### Yale University

Department of Statistics

Seminar

#### Monday, November 27, 1995

Scott L. Zeger, Ph.D.,

Johns Hopkins University

#### Marginal Regression Models for Ordered Categorical Item Responses

Seminar to be held in Room 309, LEPH 60 College, at 4:15 pm

In an investigation of the natural history of disease and disability among
elderly women, we attempt to assess physical and mental functioning through a
relatively large number of questions and performance-based measures. While the
response, {\it physical function} is easily conceived of, it can only be
measured in terms of high dimensional observation.
There are at least three distinct strategies for regression analysis with
high-dimensional responses. In the first, we derive summary variables and
characterize their change as a function of covariates using standard
regression methods. In the second, we posit the existence of underlying,
unobservable {\it function variables} that satisfy a regression model. Our
observed items are assumed to be imperfect measures of subsets of these latent
variables. In the third approach, the focus of this paper, we simultaneously
regress each of the many responses on explanatory variables while also modeling
the interdependence amony the multivariate responses. The regression
coefficients are then summarized to indicate the overall relationship with
covariates. This third approach allows us to identify items whose relationship
deviates from the majority with respect to dependence on covariates.
This paper will present the third approach which we refer to as {\it marginal
modelling} (Dale, 1986). We simultaneously specify two sets of regression
models:
(i) for the mean response of each ordinal item response on; and (ii) for
each pair-wise
association. We first consider maximum likelihood estimation but because it is
computationally impractical except in very small problems, an estimating
equation
alternative is proposed. The methods will be illustrated with analysis of
high-dimensional cross-sectional data from the first round of the Johns Hopkins
University-NIH Women's Health and Aging Study (WHAS).