Message/Author 

Laney Sims posted on Thursday, August 31, 2006  9:02 am



I have a simple model for a longitudinal study with two variables over three points in time. My input statement is: Analysis: type = missing H1; estimator=ML; Model: pbrt2 on pbrt1 aainv1; aainv2 on pbrt1 aainv1; pbrt3 on pbrt2 aainv2; aainv3 on pbrt2 aainv2; pbrt1 with aainv1; pbrt2 with aainv2; pbrt3 with aainv3; Output: sampstat; standardized; I am getting the following message in the output: THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.176D13. PROBLEM INVOLVING PARAMETER 23. Could you explain how my results might be affected by this? Thank you. 


The results are not valid if a model is not identified. If you ask for TECH1 in the OUTPUT command, you can see what parameter 23 is. If this does not help, please send your input, data, output, and license number to support@statmodel.com. 

Laney Sims posted on Friday, September 01, 2006  7:37 am



Parameter 23 is the value in the PSI matrix corresponding to aainv1 vs. aainv1, which appears to be the variance of that variable. I don't see anything unusual about the variance of aainv1 (0.234) compared to the others in the SAMPSTAT output or the MODEL output. Do you have any suggestions, or should I email my files for additional help? Thank you. 


Please send your input, data, output, and license number to support@statmodel.com. 

Kelvin Choi posted on Thursday, September 04, 2008  6:52 pm



I have a similar problem as described above. I asked for TECH1 and found out the parameter is edu vs. edu (covariance coverage=0.935). Are the results still trustworthy? If not, how can I resolve this issue? Thanks. 


Please send your input, data, output, and license number to support@statmodel.com. 


I am having a similar problem when I weight my data. That is, the model converges fine with unweighted data, but when I add the weight, I get the same error message: THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.209D10. PROBLEM INVOLVING PARAMETER 114. If the results were fine with unweighted data, can I trust the weighted results? 


I could not say without more information. Please send your input, data, output, and license number to support@statmodel.com. 


I'm having a similar problem. I am running a multigroup analysis. The warning also points to the variance of one of my variables. I looked at the descriptives for this variable and everything looks ok, but there is a lot of missing data on this variable. Could the amount of missing data cause this problem? Is there a way that I can still include this variable in my model? It is a very important control. Thanks! 


I could not say without more information. Please send your input, data, output, and license number to support@statmodel.com. 


Dear Linda, I am testing a sequential mediation model with Mplus. However, when I reverse my model (to say something about causality), I get the following error message: MAXIMUM LOGLIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS 5603.305 THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.236D12. PROBLEM INVOLVING PARAMETER 45. It does run my model, but my reversed model indicates better fit, which makes no sense theoretically. Is it possible this error message influences my results? Kind regards, Kim 


I would need to see the full output to answer this. Please send it and your license number to support@statmodel.com. 

Elise Pas posted on Friday, June 24, 2011  11:40 am



I have gotten the same error as discussed above for a CFA conducted with a clustering variable. THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.260D17. PROBLEM INVOLVING PARAMETER 23 In addition, my output said: THIS IS MOST LIKELY DUE TO HAVING MORE PARAMETERS THAN THE NUMBER OF CLUSTERS MINUS THE NUMBER OF STRATA WITH MORE THAN ONE CLUSTER. I entered the cluster variable to account for nesting in my data but will not be including any betweenlevel specifications. To test if the issue is in fact the cluster size, I ran the same CFA without the cluster ID (or the type=COMPLEX command) and the entire error message disappeared. It seems I received this message because of my cluster size (n = 23) being smaller than the number of freed parameters (i.e., 31) but what I do not understand is why this error message would also indicate an issue with a parameter (which in this case was the psi of an observed variable). Are the number of freed parameters actually the problem? And if so, how do I solve this problem? Thanks, Elise 


The number of clusters is the number of independent observations in your data set. The warning is telling you that you have more parameters than you have independent observations. The impact of this on the results has not been studied. This is simply a warning. 


Hi, I am running a path model with three latent "predictors", a single outcome, and 4 covariates (age, gender, two dummy codes for ethnicity). When I run the path model without any of the covariates, my model converges and achieves adequate fit. However, when I include paths from each of the 4 covariates to the outcome variable, I recieve the following error messages: THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.316D18. PROBLEM INVOLVING PARAMETER 52. 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 PGENDER. There are no negative residual variances, correlations greater than 1, etc. Also, with parameter 52, this is a covariance between PGENDER and PAGE, and I cannot find a problem in the data. Can you make any recommendations about how to proceed? Thanks! 


