I am running the following model: MODEL: AKZ BY Akz1 Akz2; GEi BY GewI1 GewI2; GEA BY GewA1 GewA2; BEW BY Bewu1 Bewu2; NRE BY Nrea1 Nrea2; EXP BY Expo1 Expo2; REL BY Rela1 Rela2; EIN BY eins1 eins2; gew by gei gea; atti by EXP AKZ NRE REL EIN; atte by BEW gew; atte with atti;
in three independent samples (n=300, n=200 and n=160). In two of them the model works (i.e. I do not get any error message and all coefficients look fine) but in the n=300 sample I get the following error message.
WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE. THIS COULD INDICATE A NEGATIVE VARIANCE/RESIDUAL VARIANCE FOR A LATENT VARIABLE, A CORRELATION GREATER OR EQUAL TO ONE BETWEEN TWO LATENT VARIABLES, OR A LINEAR DEPENDENCY AMONG MORE THAN TWO LATENT VARIABLES. CHECK THE TECH4 OUTPUT FOR MORE INFORMATION. PROBLEM INVOLVING VARIABLE ATTENT.
Since the model works in two samples I guess the problem does not have to do with the model itself. How could I fix the problem?
It sounds like the model is not correct for the sample of 300. Look at TECH4 to see what the problem is. It is likely that attent has a negative residual variance.
ClaudiaB posted on Monday, February 11, 2013 - 2:50 am
I think the problem is that ATTENT and ATTITU have a correlation greater than 1.
According to the fit indices, it is the model that suits best to the data (in all three samples) when compared to other hierarchical models. Even in the sample of 300, despite the error message, the Chi square is significantly better than in the comparison models. Thus the results seem to suggest that this is the model that I should retain.
Is there some other way I can calculate this model in this sample?
When two variables correlate greater than one, they cannot both be kept in the model. Any fit statistics and results should not be interpreted in this case. It appears the same model is not appropriate for this sample.
ClaudiaB posted on Tuesday, February 12, 2013 - 3:55 am
Thank you Linda.
The model is actually giving the same error even in the sample of 200, I overlooked that before. It thus works only in the sample of 160. The correlation which is greater than 1 in both other samples (200 and 300), is very near to 1 (.97) even in the sample of 160. Which makes me suspicious with reference to the model.
I checked that the error does not have to do with the small number of observed variables and it does not: I get the same error when I calculate the model from the items (4 to 5 per factor instead of 2 parcels).
I am puzzled because the model is theoretically meaningful and would be consistent with previous results. I am not sure if the model just does not fit for my samples or if I did some mistake in the model specification. I would be glad for any tip about possible causes I could check. Thank you.