Categorical Principal Components Analysis (CATPCA)

This procedure simultaneously quantifies categorical variables while reducing the dimensionality of the data. Categorical principal components analysis is also known by the acronym CATPCA, for categorical principal components analysis.

The goal of principal components analysis is to reduce an original set of variables into a smaller set of uncorrelated components that represent most of the information found in the original variables. The technique is most useful when a large number of variables prohibits effective interpretation of the relationships between objects (subjects and units). By reducing the dimensionality, you interpret a few components rather than a large number of variables.

Standard principal components analysis assumes linear relationships between numeric variables. On the other hand, the optimal-scaling approach allows variables to be scaled at different levels. Categorical variables are optimally quantified in the specified dimensionality. As a result, nonlinear relationships between variables can be modeled.

Example. Categorical principal components analysis could be used to graphically display the relationship between job category, job division, region, amount of travel (high, medium, and low), and job satisfaction. You might find that two dimensions account for a large amount of variance. The first dimension might separate job category from region, whereas the second dimension might separate job division from amount of travel. You also might find that high job satisfaction is related to a medium amount of travel.

Statistics and plots. Frequencies, missing values, optimal scaling level, mode, variance accounted for by centroid coordinates, vector coordinates, total per variable and per dimension, component loadings for vector-quantified variables, category quantifications and coordinates, iteration history, correlations of the transformed variables and eigenvalues of the correlation matrix, correlations of the original variables and eigenvalues of the correlation matrix, object scores, category plots, joint category plots, transformation plots, residual plots, projected centroid plots, object plots, biplots, triplots, and component loadings plots.

Categorical Principal Components Analysis Data Considerations

Data. String variable values are always converted into positive integers by ascending alphanumeric order. User-defined missing values, system-missing values, and values less than 1 are considered missing; you can recode or add a constant to variables with values less than 1 to make them nonmissing.

Assumptions. The data must contain at least three valid cases. The analysis is based on positive integer data. The discretization option will automatically categorize a fractional-valued variable by grouping its values into categories with a close to "normal" distribution and will automatically convert values of string variables into positive integers. You can specify other discretization schemes.

Related procedures. Scaling all variables at the numeric level corresponds to standard principal components analysis. Alternate plotting features are available by using the transformed variables in a standard linear principal components analysis. If all variables have multiple nominal scaling levels, categorical principal components analysis is identical to multiple correspondence analysis. If sets of variables are of interest, categorical (nonlinear) canonical correlation analysis should be used.

To Obtain a Categorical Principal Components Analysis

This feature requires the Categories option.

  1. From the menus choose:

    Analyze > Dimension Reduction > Optimal Scaling...

  2. Select Some variable(s) not multiple nominal.
  3. Select One set.
  4. Click Define.
  5. Select at least two analysis variables and specify the number of dimensions in the solution.
  6. Click OK.

You may optionally specify supplementary variables, which are fitted into the solution found, or labeling variables for the plots.

This procedure pastes CATPCA command syntax.