Please send your output and license number to support@statmodel.com. 

EFried posted on Friday, May 11, 2012  4:47 am



I am facing the same problem, in a GMM with 5 measurement points, trying to run a model with 3 classes. THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.937D11. PROBLEM INVOLVING PARAMETER 19. TECH1 output looks normal, as does TECH4 (no PSI problems). The solution that MPLUS finds is implausible for this model, so I would need to explore what causes these issues. Thank you 


Please send the output and your license number to support@statmodel.com. 

Susan Pe posted on Tuesday, August 28, 2012  4:58 pm



Hi I am doing 2level, different time points nested within individuals. I have 3 items. My Mplus commands include cluster = firmid; within = time; Analysis: Type = twolevel; Model: %within% RD by exp newcar oldcar; If I run CFA with 2 items, I get: THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX If I run CFA with 3 items, I get: THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO AN ILLCONDITIONED FISHER INFORMATION MATRIX. CHANGE YOUR MODEL AND/OR STARTING VALUES. THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO A NONPOSITIVE DEFINITE FISHER INFORMATION MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.562D10. THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE COMPUTED. THIS IS OFTEN DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. CHANGE YOUR MODEL AND/OR STARTING VALUES. PROBLEM INVOLVING PARAMETER 5. What is the problem? Thank you. 


A factor with two indicators is not identified. Please send the output and your license number to support@statmodel.com. 


I have a similar problem. I have received the error: THE MODEL ESTIMATION TERMINATED NORMALLY THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.148D09. PROBLEM INVOLVING PARAMETER 149. I’m running a multigroup model and this is the free model. This error did not occur for the constrained model. I believe this parameter is the disturbance covariance for two of the outcome variables. Would you please tell me how this affects my results? Thank you very much! 


Please send the output and your license number to support@statmodel.com. 


I'm running a basic regression model with an interaction. I'm also using auxiliary variables. I received the following error message when I tried to probe the interaction. THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.227D10. PROBLEM INVOLVING PARAMETER 13. THIS IS MOST LIKELY DUE TO VARIABLE M11WORKR BEING DICHOTOMOUS BUT DECLARED AS CONTINUOUS. Parameter 13 is the variance of my interaction term. M11WORKR is one of my auxiliary variables. I have it listed using the command auxiliary = (m). It is dichotomous, but I'm not sure where in my syntax it is declared as continuous. 


Variables on the AUXILIARY list are treated as continuous variables. If a variable on this list is binary, it can prompt the message above because the mean and variance of a binary variable are not orthogonal. If this is the cause of the message, you can ignore it. All variables are assumed to be continous unless they are put on a list like CATEGORICAL, CENSORED, COUNT etc. 


Hello, I'm trying to conduct an LPA with four indicators. I have received the error: THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.102D15. PROBLEM INVOLVING PARAMETER 1. I have checked parameter 1  it's on the NU matrix, but I'm not sure what this means. Can you please help? Thanks, Danyel 


Please send the output and your license number to support@statmodel.com. 


Hello, I'm running into a similar issue. When running a fairly simple path analytic model, I get this message: THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS0.202D19.PROBLEM INVOLVING PARAMETER 99. Parameter 99 is the variance of one of the variables in the model,and is rather large (as it should be). The model still runs, and standard errors are still estimated. Is this message ignorable? If not do you have suggestions for how to handle this issue? Thanks! Jami 


Please send the output and your license number to support@statmodel.com. 


Hello, I encountered a NPD matrix recently while fitting a structural model with composite variables. The offending factor had a small negative residual variance. I addressed the problem, on the advice of a colleague, with this syntax: factor@.00001; which eliminated the NDP, and appeared to have little or no effect on the fit of the model. Looking through the user's manual, I can't figure out what exactly this syntax means, why it seems to serve this function, and whether it is appropriate. If it is not appropriate, can you suggest another means of addressing small negative residual variances? Many thanks! 


You are fixing the residual variance of factor to .00001. If a residual variance is estimated at a small negative nonsignificant value, many fix it to zero. 


Hello, I'm running a multigroup model with dummy variables as predictors. One of my groups is very small (n= 14). I received this error. Does this mean by results are not valid and I cannot perform a multigroup tests? Thank you, Danyel THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.128D17. PROBLEM INVOLVING PARAMETER 24. THIS IS MOST LIKELY DUE TO HAVING MORE PARAMETERS THAN THE SAMPLE SIZE IN ONE OF THE GROUPS. 


