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).