GSEM Factor Analysis -- Can it output variance explained?

[Daniel Tylee]

Hello.    Have recently used the package and github guidelines for factor analysis among a set of variables.     I know that I can use the EFA in order to estimate the variance explained by each of the resulting factor solutions.    Was wondering if possible to do the same with the CFA, since the "rotation"/loadings of the CFA solution is plausibly different.  

Thanks,

Dan

[Elliot Tucker-Drob]

Hi Dan,

We don't have that automated at present. You'd need to calculate variance explained using either path tracing rules or LISREL matrix algebra. For  a CFA with simple structure (one loading per indicator), the % of variance explained in each indicator is the sum of that indicator's squared (fully) standardized loadings. To get the percentage of genetic variance accounted for by the factor model that is akin to what you'd get out of an EFA of the genetic correlation matrix, you simply average these proportions across all indicators. When there are cross loadings, it's a bit more complicated (when an indicator has 2 loaindgs; in addition to summing the squared the loadings you also add in 2cor(F1,F2)).

I should note that, although it is conventional in EFA to use % of variance accounted for to decide on the number of factors, in CFA model fit comparisons are often used to decide on the number of factors. 

Cheers,

Elliot

--

Elliot M. Tucker-Drob, Ph.D.
Professor

Department of Psychology
Faculty Research Associate
Population Research Center
The University of Texas at Austin
108 E. Dean Keeton Stop A8000
Austin, TX 78712-0187
tucke...@utexas.edu
www.lifespanlab.com

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