Define Scale and Weight in CATPCA
You can set the optimal scaling level for analysis variables and supplementary 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.
Variable weight. You can choose to define a weight for each variable. The value specified must be a positive integer. The default value is 1.
Optimal Scaling Level. You can also select the scaling level to be used to quantify 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.
- Multiple 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 in the centroid of the objects in the particular categories. Multiple indicates that different sets of quantifications are obtained for each dimension.
- 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 an Optimal Scaling Scale and Weight in CATPCA
- Select a variable in the Analysis Variables list in the Categorical Principal Components dialog box.
- Click Define Scale and Weight.
- Enter the weight value for the variable.
- Select the optimal scaling level to be used in the analysis. If you choose a spline transformation, you must also specify the degree of the polynomial and the number of interior knots.
- Click Continue.
You can alternatively define the scaling level for supplementary variables by selecting them from the list and clicking Define Scale.