Hi. I am running a CFA on a commonly used questionnaire with 14 items that load from 7 latent constructs. Total N is 308. The SEM shows a covariance between two of the latent constructs above 1 when standardized. However, when I run bivariate correlation analysis of the seven constructs in SPSS (as manifest variables off cause) the correlation between this pair is .71. Which is the highest correlation among the constructs. The others range between .24 and .57.
When analyzing the estimated covariances in AMOS the problematic one has .55 and is not the strongest covariance. One of the two problematic latent constructs has a covariance of .60 with another latent construct.
I also checked all variables for multicollinearity by running linear regression with all variables included, leaving one as the dependant, and then shifted for each time I ran it. It did not identify any VIF above 2.3 between any of the 14 variables. I also ran the same test on the seven constructs. Again no VIF above 2.3, so it should not be a multicollinearity problem, should it?
Any suggestions for what I am doing wrong?
I suppose that if you have 7 factors with 14 items must be two items per factor which is questionable and take into account factor loads greater than .50 of the indicators.
Thanks for your answer, and yes each factor has two items each. Thats how the system is built up and it is validated several times, even if two items is low.
However, regarding factor loadings for the two factors with the covariance above 1. The first one has .69 and .81, The second one has .52 and .73. But there are other factors that has even stronger factor loadings in this questionnaire system, one as high as .72 and .89 but the covariances to other factors are not out of range because of that.
Hello Rune,
Not to question your work, but are you certain that the AMOS output is showing standardized values? The reason I ask is that standardized values are not the default in AMOS, and have to be specifically elicited.
Of course, for factor identification, the ideal situation is to have at least three indicators per factor, but you are dealing with an existing measure, so there's likely no payoff to trying to change that!
Unless you're seeing error variance estimates that are negative, the presence of a covariance that exceeds 1 is not an automatic indication of a problem, especially when you're entertaining a model that has correlated factors. Check this brief note by Karl Jorsekog: http://www.statmodel.com/download/Joreskog.pdf
Good luck with your work.
Thanks David,
Yes I am referring to the standardized values. The unstandardized estimate for the problematic covariance is .55
Thanks for the reference to the note by Karl Joreskog. That was new information for me, but not sure if I could reference it when publishing
You should read Kline 2016, 195 Kline 2016, 252 Henseler et al. 2015, 122
Kline, R. B. 2016. Principles and practice of structural equation modeling (4th ed.). New York: Guilford.
Thanks Otto Ilmari Burman
I have got the Kline 2016 book but don't find a clear answer there. Problematic correlations is mentioned at page 302 but the solution offered is problematic since I have predefined factors ( a well known questionnaire). Off cause chapter 2 explaining the regression fundamentals of SEM lays the foundation for the posibility of a result above 1.
I am not sure if you were referring to page 195 and 252, but at page 195 possible problems when there are only two indicators are mentioned. At page 252 covariance residuals are mentioned, but I don't understand if that is related.
http://www.ottoburman.fi/documents/Burman_vaitos_19062019.pdf page 243 has a picture which is referring to Kline p. 252-253 and how the AMOS Residual moments gives the values... Kline (2016) says that model development also involves including statistically uncertain variables when it is theoretically justifiable :)
Correlation Residuals = ABS(Implied Correlations (AMOS) - Pearson Correlations (SPSS)) Absolute correlations residuals that exceed 0,10 may indicate poor prediction for that variable pair ((Kline 2016, 251-252) .
But he does not like the situation with too few indicators... I'm sorry that my thesis is in finish language but you can use the translator;/
Hello,
May be you have the same problem like the negative variance in the model.
Please consult the link for possible solutions.
https://www.ibm.com/support/pages/amos-states-some-model-variance-values-are-negative
Otto Ilmari Burman , I have tried to understand the text and illustration in your thesis and have read the suggested pages (252 and 253 in Kline a couple of times, but cannot see that it is explaining the problem I have met. I see in the table in your thesis a standardized residual covariance value of 2.13. But has not enough knowledge do understand how you explain that.
Since one of the suggestions in the link of Moez Bellaaj was to change the method of estimation I tried that, but it does not run without maximum-likelihood-estimation.
So far, I find the suggested reading of Jøreskogs article the best explanation, but I am more than open for a deeper understanding.
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