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We are often confronted with brand attribute associations (Yes/No) in Market Research, and more often than not we need to do Factor Analysis (we use PCA under Factor in SPSS) in order to reduce the data to something useful and interpretable.

What is the best method of data reduction when you have binary data? Surrogate variables runs the risk of potentially misleading results by selecting a single variable to represent a more complex result. Factor scores do not seem to be ideal either because the data is binary. And if we are using summated scales, should we use the total or the mean, or perhaps another measure of central tendency?

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You might read my own current opinion about binary variables here. In short, it is not a sin to use binary vars with PCA if you use the analysis simply as variable-reduction technique - for example, for plotting purpose, - without attempting to interpret the components as latent features. If you go as far as to interpret you should better use factor analysis in proper sense, not PCA; and then binary variables posit a problem since factor analysis assumes contunuous variables, what binary variables are clearly not.

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