A sample size of 14 is too small for multiple group analysis. 


Thank you very much. Danyel 


Hi, I am having a similar problem as many of the previous posters in terms of the following error messages: THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.149D17. PROBLEM INVOLVING PARAMETER 54. THE NONIDENTIFICATION IS MOST LIKELY DUE TO HAVING MORE PARAMETERS THAN THE NUMBER OF CLUSTERS. REDUCE THE NUMBER OF PARAMETERS." I have checked the parameter and still can't make sense of the error message. Thanks. 


You most likely have more parameters than clusters. Check that. This warning is reminding you that independence of observations is at the cluster level. The effect of having more parameters than clusters may have an effect on the results. 


Thank you for the reply. I do have about 63 parameters and 52 clusters. Does this affect only the parameter estimates (due to standard errors) or does this influence the chi squared tests and fit indices as well? I recall my mplus instructor suggesting that one may use Bayes to get more accurate parameter estimates. In the case that I cannot get more clusters, is it acceptable to report the chisquared results and fit indices from the ML solution and the parameter estimates from the Bayes solution? Thanks! 


This would effect that standard errors and fit statistics. The only way to know how much would be to do a Monte Carlo simulation study based on your analysis. I don't think Bayes would make any difference. You should report only results from one estimator. 


Thank you. I ran the Bayes estimator but I did not get any error messages. The parameter estimates are similar to those obtained from the ML solution. 


Bayes estimation does not do this particular kind of check; it is MLoriented. This doesn't mean that the Bayes solution is free of the potential problem listed in the ML run. 


Thank you. It seems like my options are to increase the number of clusters in my data or reduce the number of parameters estimated (difficult in this case because of the theoretical model of interest). 


Or, you can do a little simulation in Mplus to check if you don't need to worry (that may very well be true). This would be a suitable topic for a methods grad student to work on. 


How does Mplus check if a given matrix (in this case the Psi matrix) is positive definite? While running a simulation designed to test for model identification (using Bayes estimation) I ran into the following note from Mplus about 200 times: THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY. THE POSTERIOR COVARIANCE MATRIX FOR PSI IS NOT POSITIVE DEFINITE, AS IT SHOULD BE. THE PROBLEM OCCURRED IN CHAIN 1. For each of the 200, I extracted the most recent update of values corresponding to the PSI matrix of the respective chain (either chain 1 or 2). Then I performed a series of tests: First: All Psi matrices were full rank, and none contained negative variances on the the diagonal. 50 contained negative eigen values. Many of the remaining 150 contained small eigen values (e.g. .000000001), so I imagine Mplus (given double precision) rounds this to 0 and assumes an eigen value equal to 0. BUT in some of those 150, the smallest eigen value was positive and (somewhat) large. For example, one replication had the smallest eigen value of .003. Furthermore, the determinants of the remaining 150 replications were also positive. Therefore, I am wondering how Mplus determines if a given matrix is positive definite. Would it round an eigen value of .003 to 0? Any help is greatly appreciated. Jon 


We consider a matrix to be not positive definite if when we attempt to invert it a pivot (something we need to divide by) is less than 10^10. To avoid these problems you can add a weakly informative prior for the psi matrix. That is an inverse wishart prior IW(I,p+1) see Section 10.2 http://www.statmodel2.com/download/BayesAdvantages18.pdf Also in order for you to get this kind of precision you need to get the trace parameters with 16 significant digits which I don't think you can do. 

Nara Jang posted on Monday, June 23, 2014  3:27 pm



Dear Dr. Muthen, I ran the Latent interaction to see if there is moderating effects, resulting in no significant moderating effects. And there was warning. I tried to delete or make correlation with other indicators and then the other parameters were problematic. THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.902D18. PROBLEM INVOLVING PARAMETER 27. I used FIML imputation and ran it, resulting in significant moderating effects and no such a warning. The reason of FIML imputation was the moderator indicators has lots of missing data. Would you answer following questions. (1) Would you explain to me why a warning of nonpositive derivative matrix appeared. (2) If there is a solution, would you tell me? (3) Would you tell me which one I should report either the result without imputation or the result with FIML imputation? If there is no problem with FIML imputation. (4) If the missing values are large, the moderating effects are not trustworthy? (5) If so, would you tell me the criteria of percentage of missing values in the dataset. Thank you so much for your valuable time and advice! Best regards, Nara Jang 


If you can do FIML without imputation, I think that is preferable. So you want to understand why you get the warning you show here. You can send your output, data, and license number to Support. But if you want, you can also send the imputation run. 

