SMABS 2004 Jena University
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European Association of Methodology

Department of methodology and evaluation research

Jena University

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Contributions: Abstract

Marginal regression models for incomplete ordinal response variables

Nicola Falocci
University of Perugia

We outline a likelihood-based regression model appropriate foranalyzing incomplete multivariate categorical responses. When thenon-response mechanism is non ignorable, valid inferencescan only be obtained by incorporating a model for the missing data.

Log-linear models are usually used in this cases, considering anaugmented 2q-dimensional table with q response variables andq missing indicators. Since one is most often interested inmodelling marginal distributions of low order, we alternativelyfocus in a marginal model of the form h = Clog( Mp ), where marginaldistributions of both response and missing data indicators arerelated to a set of discrete covariates. In particular, we referto the multivariate logistic transform of Glonek & McCullagh(1995).

We consider two extensions to the classical formulation ofthe link function particularly relevant for ordinal responsevariables. In addition to local and global logits, continuation orreverse continuation logits could also be appropriate for certainvariables, so that four different types of logit can be used tomodel univariate marginal distributions.

The second extension allows models to be defined also by inequality constraints, arising especially in testing stochastic orderings, positive association between pairs of variables or when the degree of dependence increases with respect to a set of covariates. The problem of boundary solutions in non-ignorable models is well known in literature. Models with inequality constraints on the missing-data mechanism are also useful in avoiding this problem.

The likelihood function is maximized via the EM algorithm. Wepropose for the E step a useful matrix formulation valid forgeneral patterns of non responses. For the M step we present theFisher scoring algorithm and the Aitchison-Silvey algorithmextended to involve equality and inequality constraints on thevector of marginal parameters.

Finally, we present an application of the method for the analysisof social mobility tables from the General Social Survey.