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At the moment i'm doing a CFA (first and secondorder) for 23 items which should reflect three factors:  ANALYSIS: TYPE = GENERAL MISSING H1; ESTIMATOR = ML; MODEL: gedvis BY gv1* gv2 gv3 gv4 gv5 gv6 gv7 gv8; partic BY par1* par5 par6 par7 par8; samenw BY sam1* sam2 sam3 sam4 sam5 sam6 sam7 sam8 sam9; gedvis@1 partic@1 samenw@1; gedvis WITH partic samenw; partic WITH samenw; OUTPUT: MODINDICES RESIDUAL stand;  Altough this syntax did work well for my data of 2003, running this syntax for 2004 gives me the next error: NO CONVERGENCE IN THE MISSING DATA ESTIMATION OF THE SAMPLE STATISTICS. THIS MAY BE DUE TO SPARSE DATA LEADING TO A SINGULAR COVARIANCE MATRIX ESTIMATE. After listwise deletion, I did run it again, got the same error and so runned my syntax just for "cooperation" (=SAM). Too i used the BASICcommand and did get the next error: RESULTS FOR BASIC ANALYSIS ESTIMATED SAMPLE STATISTICS THE MISSING DATA EM ALGORITHM FOR THE H1 MODEL HAS NOT CONVERGED DUE TO ESTIMATED COVARIANCE MATRIX BEING NON POSITIVE DEFINITE. PROBLEM INVOLVING VARIABLE: 5 I understand SAM5 is here the problem, but leaving out this variable brings me to SAM8 as problem involving variable. Leaving this one out too, the problems are solved (as i can estimate now). What is/could be the main problem of this error (especially the last one)? What is wrong with my data? And how can i solve it? Thanks! 


This cannot be answered without looking at your data. Please send your input, data, output, and license number to support@statmodel.com. 


Hello, 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? Thanks. 


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. 


It sounds like you should try an EFA to see if the CFA specified is reasonable for the data. It sounds like it is not. You sample sizes are small for the size of your model. 


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? 


1) I think it is a good idea to do CFA on the measurement part first. I would investigate why SEM doesn't show the high correlation when CFA does. 2) You can yourself set up the restrictons for a configural, metric, or scalar model for the measurement part of a SEM. And do the testing by comparing two runs. 


This is indeed what I knew from my training! However, here is the full SEM model: ANALYSIS: ESTIMATOR IS MLM; MODEL: BENEFITS BY v4v6; PBC BY v7v9; MN BY v10v12; SN BY v12v15; ATU BY v16v18; 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 When I run the SEM model I get: ESTIMATED CORRELATION MATRIX FOR THE LATENT VARIABLES BENEFITS PBC MN SN ATU ________ ________ ________ ________ ________ BENEFITS 1.000 PBC 0.827 1.000 MN 0.890 0.784 1.000 SN 0.674 0.853 0.681 1.000 ATU 0.934 0.772 0.831 0.630 1.000 V19 0.754 0.826 0.714 0.623 0.719 Any explanation? 


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 justidentify your structural part of the model, the problem will reoccur. 


Dear Professors Muthen, When one runs CFA, and the output highlights nonpositive definite covariance matrix problem, 1) Does the fit get affected by this? 2) Is it even meaningful to interpret the fit indices? 3) Can I have trust in the correctness of item loadings, and their significance? Thanking you in advance Kind regards Alex 


The results are not interpretable. You should send the output and your license number to support@statmodel.com. 

mdehne posted on Monday, June 11, 2018  4:40 am



Dear Profs Muthén I am conducting a CFA with 11 factors and a sample size of N = 3930 students. In my output, the following message is displayed: WARNING: THE LATENT VARIABLE COVARIANCE MATRIX (PSI) IS NOT POSITIVE DEFINITE. [...] However, I neither found a Heywood case nor a correlation greater 1. How can I solve this problem? 


Send your output to Support along with your license number. 

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