For exploratory purposes, should PCA (Principal Component Analysis) be done for one latent variable at a time or should it done for all the latent variables at once? I seem to get better results with each of my latent construct's item loadings if I do PCA one latent construct at a time. Is this incorrect? Thank you.
PCA latent variables
- Thread starter rajarshic
- Start date
- Tags latent construct latent variable pca
well, the fact that you're using prinicipal components analysis instead of factor analysis to model latent variables is kind of wrong it itself from the very beginning. now, what do you mean by "better results" (do you mean simple structure? do you mean you get as many principal components as you were kind of expecting? i am a little bit confused) and by "done for one latent variable at a time"? aren't you doing principal components on the matrix and getting all your eigenvalues at once? or how are you doing it...?
Thanks for the response. Would you suggest starting with Partial Axis Factoring instead?
What I meant by "better results" was the following: all the items of my dependent variable load together reasonably well (each > 0.7) when I do PCA on the subset of the dataset selecting only the columns corresponding to those items. On the other hand, when I do PCA on the entire dataset (i.e. include all other columns), my intended items for the dependent variable don't seem to load to the same factor/component anymore.
I hope I'm making myself clear. Thank you.
What I meant by "better results" was the following: all the items of my dependent variable load together reasonably well (each > 0.7) when I do PCA on the subset of the dataset selecting only the columns corresponding to those items. On the other hand, when I do PCA on the entire dataset (i.e. include all other columns), my intended items for the dependent variable don't seem to load to the same factor/component anymore.
I hope I'm making myself clear. Thank you.
oh, i see... well, you should NEVER do that. the loading of your items and the apparent niceness of your results is nothing more than a statistical artifact of how you're getting your factors. factors and latent structures are defined over the joint covariance of your variables (or items in this case). if you chop up that covariance structure then you are really not dealing with factors.
although there is debate on the literature, i have never seen a clear solution as for what is the best way to extract factors, all of them seem fine to me. i like maximum likelihood or generalised least squares because it gives me a chi-square test of model fit, which is sometimes pretty useless anyways depending on sample size... but at least i get something. principal components analysis is not factor analysis and, to the best of my knowledge, one of the few instances where the results are the same is when the residual correlation matrix is diagonal (or the communalities are very close to 1), but that doesnt happen very often (if ever).
although there is debate on the literature, i have never seen a clear solution as for what is the best way to extract factors, all of them seem fine to me. i like maximum likelihood or generalised least squares because it gives me a chi-square test of model fit, which is sometimes pretty useless anyways depending on sample size... but at least i get something. principal components analysis is not factor analysis and, to the best of my knowledge, one of the few instances where the results are the same is when the residual correlation matrix is diagonal (or the communalities are very close to 1), but that doesnt happen very often (if ever).