PCA with panel data and groups

[Maria Ribeiro]

Dear Statalist users,

I have a panel data set (with 6 years of analysis) of all firms, classified into three categories, for a given country. My purpose is to implement principal component analysis in order to reduce the amount of variables, and then introducing the main PC into data envelopment analysis (a methodologie that suffers from dimensionality of data).

Therefore, my questions are:
1) Should I need to introduce some argument to account for panel data in the following code: pca x1 x2 x3?

2) Is it more correct to consider that there might be differences among the three categories and consider: by category, sort : pca x1 x2 x2?

3) Apart from the graphical analysis, do you have any suggestion to assess the presence of outliers with the obtained outcomes of pca?

4) After running the following code:
pca x1 x2 x3, comp(1) vce(normal)
I then performed a Wald test through_
testparm x1 x2 x3, equal eq(Comp1)
and I obtained:
(1) -Comp(1)x1+Comp(1)x2=0 and (2) -Comp(1)x1+Comp(1)x3=0
chi2( 2) = 50.61 and Prob > chi2 = 0.0000
4.1.) How shouldI interpret the fact that we are able to reject H0?
4.2.) However, if I replace vce(normal) by vce(none), then testparm code retrieves "last estimates not found". Why is that?

Thanks,
Maria

[wbuchanan]

In a longitudinal context you might want to consider testing whether constraining the loadings in years 2-6 to equal the loadings from year 1 fits the data as well as it did in the first year. There are a few good texts for dealing with these types of issues in the SEM literature, but I would recommend starting with Little, T. D. (2013). Longitudinal structural equation modeling. New York City, NY: Guilford Press.