# Define Scale in Categorical Regression

You can set the optimal scaling level for the dependent and independent variables. By default, they are scaled as second-degree monotonic splines (ordinal) with two interior knots. Additionally, you can set the weight for analysis variables.

Optimal Scaling Level. You can also select the scaling level for quantifying each variable.

• Spline Ordinal. The order of the categories of the observed variable is preserved in the optimally scaled variable. Category points will be on a straight line (vector) through the origin. The resulting transformation is a smooth monotonic piecewise polynomial of the chosen degree. The pieces are specified by the user-specified number and procedure-determined placement of the interior knots.
• Spline Nominal. The only information in the observed variable that is preserved in the optimally scaled variable is the grouping of objects in categories. The order of the categories of the observed variable is not preserved. Category points will be on a straight line (vector) through the origin. The resulting transformation is a smooth, possibly nonmonotonic, piecewise polynomial of the chosen degree. The pieces are specified by the user-specified number and procedure-determined placement of the interior knots.
• Ordinal. The order of the categories of the observed variable is preserved in the optimally scaled variable. Category points will be on a straight line (vector) through the origin. The resulting transformation fits better than the spline ordinal transformation but is less smooth.
• Nominal. The only information in the observed variable that is preserved in the optimally scaled variable is the grouping of objects in categories. The order of the categories of the observed variable is not preserved. Category points will be on a straight line (vector) through the origin. The resulting transformation fits better than the spline nominal transformation but is less smooth.
• Numeric. Categories are treated as ordered and equally spaced (interval level). The order of the categories and the equal distances between category numbers of the observed variable are preserved in the optimally scaled variable. Category points will be on a straight line (vector) through the origin. When all variables are at the numeric level, the analysis is analogous to standard principal components analysis.

To Define the Scale in CATREG

1. Select one or more variables on the variables list in the Categorical Regression dialog box.
2. Click Define Scale.
3. Select the optimal scaling level to be used in the analysis.
4. Click Continue.