On Rao score and PearsonX 2 statistics in generalized linear models

The identity of the Rao score and PearsonX ² statistics is well known in the areas where the latter was first introduced: goodness-of-fit in contingency tables and binary responses. We show in this paper that the same identity holds when the two statistics are used for testing goodness-of-fit of Generalized Linear Models. We also highlight the connections that exist between the two statistics when they are used for the comparison of nested models. Finally, we discuss some merits of these unifying results. Work financially supported by cofin. MIUR grants 2000 and 2002.     

Log-linear modelling of data from matched case-control studies

A log-linear modelling approach is proposed for dealing with polytomous, unordered exposure variables in case-control epidemiological studies with matched pairs. Hypotheses concerning epidemiological parameters are shown to be expressable in terms of log-linear models for the expected frequencies of the case-by-control square concordance table representation of the matched data; relevant maximum likelihood estimates and goodness-of-fit statistics are presented. Possible extensions to account for ordered categorical risk factors and multiple controls are illustrated, and comparisons with previous work are discussed. Finally, the possibility of implementing the proposed method with GLIM is illustrated within the context of a data set already analyzed by other authors.     

Subject-specific odds ratios in binomial GLMMs with continuous response

In a regression context, the dichotomization of a continuous outcome variable is often motivated by the need to express results in terms of the odds ratio, as a measure of association between the response and one or more risk factors. Starting from the recent work of Moser and Coombs (Stat Med 23:1843–1860, 2004) in this article we explore in a mixed model framework the possibility of obtaining odds ratio estimates from a regression linear model without the need of dichotomizing the response variable. It is shown that the odds ratio estimators derived from a linear mixed model outperform those from a binomial generalized linear mixed model, especially when the data exhibit high levels of heterogeneity.     

Networks as mediating variables: a Bayesian latent space approach

Statistical Methods & Applications - The use of network analysis to investigate social structures has recently seen a rise due to the high availability of data and the numerous insights it can...