For development of a scale, I applied CFA using AMOS. Model fit indices such as RMSEA, SRMR, CFi, etc, are acceptable. However, the correlation between the factors are high, even a values of 1.03 is evident. Is this an issue? Or this is ok to report. Please suggest with some supportive references. Thanks
I am worried about your data or the output tables that you are looking for correlation in AMOS. Another suggestion is for imputed data and use SPSS for correlation where you will also get the results of the significant and insignificant correlation. Because AMOS does not tell about significant correlation.
Hello Shamas,
First, be sure that you are actually looking at an estimate of a correlation and not a covariance (while correlations are bound between 0 and |1|, covariances are unstandardized measures of association and are not bound). AMOS does not present values in standardized form by default; you have to include a specific request for them (see this link: https://www.ibm.com/support/pages/how-can-amos-display-standardized-estimates-drawing-area).
If you are, in fact, describing an instance of an estimated correlation or standardized path coefficient being in excess of |1|, then there are several possible explanations:
1. You have an instance of a Heywood case in your data set, which is often signaled by negative error variance estimates (which can be made more likely by using methods like pairwise deletion); or
2. See this brief explanation of some of the other reasons for "improper" solutions:: http://web.pdx.edu/~newsomj/semclass/ho_improper.pdf
Good luck with your work.
The fit of a model can be excellent and at the same time factors in the model can be highly or even perfectly correlated. This is not an issue per se, unless you hypothesize that there should be substantial discriminant validity between the factors. (A very high correlation may indicate a lack of discriminant validity between factors/constructs.) In case the correlation between two factors is very close to 1, the two factors could be collapsed into a single factor.
Syed Azamussan where do you get this very specific cutoff criterion from if you do not mind me asking? I am aware that multicollinearity can become an issues with highly correlated factors, but I have not come across this exact value before.
Shamas Suleman Arshad The indicators that you have taken for each constructs in running CFA, should be changed into composite variables with the help of SPSS and then compare the correlation, you will not get them highly correlated if you had performed EFA first.
Syed Azamussan I like Professor Gaskin's YouTube videos, I will go and take a look. Thank you.
Aslam Hasan Forgive me, but how would any of your suggestions adress the issue of higly correlated factors? Creating a composite score out of the manifest indicators would be a step back since latent variables have already been computed - with "acceptable" fit indices according to the author. Also, conducting an EFA does not prevent you from having highly correlated factors.
usually high correlation among factors are due to cross loading in performing EFA. If we remove the cross loaded indictors (if possible) and forward these indicators to their respective construct while running CFA, there is minimal chance of high correlation. if high correlation still exists (that may be possible due covarying independent construct in CFA and SEM), you can compute composite variable from indicators taken after running CFA and perform correlation in SPSS. these factors may be not so highly correlated as in case of correlation from SEM model. Syed Azamussan Marcel Grieger
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