semTools AVE/reliability functions

[Ibrahim Nasser]

*Please note. I have posted this question also on SEMnet. Since it has a lavaan/semTools link, I would like to post the question here as well. Sorry, for the cross posting. I still look forward to feedback ...*

What does AVE mean? This may be a stupid question. I ask it anyway. Fornell and Larcker use terms like "variance extracted" or "variance captured by the construct" in their 1981 publication. They seem to avoid the term "explained". Average variance explained to me would clearly be the mean over the squared standardized factor loadings and thus the average R squared. The internet is full of examples that follow this logic. 

I find no references to standardization in the FL paper. If one uses non-standardized factor loadings, a higher AVE should usually result and thus be less conservative. semTools seems to apply this logic (correct me If I'm wrong).

What is the "correct" solution and what is the FL meaning of "extracted"? Is it "explained" or something else?

Best. 

Ibrahim 

[Terrence Jorgensen]

AVE is not a reliability measure, but used as a sort of validity check.  If you have a good/reliable measure, then most of the indicators' variance should be attributable to the construct they were designed to measure.  So that is what AVE quantifies: how much variance (on average across indicators) is "extracted" from / attributable to the common factor.  The common-factor variance component for each indicator is the factor variance times the squared factor loading:

Lambda %*% Psi %*% Lambda.

In a standardized solution, Psi = 1, so the squared loading is the common-factor variance component.  Furthermore, the standardized error variance is the proportion not attributable to the common factor.  So I suppose in models with simple structure, one could just average the standardized error variances, then take 1 minus that to calculate AVE.  But I don't have the paper in front of me to verify that.

Terrence D. Jorgensen    (he, him, his)
Assistant Professor, Methods and Statistics
Research Institute for Child Development and Education, the University of Amsterdam
http://www.uva.nl/profile/t.d.jorgensen