Model Fit and Coefficients
The Categorical Regression procedure yields an R 2 of 0.948, indicating that almost 95% of the variance in the transformed preference rankings is explained by the regression on the optimally transformed predictors. Transforming the predictors improves the fit over the standard approach.
The following table shows the standardized regression coefficients. Categorical regression standardizes the variables, so only standardized coefficients are reported. These values are divided by their corresponding standard errors, yielding an F test for each variable. However, the test for each variable is contingent upon the other predictors being in the model. In other words, the test determines if omission of a predictor variable from the model with all other predictors present significantly worsens the predictive capabilities of the model. These values should not be used to omit several variables at one time for a subsequent model. Moreover, alternating least squares optimizes the quantifications, implying that these tests must be interpreted conservatively.
The largest coefficient occurs for Package design. A one standard deviation increase in Package design yields a 0.748 standard deviation decrease in predicted preference ranking. However, Package design is treated nominally, so an increase in the quantifications need not correspond to an increase in the original category codes.
Standardized coefficients are often interpreted as reflecting the importance of each predictor. However, regression coefficients cannot fully describe the impact of a predictor or the relationships between the predictors. Alternative statistics must be used in conjunction with the standardized coefficients to fully explore predictor effects.