I am having huge number of independent variables which are highly correlated and I want to run clogit. I tried all combinations of independent variables. It is a very laborious process. So I tried PCA and run the clogit with PCs scores, is it correct to use PCA before running clogit?
In short the answer is yes. You have to remember that the purpose of a PCA is to reduce the dimentionality of the data by coming up with linear combinations of the variables that maximize the variance explained. So I've had a set of 13 variables be reduced down to 2 PCs that explain 90% of the data. Each of the PC axes is orthogonal to all the others so treating them as independent is fine. The key is in interpreting what the PCs mean. You have to look at the loadings on each of the PCs to do that. I'm attaching a paper where we performed a PCA on measurements of crab embryos. The first PC explained 80% of the data and was easily interpreted as the maturity of the embryos (the lower the score the closer they were to hatching), we then ran an ANOVA on the PC to look at differences among our treatments and interpreted and significant terms as affect the maturity of the embryos.
Article Effects of high pCO2 on Tanner crab reproduction and early l...
As William says PCA is ideal for this, so you are on the right lines. PCA is specifically intended to summarise correlated variables succinctly and you've indicated this is a feature of your dataset.
Another avenue worth exploring is variable selection to reduce the number of variables used as input (can even be done before PCA if the variance explained is low in the first few PCs) . There are many ways of performing variable selection, such as a basic significance test (set alpha at this stage higher than the final alpha you want as some variables alone may be insignificant but when combined with others may still be useful).
Using obliques solution and factor scores will help as data reduction technique in addition to establishing the CONSTRUCT VALIDITY of data but using factor scores in multivariate analysis is highly possible to give low R SQR.
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