Editing Factor analysis (section)

===Types of factor extraction===
[[Principal component analysis]] (PCA) is a widely used method for factor extraction, which is the first phase of EFA.<ref name=Polit/> Factor weights are computed to extract the maximum possible variance, with successive factoring continuing until there is no further meaningful variance left.<ref name=Polit/> The factor model must then be rotated for analysis.<ref name=Polit/>

Canonical factor analysis, also called Rao's canonical factoring, is a different method of computing the same model as PCA, which uses the principal axis method. Canonical factor analysis seeks factors that have the highest canonical correlation with the observed variables. Canonical factor analysis is unaffected by arbitrary rescaling of the data.

Common factor analysis, also called [[principal factor analysis]] (PFA) or principal axis factoring (PAF), seeks the fewest factors which can account for the common variance (correlation) of a set of variables.

Image factoring is based on the [[correlation matrix]] of predicted variables rather than actual variables, where each variable is predicted from the others using [[multiple regression]].

Alpha factoring is based on maximizing the reliability of factors, assuming variables are randomly sampled from a universe of variables. All other methods assume cases to be sampled and variables fixed.

Factor regression model is a combinatorial model of factor model and regression model; or alternatively, it can be viewed as the hybrid factor model,<ref name="meng2011">{{cite journal|last=Meng |first=J. |title=Uncover cooperative gene regulations by microRNAs and transcription factors in glioblastoma using a nonnegative hybrid factor model |journal=International Conference on Acoustics, Speech and Signal Processing |year=2011 |url=http://www.cmsworldwide.com/ICASSP2011/Papers/ViewPapers.asp?PaperNum=4439 |url-status=dead |archive-url=https://web.archive.org/web/20111123144133/http://www.cmsworldwide.com/ICASSP2011/Papers/ViewPapers.asp?PaperNum=4439 |archive-date=2011-11-23 }}</ref> whose factors are partially known.