Small Area Estimation of Dependency: Final Report. Statistical Package

01/13/1989

The dependent variable necessitated the use of a statistical procedure that accounted for its three levels. As the variable is theoretically ordered, it seemed logical to consider using an ordered method. The use of ordered logistic regression, a method commonly used in such situations and one that corresponds to a proportional odds ratio model, therefore was evaluated. However, the structure such a model imposes on the data was found to be inappropriate. This was learned by estimating two logistic component equations: ADL or IADL dependent verses no dependency; and ADL dependent verses IADL or no dependency. While the parameter estimates for race, age, and age-squared were similar for each of the two component models and thereby compatible with the proportional odds model, the parameter estimates for sex contradicted it by differing by almost 19 fold. Thus, the proportional odds ratio model imposed by logistic regression was considered inappropriate for modelling our dependent variable.

Instead a multicategory extension of logistic regression which provides a more general structure was used. The log-linear model was fit using a SAS supported procedure designed for categorical data modeling, PROC CATMOD. For log-linear model analysis CATMOD uses maximum likelihood estimation. Given the three category dependent variable, two sets of parameter estimates were produced: one for the logged ratio of not dependent to ADL dependent, and one for the logged ratio of IADL dependent to ADL dependent. Working with these two equations simultaneously yielded a formula for each category of the dependent variable: (1) not dependent; (2) IADL dependent; and (3) ADL dependent. (See Appendix A.)

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