PCA question

[MB Ross]

I have a panel of firm and worker characteristics. Part of the panel is questions answered by the firm and part is workers within each firm. I want to use PCA to reduce the firm level qualitative variables into a single index that I can then attach to my worker-level panel.

The question I have is whether I should run PCA on the firm panel... i.e. there is one response for each frim on each question. I would run PCA on just the firm panel and then attach the predicted component onto the worker level panel.... OR whether I should first do a m:1 merge between the firm and worker panel... and then use PCA to predict the component.

I know these procedures yield different results and I am not sure one way is right/wrong but I thought to ask for others insight. Thanks.

[Carlo Lazzaro]

MB (please note the preference for full given names too on this forum. Thanks):
I'm not completely clear with your research goal but my jerk-knee reaction would be to

first do a m:1 merge...

.

[Oded Mcdossi]

Dear Ross,
Carlo suggestion for more details is inevitable, otherwise you'll get answers for either way. Having said that, I would suggest to begin with the firm level data and calculate the factor scores and then to attach any score to the individual (worker) level data. That means, begin with calculation of the PCA score on the firm level (when each firm appears only once) and then, attach the score to the worker level. Choosing the other way, will inflate the and bias the PCA by large and small firms.

[ben earnhart]

Obviously, this board is about Stata. And Stata has great multi-level capabilities. But to do it really right, see if you can get access to Mplus, which can do multilevel EFAs.