Do you have any estimated error variances (residual variances) that are negative?
Anonymous posted on Tuesday, April 16, 2002 - 6:49 am
Yes.The residual variance of the variable wich the loading is greater than one is negative (-0.07). I have tried to fix this residual variance to zero, but I have got the same result for the loading. How can I resolve this problem? Thank you for any suggestion ?
Theoretically, a solution with a negative residual variance is inadmissable. You could accept the solution for one less factor. You could not use this variable. However, if the solution fits your theory best and all of the factors are interpretable, you could just accept the fact that in your sample, this factor loading is slightly greater than one. Perhaps this item is extremely reliable.
By the way, I'm not sure how you tried to fix the residual variance to zero in EFA.
Anonymous posted on Friday, January 30, 2004 - 12:46 pm
If the answer to your follow-up question (April 15) is that I have no "estimated error variances (residual variances) that are negative" (in other words, I have a factor loading > 1 and the residual variance is positive), then everything is okay given the explanation by Joreskog in his 1999 article "How Large Can a Standarized Coefficient be?"?
John posted on Saturday, April 30, 2005 - 11:03 am
In doing EFA, I have observed the following situations. A factor loading >1 with estimated variance negative and (also positive for other variable), A factor loading <1 with negative error variance.What is your suggestion? Thank you
bmuthen posted on Saturday, April 30, 2005 - 11:28 am
Negative residual variances suggest that too many factors are being extracted, although they can also be obtained with small samples. Apart from the case of negative residual variances, loadings > 1 are possible when there are several correlated factors (see also writings by Joreskog on the LISREL web site).
Anonymous posted on Sunday, May 01, 2005 - 10:47 pm
Thank you bmuthen for your explanation. I have also a problem like John. The situation may happen due to multicollinearity problem. May you suggest a remedial measure to fix negative residuals? Is that possible to report loadings>1?And last question is to do EFA analysis we need too many observations,say at least 200.What are the problems if we use EFA with 90 cases and 30 variables?
If you have negative residual variances you need to change your model. As stated above, you may have extracted too many factors. Loadings greater than one can occur. If this happens without negative residual variances, they can be reported. The sample size depends on many factors. The only way to know for certain how many observations are needed is to do a simulation study.
I've read these different comments and it seems that a way to avoid loading greater than one and/or negative residual, one have to increase ones sample size or to decrease the number of factor retained. What could I do in my case if I have only one factor and a sample size of more than 9,000 subjects and nevertheless one loading of 1.012 with a negative residual variance?