# AVE & composite reliability with SPSS

I have some issues with an exploratory factor analysis.

Can anybody please tell me how to calculate the Average Variance Extracted (AVE) and the Composite Reliability from two factors, each with three items using SPSS? If not with SPSS, Stata might help too.

-

The following is shamelessly extracted from the following link.

\begin{shamelesscopyandpaste}

Finally, the "average variance extracted" measures the amount of variance that is captured by the construct in relation to the amount of variance due to measurement error and can be calculated using the following formula: (summation of squared factor loadings)/(summation of squared factor loadings) (summation of error variances) (Fornell & Larcker). If the average variance extracted is less than .50, then the variance due to measurement error is greater than the variance due to the construct. In this case, the convergent validity of the construct is questionable.

\end{shamelesscopyandpaste}

I haven't used SPSS in some time, and I don't remember seeing an option to perform these calculations, but you can certainly do it using the syntax.

These two links give you an introduction to SPSS syntax. What I would do from here is examine the syntax SPSS gives you when you perform an FA, and use the variables named to compute the average variance explained.

Sorry for the lack of a definitive answer, but I felt that some response was definitely better than none.

-
Here's another link, with Mplus: statmodel.com/discussion/messages/9/258.html?1237657036. I didn't find anything for SPSS specifically. Your suggestion of writing some SYNTAX is the best way to go, IMO. – chl Mar 24 '11 at 15:01

In case richiemorrisroe's response doesn't give you quite enough, I suggest...

• right-clicking your SPSS factor analysis output and choosing Results Coach to clarify the contents of the Variance Explained table
• searching the Help files or Tutorial for Reliability Analysis. I'm thinking that by "composite reliability" you mean internal consistency reliability
(Cronbach's alpha).
-
2, thats good advice, my rustiness with SPSS sure is showing. – richiemorrisroe Mar 26 '11 at 18:45
I seem to remember that Cronbach's alpha will only equal composite score reliability for essentially tau-equivalent tests. It is very shortly discussed on Garson's SPSS website, faculty.chass.ncsu.edu/garson/PA765/reliab.htm; but I will also check for more recent academic references. – chl Mar 26 '11 at 19:51
@chl: nice citation. Garson sure has a lot to offer, although [side comment] I believe I have found a chink in his armor when it comes to centering in regression (he advocates it unnecessarily). – rolando2 Mar 30 '11 at 20:53
Good to know. I came across his website because some of my colleagues use SPSS for psychometrics, esp. for factor analysis or reliability studies. Centering remains useful when one wants to avoid spurious collinearity effects or to interpret the effect of a predictor as deviation from its means (e.g., age). – chl Mar 30 '11 at 21:02

The average variance extracted (AVE) calculated as follows: total of the squared multiple correlations plus the total sum of each variable, then divides it by the number of factors in that variable.

In order to get square multiple correlation of each item, you need to find square of each item Standardized Regression Weight / Estimate. AVE- average variance extracted (AVE) should not be less than .05, this is to show that more than half of the variances is observed (Janssens, et. Al).

AVE can be calculated by using auto design by James Gaskin by visiting this website, and click on Excel StatTools on the left hand menu, it is an excel file with calculator for calculating AVE, reliability and validity test.