient estimators of the covariance matrix and regression coefficients is assessed using simulated data.     

The Ranges of Limiting Values of Some Partial Correlations under Conditional Independence

Pearson's partial correlation, Kendall's partial tau, and a partial correlation based on Spearman's rho need not be consistent estimators of zero under conditional independence. The ranges of possible limiting values of these correlations are computed under multivariate normality and lognormality. Students should exercise caution when interpreting these partial correlations as a measure of conditional independence.     

Design-based random permutation models with auxiliary information

We extend the random permutation model to obtain the best linear unbiased estimator of a finite population mean accounting for auxiliary variables under simple random sampling without replacement (SRS) or stratified SRS. The proposed method provides a systematic design-based justification for well-known results involving common estimators derived under minimal assumptions that do not require specification of a functional relationship between the response and the auxiliary variables.