Significance of factor correlations PreviousNext
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 anon9210 posted on Sunday, March 27, 2011 - 1:38 pm

I am running some EFAs for a couple of large datasets with Ns > 3000 and > 5000, respectively. I noticed that despite the large Ns, when I run EFAs with these datasets, I sometimes get results with interfactor correlations that are not significant. The parameter estimates look normal. I understand what's happening computationally - i.e., that the factor correlations estimated by the model are relatively small and/or standard errors are relatively large. But, in some cases I get a correlation of approx .20 between factors, it's hard to believe that it is not significant given the size of my sample. How would I interpret this practically in relation to the data - e.g., that there are a few people in the dataset that are driving these correlations between factors?

Also, just to double-check, I generated factor scores using ESEM and tried using a regular Pearson correlation. These are generally larger in magnitude than the EFA factor correlations in Mplus. However, even rs of about .06 or .07 end up statistically significant. So, would I be right in assuming that the meaning of this statistical significance is very different from the EFA factor correlation significance?

Thanks for your help in advance.
 Linda K. Muthen posted on Monday, March 28, 2011 - 10:07 am
Please send the input, data, outputs and your license number to
 Sean Delaney posted on Saturday, February 04, 2012 - 7:31 am
Hello, I did an EFA using Mplus and it calculated the promax factor correlations. I wish to report on the 3-factor solution and on the correlations among the factors. A journal reviewer has asked me to state if the correlation among the factors is significant. I would be grateful if you could tell me where in the output table I can find the significance of the correlations. I have tried, unsuccessfully, to find this in the OUTPUT command chapter. Thank you.
 Linda K. Muthen posted on Saturday, February 04, 2012 - 7:45 am
These values are given in the output. First come the estimates of the correlations, then the standard errors, and then the ratio which is a z-test in large samples.
 Sean Delaney posted on Saturday, February 04, 2012 - 10:31 am
Thanks for your speedy reply. My output seems to be different. In the section of the Output under the heading "EXPLORATORY FACTOR ANALYSIS WITH THREE FACTORS" the headings I have are the "RMS Residual," "Promax Rotated Loadings," "Promax Factor Correlations," "Estimated Residual Variances" (for each item), "Factor Structure" and "Factor Determinances." I can't find the standard errors or the ratio of the correlations.

I have noted the Promax Factor Correlations in the article and the reviewer wants me to state the significance of the correlations among the factors. I am not sure where to find that information or if I need to change my commands to get them. I am using an older version of MPlus (version 5).
 Linda K. Muthen posted on Saturday, February 04, 2012 - 4:42 pm
These values have been available for some time. It sounds like they were not available in Version 5.
 H Steen posted on Wednesday, May 15, 2013 - 8:04 am
Hi Linda,

If doing a CFA with WLSMV estimator, are the correlations between factors still pearson correlations, or a different type?

Thank you very much in advance.
 Linda K. Muthen posted on Wednesday, May 15, 2013 - 8:44 am
Factors are continuous variables. Correlations among continuous variables are Pearson correlations.
 Lin Xiangbin posted on Tuesday, June 30, 2015 - 11:05 pm

I'm using version 6, and it seems that significance of factor correlations are not stated in my EFA output, as per Sean's post. May I know how can I calculate them myself?

Thank you.
 Bengt O. Muthen posted on Wednesday, July 01, 2015 - 5:02 pm
That is very complex and can only be done using a computer program with matrix algebra. It is better to get Mplus Version 7.31.
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