CORRESPONDENCE ANALYSIS

Overview

Correspondence analysis is useful when the research focus is on mapping values (levels) of categorical variables. It is a method of factoring categorical variables and displaying them in a property space which maps their association in two or more dimensions. Correspondence analysis is a special case of canonical correlation, where one set of entities (category levels rather than variables as in conventional canonical correlation) is related to another set. Correspondence analysis is often used where a tabular approach is less effective due to large tables with many rows and/or columns, and/or due to categories being nominal, with no particular order. Correspondence analysis been popular in marketing research, used to display customer color preference, size preference, and taste preference in relation to preferences for Brands A, B, and C. for instance.

Correspondence analysis starts with tabular data on categorical variables, usually two-way cross-classifications. However, the technique is generalizable to n-way tables with more than two variables though only two are supported by SPSS. The variables must be discrete: nominal, ordinal, or continuous variables segmented into ranges. The technique defines a measure of distance between any two points, where points are the values (categories) of the discrete variables. Since distance is a type of measure of association (correlation), the distance matrix can be the input to principal components analysis just as correlation matrices may be the input for conventional factor analysis. However, where conventional factor analysis determines which variables cluster together, correspondence analysis determines which category values are close together. This is visualized on the correspondence map, which plots points (categories) along the computed factor axes.

Because the definition of point distance in correspondence analysis does not support significance testing, it is recommended that some other technique compatible with discrete data, such as log-linear modeling or logistic regression, be used to test alternative models. After selecting a best-fitting model using another technique, then correspondence analysis may be very useful in exploring relationships within that model.

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```CORRESPONDENCE ANALYSIS
Overview	5
Key Concepts and Terms	6
Correspondence analysis	6
Correspondence table	6
Points	6
Point distance	6
Correspondence map	6
The SPSS correspondence analysis interface	8
The main correspondence analysis dialog	8
The model dialog	8
Dimensions in the solution	9
Distance measure	9
Standardization method	10
Normalization method	10
The statistics dialog	14
The plots dialog	14
SPSS correspondence analysis output	15
Example	15
The summary of dimensions table	16
The correspondence table	18
The perceptual map	18
Row points and column points scatterplots	20
Row profiles and column profiles tables	20
Contribution tables	21
Row and column confidence points tables	23
Line Plots	24
The permuted correspondence table	25
Assumptions	26
Data level and distribution	26
Data do not need to be detrended	26
Correlated variables which meet assumptions	26
Model specification and significance testing	27
Homogeneity of categories	27
Correct labeling of dimensions	27
Numerous categories	27
Non-negative values	28