I wanted to do a Principal Component Analysis to reduce the number of variables used in the vulnerability analysis. Before running the PCA, it's necessary to standardize the variables collected in nominal (Yes/No) and in ordinal (rank). How can I do that? Any suggestion will be appreciated.
Hello Husen,
Standardizing typically means adjusting scores to have a specific distributional characteristic. This could include: (a) fixing the range (e.g., to fall between 0,1); (b) fixing the mean or median to some constant value; (c) fixing the variance or spread to some constant value; (d) some combination (as in the case of z-scores, which fix the values to have a mean of 0 and variance or SD of 1).
Normalizing has multiple meanings, which could include making the shape of a score distribution match that of a normal (Gaussian) distribution, transforming the values so that the sum of squared values = 1 (vector arithmetic), and others. In general, you'll never get a categorical variable to have a normal distribution.
For dichotomous variables, just code them as 0,1 (or 1,2). Any linear transformation of these values (e.g., to z-scores) will not change either the shape of the distribution or the correlation of scores on that variable with those of any other variable. For PCA based on correlations, rescaling via linear transforms will not impact the resultant structure or solution. For PCA based on covariances, yes, variables having larger variances will have larger initial communality estimates and other parts of the solution will differ. The fix for that is simple: Use correlation-based PCA (which automatically standardizes all variables).
For categorical variables with more than two levels, you'll have to re-express those as a set of k - 1 dummy variates (or similar), for a variable with k levels. So, there's really no standardizing that would make much sense for these for the same reason as that of a dichotomous variable.
Good luck with your work.
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