Example 4

Polytomous Regression : Unordered Response Model.

The following data come from a study of mental health for a random sample of adult residents of Alachua County , Florida . The data relate mental impairment (MENTAL) to socio economic status (SES) and life events index (LIFE).
(Data Codes: MENTAL: 1-well, 2-mild, 3-moderate, 4-impaired; SES : 0-low, 1-high; LIFE : 0-9).

The above data were analyzed using Polytomous regression models relating the response variable MENTAL with the covariates SES and LIFE. The results of the analyses are shown in the following pages.

Reference: Agresti, A (2002). Categorical Data Analysis. John Wiley & Sons, New Jersey

Analysis 1: Polytomous Response: Unordered Response : Common Beta method.

Notice the difference between the asymptotic and exact p-values for the coefficient of the covariate ‘life’. While the asymptotic p-value (0.07821) indicates non-significance, the exact p-value (0.03529) indicates significance.

Analysis 2: Polytomous Response: Unordered : Individual Beta method.

Notice the differences between the asymptotic and exact p-values for the coefficients of the covariates in the model.