There are variables increasing vulnerability while others decrease it. What are the best pre-processing methods to account for this relationship to ensure adequate results? Is it always necessarily a max-normalization or another rescaling procedure?
you can just do the PCA analyse with SPSS directly ,and giving the result which Components affect the urban vulnerability,maybe the increasing vulnerability factors can cluster together ,while decreasing factors cluster together.you do not need normalization or another procedure,it has been normalized in the computing procedure already.
thanks for your answer guys. Actually @Alessandro I´ve tried both, but results were not "coherent". Inverse variables clustered with direct ones... Thats why I started wondering whether I should attempt some preprosesing before running PCA...
Thank you @george for your suggestions. However I am trying PCA with socio-economic variables, which makes the interpretation a bit tricky, that's why I am interested in pre-processing techniques to facilitate results analysis.
If you have scales that are inverted with respect to each other, max normalisation makes no sense - on one variable you will be normalising to high vulnerability and on an inverse scale variable you will be normalising to low vulnerability. Mean normalisation is a more sensible alternative to max normalisation, but see below for other ideas.
Are the magnitudes of the numerical scales different? Are any of the original scales negative? If so normalisation by a negative number will invert the scale and this would need to be kept in mind for interpretation. If negative numbers are involved try normalising to magnitudes to preserve the sign.
Are there any differences in the magnitude and variance of the responses? If so, have you tried mean centring and normalising to unit variance? If the scales are not equivalent PCA will be biased towards variables with bigger numbers and bigger spreads. Mean centring and standardising to unit variance avoids this bias.
The loadings (including PC1 if mean centred or if some variables are on negative scales) should clearly show inverse relationships between variables as positive and negative contributors to the PCs (note that which one is positive and which one is negative is completely arbitrary as PCA is a least squares minimisation method, so the squaring eliminates the sense of positive and negative). If not mean centred and data is all on positive scales you would expect PC1 to show some variable to be high when the others low if they have an inverted relationship.
Thank you James, your suggestions make lot of sense. Now I am reviewing the data set and the selection of variables again. I will consider your comments. I hope they will work out, within the restrictions of the method and the data set I am using. We´ll see :)
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