SPSS Categories® 11.0

8 Chapter 1
Categorical Regression
The use of Categorical Regression is most appropriate when the goal of your analysis is
to predict a dependent (response) variable from a set of independent (predictor) variables.
As with all optimal scaling procedures, scale values are assigned to each category
of every variable such that these values are optimal with respect to the regression. The
solution of a categorical regression maximizes the squared correlation between the
transformed response and the weighted combination of transformed predictors.
Relation to other Categories procedures. Categorical regression with optimal scaling is
comparable to optimal scaling canonical correlation analysis with two sets, one of which
contains only the dependent variable. In the latter technique, similarity of sets is derived
by comparing each set to an unknown variable that lies somewhere between all of the
sets. In categorical regression, similarity of the transformed response and the linear
combination of transformed predictors is assessed directly.
Relation to standard techniques. In standard linear regression, categorical variables can
either be recoded as indicator variables or can be treated in the same fashion as interval
level variables. In the first approach, the model contains a separate intercept and slope
for each combination of the levels of the categorical variables. This results in a large
number of parameters to interpret. In the second approach, only one parameter is estimated
for each variable. However, the arbitrary nature of the category codings makes
generalizations impossible.
If some of the variables are not continuous, alternative analyses are available. If the
response is continuous and the predictors are categorical, analysis of variance is often
employed. If the response is categorical and the predictors are continuous, logistic
regression or discriminant analysis may be appropriate. If the response and the predictors
are both categorical, loglinear models are often used.
Regression with optimal scaling offers three scaling levels for each variable. Combinations
of these levels can account for a wide range of nonlinear relationships for which
any single “standard” method is ill-suited. Consequently, optimal scaling offers greater
flexibility than the standard approaches with minimal added complexity.
In addition, nonlinear transformations of the predictors usually reduce the dependencies
among the predictors. If you compare the eigenvalues of the correlation matrix for
the predictors with the eigenvalues of the correlation matrix for the optimally scaled predictors,
the latter set will usually be less variable than the former. In other words, in
categorical regression, optimal scaling makes the larger eigenvalues of the predictor
correlation matrix smaller and the smaller eigenvalues larger.