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.
I have been running a CFA on data from different countries. In one country, the model (which is a standard TPB model) continues to give problems of positive definite matrix). Dropping some variable does not help neither adding WITH statemnts. Inspecting TECH4 one factor (PBC) has correlation above 1 with other two factors. Which means it probably they are not distinguishable or dependent.
In my acse CFA is just preliminary to SEM, where this dependencies are indeed modelled. In fact, when I run the same model as SEM adding ON statements the problem resolves. My question is: 1) is it legitimate to run a full SEM model if the CFA (measurement) exhibits problems of non positive definite PSI? Or, put in other words, when you have a full SEM model in mind, should one start directly with that or should before run a separate CFA model only? 2) when I test for the country measurement invariance using MODEL: CONFIGURAL METRIC, I obviously get the same error message for that specific country. However, since I cannot model ON variables using MODEL, it means that I CANNOT test equivalence of a causal structure in that way, as is quite clear reading the manual ("only BY statements are allowed", "no partial measurement invariance is allowed"). To do that I need to run two separate models for the configural and metric model and do the testing, or are there any shortcuts?
This is indeed what I knew from my training! However, here is the full SEM model: ANALYSIS: ESTIMATOR IS MLM; MODEL: BENEFITS BY v4-v6; PBC BY v7-v9; MN BY v10-v12; SN BY v12-v15; ATU BY v16-v18; ATU ON BENEFITS; v19 ON ATU PBC MN SN; When I run CFA (without the ON statements) I get:
ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES BENEFITS PBC MN SN ATU ________ ________ ________ ________ ________ BENEFITS 1.000 PBC 1.001 1.000 MN 0.868 0.937 1.000 SN 0.670 1.028 0.681 1.000 ATU 0.917 0.956 0.880 0.632 1.000
The explanation is that the SEM model imposes strong further restrictions on the relationships among the variables. It says that ATU is influenced only by Benefits and not by the other factors. That could be a misspecification that changes the correlations. If you just-identify your structural part of the model, the problem will re-occur.