I'm doing factor anlaysis in SPSS and the reproduced correlation saying that the residuals are computed between observed and reproduced correlations that there are 75 (15%) nonredundant residuals with absolute value >0.05? What does this mea?
Thanks a lot for any reply in advance!
Hello Jun,
One feature of factor analysis is that your resultant model loadings may be used to determine how closely the model values (variable-factor loadings) can reproduce the observed correlations in your data set. In other words, a model-data fit index. In SPSS, the default index that may be elicited is the reproduced correlations, which are then compared with the observed correlations, and (as your query indicates), the percent of reproduced correlations that differ by more than |.05| from the observed correlations is reported.
The +/- .05 threshold is a common one for determining that a model adequately reproduces the observed relationships in the data. So, the fewer such residuals that exceed |.05| you have, the better the model-data fit. How many "excessive" (more than |.05|) residuals represents a poor overall model-data fit is a judgment call. Lower is better. The exact threshold is up to the researcher: Zero would be terrific; over 50% would (to me) suggest the need for a different factor structure (measurement model).
Since you have all of the residuals, you could also compute the SRMR (standardized root mean square residual), which in SEM/measurement models is the square root of the sum all all squared (reproduced vs. observed correlation) residuals (the N here usually includes variables with themselves, which by definition should have residuals of zero unless you have, say, a Heywood case). This statistic, too, usually uses a threshold of .05 or less as suggesting "good" model-data fit.
Good luck with your work!
If you provide more information you'll likely get more responses. For example, if you have 200 variables, 75 is few. Also, providing background on things like scatterplots and correlations (i.e., things you would have checked before doing a factor analysis) would useful. If some are highly correlated you would have of course dealt with this beforehand, but sometimes it is combinations of variables causing problems. Also several types of FA.
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