Nara Jang posted on Friday, July 04, 2014  6:16 pm



Dear Dr. Muthen, In my previous result, I did not use categorical options. After adding categorical variables, a warning shows as follows. Would you give me your expert advice, please? THE ESTIMATED COVARIANCE MATRIX COULD NOT BE INVERTED. COMPUTATION COULD NOT BE COMPLETED IN ITERATION 7. CHANGE YOUR MODEL AND/OR STARTING VALUES. I really appreciate for your great help! 


Please send your output and license number to support@statmodel.com. 


Hello Drs. Muthen, When running a twolevel model with random slopes, I have received the following error on my output: THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.778D10. PROBLEM INVOLVING THE FOLLOWING PARAMETER: Parameter 13, %BETWEEN%: S2 ON GXRQ Parameter 13 is an interaction term between a binary and continuous variable. This error seems similar to Danielle Roubinov's issue posted on February 1, 2013. Unlike that situation, however, I have not specified any auxiliary variables. How might I know whether or not this warning can be ignored? Many thanks in advance for your help. 


We would have to see the output. 


Hello Drs. Muthen, I’ve received the following error on my output: THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.137D19. PROBLEM INVOLVING THE FOLLOWING PARAMETER: Parameter 33, NOCHILD MODEL COMMAND WITH FINAL ESTIMATES USED AS STARTING VALUES nochild WITH age*0.54404; nochild WITH house*0.03903; nochild WITH phyabuse*0.00280; nochild WITH age1st*0.15714; nochild WITH reftx*0.01356; I’m running a basic logistic regression with 6 variables. Can you please help identify the problem? Thank you 


Please send the output and your license number to support@statmodel.com. 


Dear Linda and Bengt, I received the following error on my output and I am not sure if I can trust it: THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.103D32. PROBLEM INVOLVING THE FOLLOWING PARAMETER: Parameter 1, %WITHIN%: [ DWEVI ] This is the model I entered. I am not sure why I get this error. There is nothing wrong with the DWEVI parameter. USEVARIABLES ARE DWEVi DWEDe DWEAbs DWL DTP DComplex DRoleConf DRAmb resp_nr; CLUSTER IS resp_nr; within are DWEVi DWEDe DWEAbs DWL DTP DComplex DRoleConf DRAmb; Define: Center DWEVi DWEDe DWEAbs DWL DTP DComplex DRoleConf DRAmb (groupmean); ANALYSIS: Type is GENERAL twolevel; iterations is 5000; Estimator is MLR; MODEL: %WITHIN% WE by DWEVi DWEDe DWEAbs; WE on DWL DTP DComplex DRoleConf DRAmb; I would appreciate your help! Andrea 


I don't think you want to groupmean center your factor indicators. 


Thanks for your prompt response. I group mean centred the variable based on previous studies. For example: Binnewies, Sonnentag, & Mojza 2010 stated in their study they the following: We had data at two levels: the person level (Level 2) and the week level (Level 1). Weeklevel data were nested within persons. We used the MLwiN software (Rasbash et al., 2000) to analyse the data with hierarchical linear modelling (Snijders & Bosker, 1999). To test for indirect effects of recovery experiences during the weekend on weekly performance, we applied multilevel structural equation modelling to our data (Mehta & Neale, 2005) using the Mplus software (Muthén & Muthén, 2006). To test our hypotheses, personlevel predictor variables were centred around the grand mean while weeklevel predictor variables were centred around the respective person mean (group mean centring). We applied group mean centring because we were interested in withinperson relations. In my study, I am also interested in within person relations. I used ESM to collect data for 3 different moments within a day, and these days are nested within individuals. I want to examine the effect that different demands have on engagement, which is all happening at the within moment level. Based on that reason, I also centred my predictors. However, is there a better way to do it? I appreciate your help! 


The factor indicators are not predictors, they are DVs (influenced by the factor). Do you get the same error message when you exclude the factor indicators from the groupmean centering? 


of course!! The error is gone :D Thanks a lot!!! 


