Dr. Guido Consonni

Department of Economics and Quantitative Methods

University of Pavia (Italy)

Title: " Tests based on intrinsic priors for the equality of two correlated proportions "

Abstract:
Correlated proportions arise in longitudinal (panel) studies. A typical example
is the "opinion swing'' problem: "Has the proportion of people favoring a
politician changed after his recent speech to the nation on TV?''.

Since the same group of individuals is interviewed before and after the speech,
the two proportions are correlated. A natural null hypothesis to be tested is
whether the corresponding population proportions are equal.

A standard Bayesian approach to this problem has already been considered in the
literature, based on a Dirichlet prior for the cell-probabilities of the
underlying two-by-two table under the alternative hypothesis, together with an
induced prior under the null.

In lack of specific prior information, a diffuse (e.g. uniform) distribution may
be used. We claim that this approach is not satisfactory, since in a testing
problem one should make sure that the prior under the alternative be adequately
centered around the region specified by the null, in order to obtain a fairer
comparison between the two hypotheses, especially when the data are in reasonable
agreement with the null.

Following an intrinsic prior methodology, we develop two strategies for the
construction of a collection of objective priors increasingly peaked around the null.
We provide a simple interpretation of their structure in terms of weighted imaginary
sample scenarios. We illustrate our method by means of three examples, carrying out
sensitivity analysis and providing comparison with existing results.

(This is joint work with Luca La Rocca, University of Modena and Reggio Emilia, Italy)