Correspondence Analysis - Program Overview

The Correspondence Analysis module is a full-featured implementation of simple and multiple correspondence analysis techniques (see, for example, Greenacre, 1984; see also the Introductory Overview and Introductory Overview - MCA sections).

Input data. STATISTICA accepts, as input data, files with grouping (coding) variables that are to be used to compute the crosstabulation table, data files that contain frequencies (or some other measure of correspondence, association, similarity, confusion, etc.) and coding variables that identify (enumerate) the cells in the input table, or data files with frequencies (or other measure of correspondence) only (e.g., the user can directly type in and analyze a frequency table). For multiple correspondence analysis the user can also directly specify a Burt table as input for the analysis.

Descriptive statistics. STATISTICA computes various tables, including the table of row percentages, column percentages, total percentages, expected values, observed minus expected values, standardized deviates, and contributions to the Chi-square values. All of these statistics can be plotted in 3D bivariate histograms.

Results. STATISTICA computes the generalized eigenvalues  and reports all standard diagnostics including the singular values, eigenvalues, and proportions of inertia for each dimension. You can either manually choose the number of dimensions or specify a cutoff value for the maximum cumulative percent of inertia. STATISTICA computes the standard coordinate values for column and row points. You have the choice of row-profile standardization, column-profile standardization, row and column profile standardization, or canonical standardization. For each dimension and row or column point, STATISTICA computes the inertia, quality, and cosine² values. In addition, you can display the matrices of the generalized singular vectors; these matrices can be accessed via STATISTICA Visual BASIC, for example, in order to implement a non-standard method of computing the coordinates.

Supplementary points. You can compute coordinate values and related statistics (quality and cosine² values) for supplementary points (row or column), and compare the results with the regular row and column points. Supplementary points can also be specified for multiple correspondence analysis.

Graphical results. In addition to the 3D bivariate histograms that can be computed for all tables, the user can produce a line plot for the eigenvalues, and 1D, 2D, and 3D plots for the row or column points. Row and column points can also be combined in a single graph, along with any supplementary points (each type of point will use a different color and point marker, so the different types of points can easily be identified in the plots). All points are labeled, and an option is available to truncate the names for the points to a user-specified number of characters.

Alternative procedures. The Basic Statistics module contains numerous options for computing multi-way frequency tables, and measures of association for those tables. The Log-Linear Analysis of Frequency Tables module will also analyze multi-way frequency tables, and includes facilities for analyzing relationships between categorical variables. For continuous variables, the Multidimensional Scaling and Factor Analysis modules produce results that are similar in nature and interpretation (see Greenacre, 1984; see also the Introductory Overview).