Hi Bengt, I jus realised that the error is gone, but in the manual it is stated on chapter 9 pg.261 that "The WITHIN option is used to identify the variables in the data set that are measured on the individual level and modeled only on the within level. They are specified to have no variance in the between part of the model." However, my variables have variance in the between part. I am not interested in these relations, but by group mean centring I was controlling for this between level variability. However, if I just leave my indicators in the within option part without being groupmean centred (otherwise I get an error as they are indicators of a within latent variable) would this between person variability would be controlled for? I am not sure how else would I be able to control for this between variability? 


I would add a betweenlevel factor for these indicators to capture their betweenlevel variances. See twolevel factor analysis examples in the UG. 


Great! Thanks! I did the following just to make sure I did it correctly following the instruction from the UG. All the variables (except resp_nr TWE) are measure at different moments asking people about how they feel right now. Thus they are nested within the person (resp_nr). I did not specify within for them, but created their respective latent variable at the between and within level. Thus, expecting Mplus to person centred them implicitly without me specifying it. Thus, may I assume now that the between and within variability are taken care of? I did not get any errors I am not interested in their relations at the between level, except for the relation between momentary engagement and trait engagement, which I model by BWE ON TWE. USEVARIABLES ARE Pressure Workload Variety Import Auto Feedback Vigor Dedic Absorpt resp_nr TWE; BETWEEN are TWE; CLUSTER IS resp_nr; DEFINE: CENTER TWE (grandmean); ANALYSIS: TYPE = TWOLEVEL RANDOM; MODEL: %BETWEEN% BJD by Pressure Workload; BJR by Variety Import Auto Feedback; BWE by Vigor Dedic Absorpt; Vigor Dedic Absorpt Variety Import Auto Feedback Pressure Workload@0; BWE ON TWE; %WITHIN% JD by Pressure Workload; JR by Variety Import Auto Feedback; WE by Vigor Dedic Absorpt; WE ON JR JD; 


Looks good, except your statement Vigor Dedic Absorpt Variety Import Auto Feedback Pressure Workload@0; sets the residual variance at zero for only workload. You want to say pressureabsorpt@0; 


Hi Bengt, You are right, Thanks! I fixed it. However, I am unable to get standardised estimates, is there a way to obtain them with another command? Also, I am not sure I can completely understand this reasoning (below). I set the residuals to zero because on chapter 9 pg 276 it was stated that: In this model, the residual variances for the factor indicators in the between part of the model are fixed at zero. If factor loadings are constrained to be equal across the within and the between levels, this implies a model where the regression of the within factor on x1 and x2 has a random intercept varying across the clusters. MODEL: %WITHIN% fw BY y1y4; fw ON x1 x2; %BETWEEN% fb BY y1y4; y1y4@0; fb ON w Is there an article that can explain this a bit more in depth? I followed the procedure, but I would like to still understand why setting the residual variances to zero at the between level constrains the factor loadings to be equal across levels and provide a random intercept at the moment level regression? I looked it up and found articles about invariance testing, negative residuals, small sample sizes, but I am not sure if these are in line with the manual's purpose of setting the residuals to zero at the between level. Thought it would be better to ask you this instead. I appreciate your help! Andrea 


Dear Linda, I am trying to model a basic crosssection data on a binary outcome. Please see below: I however get the response: =================================== ONE OR MORE PARAMETERS WERE FIXED TO AVOID SINGULARITY OF THE INFORMATION MATRIX. THE SINGULARITY IS MOST LIKELY BECAUSE THE MODEL IS NOT IDENTIFIED, OR BECAUSE OF EMPTY CELLS IN THE JOINT DISTRIBUTION OF THE CATEGORICAL VARIABLES IN THE MODEL. THE FOLLOWING PARAMETERS WERE FIXED: Parameter 30, S ON EXP Parameter 31, S ON EV Parameter 32, S ON BT Parameter 34, [ S$1 ] ==================================== I also observe from the output that the betas are very large apart from those that are fixed. I will be very grateful for any support I can get. Thanks. VARIABLE: NAMES ARE S age siz ed exp d1 d2 d3 ac2 ac3 ac4 Ev Bt; categorical is S; Analysis: Type = random; Estimator = MLR; Model: dc by d1 d2 d3; dc@1; ac by ac2 ac3 ac4; ac@1; ac3 with ac2; d1 with ac2; d1 with ac3; ac4 with ac2; edc  dc XWITH ev; eac  ac XWITH ev; bdc  dc XWITH bt; bac  ac XWITH bt; S on age siz ed exp dc ac Ev Bt edc eac bac bdc; Output: tech1; 


Please send the output and your license number to support@statmodel.com. 


