Testing conditional independence in sets of I × J tables by means of moment and correlation score tests with application to HPV vaccine

A new testing approach is described for improving statistical tests of independence in sets of tables stratified on one or more relevant factors in case of categorical (nominal or ordinal) variables. Common tests of independence that exploit the ordinality of one of the variables use a restricted-alternative approach. A different, relaxed-null method is presented. Specifically, the M-moment score tests and the correlation tests are introduced. Using multinomial-Poisson homogeneous modeling theory, it is shown that these tests are computationally and conceptually simple, and simulation results suggest that they can perform better than other common tests of conditional independence. To illustrate, the proposed tests are used to better understand the human papillomavirus type-specific infection by exploring the intention to vaccinate. Copyright © 2016 John Wiley & Sons, Ltd.

A class of mixture models for multidimensional ordinal data

In rating surveys, people are requested to express preferences on several aspects related to a topic by selecting a category in an ordered scale. For such data, we propose a model defined by a mixture of a uniform distribution and a Sarmanov distribution with CUB (combination of uniform and shifted binomial) marginal distributions ( D'Elia and Piccolo, 2005 ). This mixture generalizes the CUB model to the multivariate case by taking into account the association among answers of the same individual to the items of a questionnaire. It also allows us to distinguish two kinds of uncertainty: specific uncertainty, related to the indecision for single items, and global uncertainty referred to the respondent's hesitancy in completing the whole questionnaire. A simulation and a real case study highlight the usefulness of the new methodology.