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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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. – Nick Cox Oct 09 '13 at 14:15
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1If 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?). – chl Oct 09 '13 at 14:16
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Related to: http://stats.stackexchange.com/q/72332/930. – chl Oct 09 '13 at 14:23
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I think it *could* change things even if all variables are on the same scale, if some questions have very different patterns than others. E.g. if some are uniform over 1 through 5 and others highly skew, they will have different sd and therefore standardizing will affect them differently, right? – Peter Flom Oct 09 '13 at 14:59
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1@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. – ttnphns Oct 09 '13 at 16:45
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1@cathy, just a few thoughts about standardizing or not standardizing before PCA of factor analysis http://stats.stackexchange.com/a/62699/3277 – ttnphns Oct 09 '13 at 17:09
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@PeterFlom: This is correct if you base the PCA on the VC-matrix (and not on the correlation matrix) – Michael M Oct 10 '13 at 10:29