I would like to represent factors in functions of each other by doing a MANOVA where all factors would be the response and but also factors to see how they may interact each other. I would really appreciate if you could describe your methods with R.
A good discussion of differences between factor analysis (FA) and principal components analysis (PCA) is available on Cross Validated (linked below). It is incorrect technically to say that FA can be performed by extracting principal components, as FA uses different estimation methods (e.g., principal axis factoring, maximum likelihood, weighted least squares). It is also debatable to say that FA and PCA are not competing methods, as the popular confusion over which is most appropriate to apply in various contexts has certainly resulted in controversy among competing ideologies.
Similarly, partial least squares (PLS) is controversial and often misunderstood as a competitor for optimal estimation of multivariate regression models. Again, the optimal choice depends on the context in question. For example, among latent factor modeling options, Wang and Cunningham (2005) found weighted least squares estimation of confirmatory factor analytic models using polychoric correlation matrices based on nonnormal ordinal data produced less biased results than maximum likelihood estimation. Some say PLS handles nonnormal data fairly well too (and also small sample sizes), but it is different from latent factor modeling in some potentially important ways (reminiscent of differences between FA and PCA; see McDonald's "Path analysis with composite variables", 1996).
http://stats.stackexchange.com/q/1576/32036
Here is a paper on Exploratory Factor Analysis in R
http://www.psych.umn.edu/faculty/waller/classes/FA2010/FAinR/FAinR.pdf
If you're looking to study correlations (including predictive interactions) among latent variables that you'll estimate as combinations of measured variables, consider the broader range of structural equation modeling methods (which subsume exploratory factor analysis). Many such methods and corresponding R functions are available. In my experience thus far, lavaan is the most versatile (see attached link), but OpenMx is also worth using in parallel for validation of any results both can produce (see http://openmx.psyc.virginia.edu/).
http://lavaan.ugent.be/
Many possibilities: correlation matrix is a good first-attempt.
I disagree with Alex Ignatov here, PCA and factor analysis are not competing methods: factor analysis can be done using PCA as extraction method, or using other strategies. It is also important to remember that one can use rotations to get more easily interpretable results (sometimes). Commands "princomp" and "factanal" in R will help you do that.
I also recommend the excellent package "FactoMineR" in R, very good supporting material at http://factominer.free.fr/index.html
And if you are looking for factors of a matrix Y to be related to factors of a matrix X, the ideal way to do it is Partial Least Squares Regression (PLS Regression).
Best regards.
A good discussion of differences between factor analysis (FA) and principal components analysis (PCA) is available on Cross Validated (linked below). It is incorrect technically to say that FA can be performed by extracting principal components, as FA uses different estimation methods (e.g., principal axis factoring, maximum likelihood, weighted least squares). It is also debatable to say that FA and PCA are not competing methods, as the popular confusion over which is most appropriate to apply in various contexts has certainly resulted in controversy among competing ideologies.
Similarly, partial least squares (PLS) is controversial and often misunderstood as a competitor for optimal estimation of multivariate regression models. Again, the optimal choice depends on the context in question. For example, among latent factor modeling options, Wang and Cunningham (2005) found weighted least squares estimation of confirmatory factor analytic models using polychoric correlation matrices based on nonnormal ordinal data produced less biased results than maximum likelihood estimation. Some say PLS handles nonnormal data fairly well too (and also small sample sizes), but it is different from latent factor modeling in some potentially important ways (reminiscent of differences between FA and PCA; see McDonald's "Path analysis with composite variables", 1996).
http://stats.stackexchange.com/q/1576/32036
Thank you very much, everyone, for your helpful answer !
Didn't know FA... This analysis look to feat my expectation !
I'll keep you inform.
Thx a lot
Can this help: https://www.researchgate.net/publication/319469038_New_Interpretation_of_Principal_Components_Analysis?
Article New Interpretation of Principal Components Analysis
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