Hello, I am running a model with TYPE=IMPUTATION and TECH9 reports the following error for dataset 4 (with the other datasets the estimation terminated normally): THE ESTIMATED BETWEEN COVARIANCE MATRIX COULD NOT BE INVERTED. COMPUTATION COULD NOT BE COMPLETED IN ITERATION 146. CHANGE YOUR MODEL AND/OR STARTING VALUES. I tried the same analysis with dataset 4 only, in order to search for problematic parameters. But with dataset 4 only, the model estimation terminated normally (and ends with iteration 241). Do you have any suggestions how to fix the MIanalysis? Relevant background information might be:  The five datasets contain identical information (and still have missings) except for two variables which are plausible value data. I randomly assigned the 5 PVs per variable to one of the five datasets.  I am running a TWOLEVEL path model with two variables being categorical (one DV and one mediator) and all others being continuous.  I use weights on both levels and INTEGRATION = MONTECARLO.  The only part I changed is the DATAStatement (dataset 4 only vs. MIdatfile + TYPE=IMPUTATION). Kind regards Katrin 


It is impossible to say what is happening without see in the outputs and data. Please send them and your license number to support@statmodel.com. Be sure you have run this with Version 7.3 as a first step. 


Hi, I'm running a longitudinal SEM model based on data collected from students at 17 sites (schools). I'd like to use type=complex to adjust for site influence but when I do, I get the following error: THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.264D16. PROBLEM INVOLVING THE FOLLOWING PARAMETER: Parameter 21, POS2 WITH POS1 THIS IS MOST LIKELY DUE TO HAVING MORE PARAMETERS THAN THE NUMBER OF CLUSTERS MINUS THE NUMBER OF STRATA WITH MORE THAN ONE CLUSTER. I dug around to see what was going on with the parameter indicated to be the problem. I thought I found the issue, but when I addressed it by constraining a residual variance across sites, the error message appeared again and implicated a different set of variables. Should I take this error message as a warning (as you have indicated to others)? Or is this a real problem that I need to dig deeper to understand and address? How do I determine which it is? Thanks! Appreciate your help. 


This message refers to the fact that independence of observations is the number of clusters minus the number of strata with more than one cluster. This must be 21 in your case. You should not have more than 21 parameters in your model. This is like having more parameters than your sample size. This is not good practice. 


Hello I have a simple model with 4 variables: Y and X1 continuous, X2 and X3 binary. I have missing values on Y and would like to benefit FIML. My model statement is as follow Y on X1 X2 X3; [X1 X2 X3]; But I have the error message related to “nonpositive definite firstorder derivative product matrix.” In previous models with more continuous dependent variables, everything worked well. I wonder if there is any restriction on the nature of independent variables when using FIML? Can we still use FIML if all the Xs are categorical? In the specific case above what can I do? (I ve checked the parameter involved everything seems ok) Thank you 


If you have the x's on the CATEGORICAL list, you should remove them. This list is for dependent variables. 


thank you i did not have the X s in the categorical list. thank you 


Comment out the variances as shown below. Y on X1 X2 X3; ![X1 X2 X3]; If the message disappears, you can put them back and ignore the message. It is caused by the fact that the mean and variance of a binary variable are not orghogonal. 


Dr. Muthen, I am receiving an error when running alpha coefficients, but cannot figure out why. Mplus refers to the variance of one of my items, but I don't see what the problem is. Can you please help? THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.213D16. PROBLEM INVOLVING THE FOLLOWING PARAMETER: Parameter 27, STU1WE7 (equality/label) Thanks, Danyel 


Please send the output and your license number to support@statmodel.com. 


I got the following error message when running a Mixture model THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.159D17. PROBLEM INVOLVING THE FOLLOWING PARAMETER: Parameter 15, %C#3%: [ GC_3R ] Do you have any idea what I can do about this? 


Please send the output and your license number to support@statmodel.com. 


