Department of Statistical Science
Duke University
presents:
Gianfranco Lovison
Instituto di Statistica Universita di Palermo - Italy
"Quasi-Symmetry Models for Hypercubic Concordance Tables"
Abstract: Suppose the same categorical variable $V$, with categories $j=1,\ldots,m$, is observed on 'component' $t=1,2,\ldots,c$ for each of $n$ 'units'. The joint frequencies $n_{j_1,\ldots,j_t,\ldots,j_c}$ of 'units' taking category $j_t$ on the $t$-th component, $t=1,\ldots,c$ can then be arranged in a {\em hypercubic concordance table} ({\em h.c.t.}) of dimension $m^c$. This kind of data naturally arises in a number of different areas such as: \begin{itemize} \item {\bf longitudinal studies}, where the 'units' are individuals and the 'components' are occasions in time; \item {\bf matched retrospective and prospective epidemiological studies}, where the 'units' are matched sets of cases and controls and the 'components' are the members of such matched sets; \item {\bf psychometric testing studies}, where the 'units' are subjects taking the test and the 'components' are items forming the test; \item {\bf agreement studies}, where the 'units' are objects rated on a categorical scale and the 'components' are the raters. \end{itemize}
In spite of the substantial diversity of the mechanisms that can generate them, data arranged in a {\em h.c.t.}, owing to their common representation, can be analyzed via the same models. Beside the usual hierarchical factorial models used for general contingency tables, models of {\em marginal homogeneity}, {\em symmetry} and {\em quasi-symmetry}, which exploit the special structure of the {\em h.c.t.}, are of particular interest. Among them, the {\em quasi-symmetry} model plays a central role, since it represents an interesting and flexible intermediate model between the saturated and the complete independence model and it comprises the {\em marginal homogeneity} and {\em symmetry} models as special cases.
The aim of the talk is to clarify the common structure which leads to the {\em quasi-symmetry} model and its different substantive interpretations in different areas of application. Moreover, since most attention has been given in the literature to the case c=2, i.e. square concordance tables, some potentially interesting extensions to more than two dimensions will be presented, with the help of real examples with c=3, i.e. cubic concordance tables, taken from sociological, psychometric, epidemiological and medical research.
Wednesday, August 30, 1995
11:45 - 12:45
116 Old Chemistry Building Any questions concerning the seminar may be addressed to Cheryl McGhee @ (919) 684-8029, e-mail cheryl@stat.duke.edu, or finger seminar@stat.duke.edu.