SPSS Categories® 11.0

12 Chapter 1
Homogeneity Analysis
analyze, or you can analyze all of them. Alternatively, the Homogeneity Analysis procedure
can be used to examine all of the variables simultaneously without the need to
construct interaction variables.
Relation to standard techniques. The SPSS Crosstabs procedure can also be used to analyze
contingency tables, with independence as a common focus in the analyses. However,
even in small tables, detecting the cause of departures from independence may be
difficult. The utility of correspondence analysis lies in displaying such patterns for twoway
tables of any size. If there is an association between the row and column variables—
that is, if the chi-square value is significant—correspondence analysis may help reveal
the nature of the relationship.
Homogeneity analysis tries to produce a solution in which objects within the same category
are plotted close together and objects in different categories are plotted far apart.
Each object is as close as possible to the category points of categories that apply to the
object. In this way, the categories divide the objects into homogeneous subgroups. Variables
are considered homogeneous when they classify objects in the same categories
into the same subgroups.
For a one-dimensional solution, homogeneity analysis assigns optimal scale values
(category quantifications) to each category of each variable in such a way that overall,
on average, the categories have maximum spread. For a two-dimensional solution,
homogeneity analysis finds a second set of quantifications of the categories of each variable
unrelated to the first set, attempting again to maximize spread, and so on. Because
categories of a variable receive as many scorings as there are dimensions, the variables
in the analysis are assumed to be multiple nominal in optimal scaling level.
Homogeneity analysis also assigns scores to the objects in the analysis in such a way
that the category quantifications are the averages, or centroids, of the object scores of
objects in that category.
Relation to other Categories procedures. Homogeneity analysis is also known as multiple
correspondence analysis or dual scaling. It gives comparable, but not identical, results
to correspondence analysis when there are only two variables. Correspondence
analysis produces unique output summarizing the fit and quality of representation of the
solution, including stability information. Thus, correspondence analysis is usually preferable
to homogeneity analysis in the two-variable case. Another difference between the
two procedures is that the input to homogeneity analysis is a data matrix, where the rows
are objects and the columns are variables, while the input to correspondence analysis
can be the same data matrix, a general proximity matrix, or a joint contingency table,
which is an aggregated matrix where both the rows and columns represent categories of
variables.