Hi, I am running a multi group comparison, controlling for the clustered nature of my data with TYPE IS COMPLEX. I have 46 clusters, but 70 parameters to estimate. I get the following warning: THE MODEL ESTIMATION TERMINATED NORMALLY THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.544D17. PROBLEM INVOLVING PARAMETER 46. THIS IS MOST LIKELY DUE TO HAVING MORE PARAMETERS THAN THE NUMBER OF CLUSTERS MINUS THE NUMBER OF STRATA WITH MORE THAN ONE CLUSTER. Since decreasing the number of parameters is not an option, nor can I collect data of more clusters, I was wondering what to do. How serious is that warning – may it be ignored? What would be a statistically adequate solution to this problem? Would it be an appropriate alternative to group standardize the variables and go without the complex type? Thank you very much for your reply. 


It can most likely be ignored. A simulation study is needed to say for sure. 


Hello Dr. Muthen, I am trying to fit a path model using Mplus with both categorical and continuous variables. My input statement is: USEVARIABLES rr13cir rr15cir rr16cir rr17cir rr18cir rr19cir rr20cir L13ext L15ext L16ext L17ext L18ext L19ext L20ext; CATEGORICAL are rr15cir rr16cir rr17cir rr18cir rr19cir rr20cir; Missing are all (999); ANALYSIS:Estimator = MLR; INTEGRATION = MONTECARLO(5000); MODEL: rr15cir ON rr13cir L13ext; L15ext ON rr13ir L13ext; rr16cir ON rr15cir L15ext; L16ext ON rr15cir L15ext; rr17cir ON rr16cir L16ext; L17ext ON rr16cir L16ext; rr18cir ON rr17cir L17ext; L18ext ON rr17cir L17ext; rr19cir ON rr18cir L18ext; L19ext ON rr18cir L18ext; rr20cir ON rr19cir L19ext; L20ext ON rr19cir L19ext; [rr13cir]; [L13ext]; OUTPUT: Sampstat Standardized Residual Tech1; When I try to fit this model, I have received two different errors, but they appear independent of each other. I either get an error telling me Mplus is deleting casewise when rr13 and L13ext are not in the MODEL or I get an error that there is a problem with one of my parameters when they are in the MODEL. There is no negative variance on the variable. What can I do to keep this variable in the model? Do you also have any suggestions for troubleshooting if I have problems using the same type of model with other variables? Thank you very much for your help. 


You say: "or I get an error that there is a problem with one of my parameters when they are in the MODEL." If they are x variables in the model and are binary and you bring them into the model what you see might be an "MLF" warning (firstorder derivatives), which can be ignored. 


Thank you for your response Dr. Muthen, however, it is a continuous variable that the error I am receiving is referring to. The error is as follows: MAXIMUM LOGLIKELIHOOD VALUE FOR THE UNRESTRICTED (H1) MODEL IS 2855.665 THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.168D15. PROBLEM INVOLVING PARAMETER 41. Thank you for all of your help! 


Please send the output and your license number to support@statmodel.com. 

Patricia posted on Thursday, May 05, 2016  9:54 am



Hello Dr. Muthen, I received the following error message when running a path analysis with an interaction term: THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.148D18. PROBLEM INVOLVING PARAMETER 24. How can I resolve? Thank you! 


Perhaps you have brought covariates into the model and one of them is binary. In which case the message can be ignored. 


Hello, Dr. Muchen, Similar to those above, I've got the error message when I ran a uncontrained multigroup analysis (b/t male and female), although the model with the whole participants was identified. THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.262D19. PROBLEM INVOLVING PARAMETER 51.MODIFICATION INDICES COULD NOT BE COMPUTED.THE MODEL MAY NOT BE IDENTIFIED. By adding TECH1 option, I found what is parameter 51, the variance of the endogenous latent variable, which seems fine (positive).The sample size is quite big (male=653, female=799). The model has 15 observed variables and about 45 parameters. The model also has a covariate, age, which is a continuous variable. One of my concerns is that one standardized factor loading among three indicators of the endogenous latent variable is lower than .3. Would you please let me know how I can handle this issue? Thank you so much! 


Please send the output and your license number to support@statmodel.com. 

Daniel Lee posted on Thursday, September 29, 2016  10:32 am



Hi Dr. Muthen, I thought I posted this question here, but cannot find my post.. weird. So my question was, why might there be a strong negative correlation between my latent factors (slope and quadratic term)? I'm confused as the sample means (from 4 time points) is really suggestive of a quadratic trend. Is there a way to remedy this issue in such a way that I can keep my quadratic term? Thank you! 


Try centering the time scores. 


