ESTIMATION PROBLEMS FOR ORDERED CATEGORICAL DATA

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Ordinal categorical data occur in the health sciences. We propose statistical research on problems concerning the use of loglinear models for analyzing ordinal data. We propose to develop methods for the isotonic estimation of association parameters in loglinear models. These methods will allow researchers to obtain parameter estimates whose ordering both reflects the ordering of categories and implies a type of monotonicity in the association. We also propose to develop and compare methods of estimating cell proportions for sparse ordinal data. Incorporating ordinal loglinear models in various smoothing processes will enable researchers to take advantage of the extra ordinality information. Other problems to be studied, time permitting, include development of multidimensional loglinear models for ordinal variables, construction of standardized association parameters, and power and robustness studies for simple ordinal loglinear models.