
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 twoway crossclassifications. However, the technique is generalizable to nway 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 loglinear modeling or logistic regression, be used to test alternative models. After selecting a bestfitting model using another technique, then correspondence analysis may be very useful in exploring relationships within that model.
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Below is the unformatted table of contents.
CORRESPONDENCE ANALYSIS Table of Contents 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 Nonnegative values 28 Frequently Asked Questions 28 What procedures are related to correspondence analysis? 28 How does correspondence analysis of three variables work in multiple correspondence analysis (MCA)? 29 Explain active vs. constrained categories. 29 Explain supplementary categories. 31 How is the distance between points computed in correspondence analysis? 32 What is detrended correspondence analysis (DCA)? 33 Bibliography 35 Pagecount: 37