Does it makes sense to standardize (z-transformation) all ordinal variables (I only have Likert-scale questions) before running a PCA? Or is the z-transformation only used when having variables with different scales?
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$\begingroup$ It's not crazy but it's usually pointless. If you wish to standardize, just use PCA based on correlations, as that's equivalent. Whether means or PCA are good choices for Likert-scale data I leave on one side. $\endgroup$– Nick CoxCommented Oct 9, 2013 at 14:15
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1$\begingroup$ If your Likert-type items are all expressed on the same scale (e.g., 5-point scale), that won't change anything. However, using PCA with ordinal data (that is, working with euclidean distance and dealing with (usually) highly skewed data) might not be the best option, depending on what you have in mind (dimensionality issue? using PCs in regression? summarizing data from a geometric perspective?). $\endgroup$– chlCommented Oct 9, 2013 at 14:16
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$\begingroup$ Related to: stats.stackexchange.com/q/72332/930. $\endgroup$– chlCommented Oct 9, 2013 at 14:23
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1$\begingroup$ @cathy, There is no sense in doing classic (linear) PCA on ordinal data (be it original or z-standardized - all the same). That PCA is for interval data. My advice: just stop pretending that your Likert scale is ordinal, release and let it be interval; do then PCA and standardizations and what not? And be happy. $\endgroup$– ttnphnsCommented Oct 9, 2013 at 16:45
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1$\begingroup$ @cathy, just a few thoughts about standardizing or not standardizing before PCA of factor analysis stats.stackexchange.com/a/62699/3277 $\endgroup$– ttnphnsCommented Oct 9, 2013 at 17:09
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