I have created a socioeconomic status index utilizing PCA after normalizing all variables as proportions, per capita, average, and median functions. A few Stata users discuss that standardization of variables are not required while using Principal Components Analysis as we would like to capture maximum variation in the original variables through PCA. Would you please let me know your opinion with citable academic reference.
You don't have to if the data are all in the same units. But the safe thing is to do it.
D. Booth
Hello Liton,
"It don't make no nevermind."
You needn't standardize the variables in advance. The reason is, that ordinary PCA/FA works from Pearson product-moment correlations, which inherently standardize the variables (remember: product of the first moment about the mean is the product of the two scores expressed as z-scores). As well, a linear transformation (e.g., converting raw scores to z-scores) does not change the relationship between a pair of variables (nor the shape of the score distribution).
Good luck with your work.
Hi Liton Chakraborty
There is really no need for manual standardization before performing PCA/FA. The test corrects it inherently. Best,
Hi all, thanks very much for your reply. I standardized all variables and then performed PCA again. Although the results in terms of number of significant components did not change as per Kaiser criterion, the total variance increased from 79% to 81%, KMO score also increased by 1%, Alpha reliability test score increased too, Index scores changed a bit, component loading scores also changed a bit. Cutter (2003) and his followers always suggested to standardize variables for accuracy after normalizing to percentages / per capita. Thus, I have to find a valid argument why these test results are changing after standardizing all variables! Do you have any suggestions? Thanks again.
Hi Liton,
You tend to use the correlation matrix when variables are on different scales and the covariance matrix when the variable scales are similar. Using the correlation matrix is equivalent to standardizing each of the variables. In general, PCA with and without standardizing will give different results. Especially when the scales are different.
see https://stats.stackexchange.com/questions/53/pca-on-correlation-or-covariance
No need, find link below...
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