# How should I interpret the generalized squared multiple correlation?

I am testing this model in SPSS AMOS.

The value of .23 above the top right corner of timedrs is the squared multiple correlation for that variable.

I also ran the same analysis as two multi-step regressions. The results came out like this:

The generalized squared multiple correlation is described by Schumacker & Lomax (2004) on p159 as a "traditional non-SEM path model-fit [index]." The relevant text is as follows:

Applying the formula for a generalized squared multiple correlation, I get:

1 – (1 - .119) × ( 1 - .227) = 0.32.

This is higher than the .23 I obtained from the path analysis run in AMOS, and from the equation I can see that it can never be lower than the smallest value of R Square that goes into its calculation. I understand that I should not be surprised that the values are not the same. However, I am unsure about how to interpret the generalized squared multiple correlation, i.e. this $R^2m$ thing. What would a high/low generalized squared multiple correlation mean? Is it a good method of assessing model fit?

Schumacker, R. E., & Lomax, R. G. (2004). A beginner's guide to structural equation modeling. Psychology Press.

• What's the generalized R²? I've never heard of this, but I'm very surprised to see you combine two R² from analyses that use different dependent variables. May 24, 2015 at 5:16
• Thanks for the question. I guess this concept is not as common as I realised. I've edited the OP to clarify this point. May 24, 2015 at 6:01
• Interesting problem. Could you show the relevant AMOS output where the R² is being reported? Some output titles/columns/rows/notes/etc. might help figure it out... May 24, 2015 at 6:04
• I've put the AMOS Estimates Output at i.imgur.com/yhYFmf7.png. The R Square estimates are the same as those I obtained from the regression function in SPSS. I'm not entirely sure this was the output you were seeking, so please let me know if there's something out from AMOS I should post. May 24, 2015 at 7:20
• But you said AMOS reported some sort of overall R² as .23? I don't see that in your output. All I see are the two R², one for each DV, which correspond exactly to the ones you obtained through SPSS. May 24, 2015 at 15:35

"The $R^2m$ for the path model would suggest that [32%] of the variance in [timedrs] is explained by the relations in the path model."