Dear Dr. Muthen, I am running a multilevel SEM model. I want to test the effect of two second level variables separately. With the first one, the model runs perfectly. But with the second variable, I run into problems. I received the following error message: THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THECONDITION NUMBER IS 0.724D16. PROBLEM INVOLVING THE FOLLOWING PARAMETER:Parameter 3, %WITHIN%: [ VALP ] So there seems to be a problem with a first level variable "VALP", but I do not seem to understand why. Many thanks in advance for your response. 


Please send the output and your license number to support@statmodel.com. 

M.Y posted on Wednesday, March 08, 2017  8:53 pm



Hi Professor Muthen, my SEM model is just identified. In order to bring more df, I fixed the covariance between two orthogonally manipulated exogenous variables at zero. However, when I set the path between the two exogenous variables at zero, I encounter the following error message. THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.327D19. PROBLEM INVOLVING THE FOLLOWING PARAMETER: Parameter 69, EXO1 THIS IS MOST LIKELY DUE TO VARIABLE EXO1 BEING DICHOTOMOUS BUT DECLARED AS CONTINUOUS. I added the exogenous variables (categorical binary) as well as several covariates (gender race etc.) as observed variables. To fix the covariance between two exogenous variables, I used the command ¡°exogenous 1 with exogenous 2@0¡±. Probably is that I fixed the covariance between two observed exogenous variables caused the current warning? However, when I modeled the two observed variables as latent variables measured with single indicator with zero error variance and then fixed covariance between two latent variables as zero, I got the same error message. So what happened? Could I just ignore the message? 


The model is estimated conditioned on the observed exogenous variables in the model. When you mention some of them in a WITH statement, you bring those variables into the model and the estimation is not conditional on them. The implication is that they covary zero with the exogenous variables not mentioned. This likely causes the problem. You cannot bring any exogenous variables into the model with weighted least squares only with maximum likelihood or Bayes. 

M.Y posted on Thursday, March 09, 2017  11:35 am



Thanks for the response! So do you mean even when I modeled all observed exogenous variables as latent variables with zero error variance, the model is still estimated conditioned on the observed exogenous variables? Also, EXO1 in the warning message is indeed a binary variable. I noticed if I forget this variable and fix the variance between exogenous 2 and other observed exogenous variables at zero, the warning disappears. What does this mean? 


Yes, but when you add a factor, they are no longer exogenous. That message comes about because the mean and variance of a binary variable are not orthogonal. You can ignore it. 

Rachel Saef posted on Monday, March 13, 2017  11:29 am



I am trying to run SEM for a moderated parallel mediation model. Where some of the variables are latent but some are not (i.e., Cond, EDM, Gender). The model terminated normally when just running the two mediator model, but when I added the two moderators, as follows: ANALYSIS: TYPE = RANDOM; C by o28o54; I by o1o27; OTI BY OTI1OTI13; A by A1A9; Sim on Cond C (m1v) CondC (m1vx) A Gender; OTI on Cond I (m2w) CondI (m2wx) SimlrChk A Gender; EDM on Sim (ym1) OTI (ym2) A Gender; I got the following error messages: THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO AN ILLCONDITIONED FISHER INFORMATION MATRIX. CHANGE YOUR MODEL AND/OR STARTING VALUES. THE MODEL ESTIMATION DID NOT TERMINATE NORMALLY DUE TO A NONPOSITIVE DEFINITE FISHER INFORMATION MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.835D16. THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES COULD NOT BE COMPUTED. THIS IS OFTEN DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. CHANGE YOUR MODEL AND/OR STARTING VALUES. PROBLEM INVOLVING THE FOLLOWING PARAMETER: Parameter 234, OTI ON CONDDIV (equality/label) I am hoping you might know how to solve this problem? Thank you very much! 


Please send the output and your license number to support@statmodel.com. 


Hi I am getting the same error: THE STANDARD ERRORS OF THE MODEL PARAMETER ESTIMATES MAY NOT BE TRUSTWORTHY FOR SOME PARAMETERS DUE TO A NONPOSITIVE DEFINITE FIRSTORDER DERIVATIVE PRODUCT MATRIX. THIS MAY BE DUE TO THE STARTING VALUES BUT MAY ALSO BE AN INDICATION OF MODEL NONIDENTIFICATION. THE CONDITION NUMBER IS 0.533D11. PROBLEM INVOLVING THE FOLLOWING PARAMETER: Parameter 229, MWARM I do not see any problem with the mwarm variable. Any suggestions? 


This is ignorable if mwarm is binary. Otherwise, send output to Support along with your license number. 

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