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I am running measurement models for my data. One of my models runs, but I get a chisquare model value of 0.000. What does this mean? Is this a poor model? Below are my output and input; the data is secure so I cannot send it ChiSquare Test of Model Fit Value 0.000* Degrees of Freedom 0 PValue 0.0000 Scaling Correction Factor 1.000 for MLR ChiSquare Test of Model Fit for the Baseline Model Value 45.180 Degrees of Freedom 3 PValue 0.0000 CFI/TLI CFI 1.000 TLI 1.000 Loglikelihood H0 Value 21243.164 H1 Value 21243.164 Information Criteria Number of Free Parameters 9 Akaike (AIC) 42504.327 Bayesian (BIC) 42548.379 SampleSize Adjusted BIC 42519.795 RMSEA 0.000 SRMR 0.000 DATA: file is "R:\Users\Sarah Strand\public\Data\MPlus Data\subequalgroups2.txt"; format is free; type is individual; VARIABLE: NAMES ARE AID FEMALE ... etc [omitted to preserve space]; IDVAR = aid; USEVARIABLES ARE par_app perc_map perc_dap; MISSING ARE .; WEIGHT IS GSWGT3; CLUSTER IS PSUNUM; ANALYSIS: TYPE=GENERAL MISSING H1 COMPLEX MODEL: approval by par_app perc_map perc_dap; OUTPUT: standardized h1se; 


Your model is just identified. It has zero degrees of freedom. In this case, model fit cannot be assessed. 

Yellowdog posted on Wednesday, October 31, 2012  2:37 am



Dear Linda, we want to test a path model (N=189) with the following observed trait variables:  four predictors (IV1 to IV4)  two mediators (M1 and M2) that are, as expected a priori, strongly negatively correlated with each other (r = .56)  with quality of life (QoL) as DV We specified the following model: qol on iv1 iv2 iv3 iv3 m1 m2; m1 on iv1 iv2 iv3 iv4; m2 on iv1 iv2 iv3 iv4; Our question refers to how to model the relationship between M1 and M2. There is equilibrium, but we cannot make assumptions on a direction of causality from one to the other. When we specify a nonrecursive feedback loop (m1 on m2 (p31); m2 on m1 (p32);), model estimation fails (see output below). If we only specify that M1 and M2 are correlated (m1 with m2 (p31);), model estimation fails too (see output below). ChiSquare Test of Model Fit Value 0.000 Degrees of Freedom 0 PValue 0.0000 RMSEA (Root Mean Square Error Of Approximation) Estimate 0.000 90 Percent C.I. 0.000 0.000 Probability RMSEA <= .05 0.000 How can we fix the problem? Many thanks for your help, Mario 


The models are not failures. They are justidentified with zero degrees of freedom. Model fit cannot be assessed in this case. I would covary m1 with m2. 

Yellowdog posted on Thursday, November 01, 2012  3:51 am



Dear Linda, thank you for your reply. We understand that with df=0, fit indices are not available. Refocusing our question, we are wondering whether the model outlined above and its results (with df=0) are valid, although we do not get information on how the model fits the data. Can we go ahead and report path coefficients from this analysis as a final result? Or should we try to change the model specification until df>0 (e.g., using MODINDICES) ? Thank you for your help, M 


These results can be reported. This is not an uncommon situation in path analysis. 


Hi, I am wondering why df=0 is not uncommon in path analysis. My model should not be justidentified because I have a sample size of 390 and am only trying to estimate 4 free parameters but my fit indices come up with a df=0. I'm wondering why this is and if there is any way to have positive df using path analysis. Even in the output examples you have on the website for linear regression they are 0 but this limits the usefulness of the model. Thank you, Melissa 


In path analysis, degrees of freedom are computed as the number of parameters in the H1 model minus the number of parameters in the H0 model. They are not in this case related to the sample size. 


Dear Linda, In situations where path analysis does not yield model fit indices how can we compare different models. Can we use an average of the Rsquares? Is it too crude? Please can you suggests some ways around this. 


Why does the model have no fit indices? Does it have zero degrees of freedom? Rsquare is not a fit measure. It is a measure of variance explained. Fit compares the observed covariance matrix to the model estimated covariance matrix. 


Dear Linda, Thank you for your response. The model has zero degrees of freedom. However, I will want to compare the fit indices of three nested models. 


You can compare the model with zero degrees of freedom to other nested models. Use 0 for chisquare and 0 for the degrees of freedom. 


Hello, I have a model with all observed variables and N=209, but I'm concerned about my fit statistics. I have 2 df. Based on reading the posts, am not sure what the problem is (I'm assuming low df?), or how to fix it. Is this problematic, or could I report these results for publication? Model: GMREL ON Partner CommScore WGDabs; GMSEX ON Partner Variety WGDabs CommScore; GMREL WITH GMSEX; Variety ON CommScore WGDabs; OUTPUT: ChiSquare Test of Model Fit Value 0.008 Degrees of Freedom 2 PValue 0.9960 RMSEA (Root Mean Square Error Of Approximation Estimate 0.000 90 Percent C.I. 0.000 0.000 Probability RMSEA <= .05 0.998 CFI/TLI CFI 1.000 TLI 1.045 ChiSquare Test of Model Fit for the Baseline Model Value 278.161 Degrees of Freedom 12 PValue 0.0000 SRMR (Standardized Root Mean Square Residual) Value 0.001 Thank you in advance for any assistance! 


Very good fit can often be caused by low correlations. You may not have the power to reject the H0 model because of this. 


Thank you for your quick response! 


Hi there, I have a (N=316) 1 factor EFA solution with WLSMV estimation of 11 ordered categorical items and the following fit statistics: CFI = 1 RMSEA = 0 90 Percent C.I. 0.173 0.202 chi square 0.00 on df=44. p=1. Now on the surface this might look like a well fitting model because chi square is not significant and I still have 44 df. All of the factor loadings are higher than .76. I have also checked the correlations between items and the lowest is .425 so doesn't suggest low correlations leading to very good fit. However I don't trust this solution as it seems too good. I have noticed that none of the item factor loadings, despite being high, load significantly on the factor. Might you suggest what is going on here or where I should look in the output to explain these results, if they are in fact, not to be trusted. 


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

Hassan posted on Friday, February 24, 2017  3:41 am



Dear Dr. Muthen, I wonder which chisquare should be reported from Mplus output in our paper? ChiSquare Test of Model Fit or ChiSquare Test of Model Fit for the Baseline Model ? Kind regards, Hassan 


ChiSquare test of model fit is for the model you specify in the MODEL command. 

Hasina posted on Saturday, August 26, 2017  12:16 am



Dear Dr. Muthen, I would like to know if it is normal to see a chisquare fit to be better (not reject the true model) than alternative fits (Ex, CFI, AGFI etc.) in a simulation study either in small or high sample size? Thank you indeed for you response, Hasina 


We don't give AGFI so I suspect your question does not relate to Mplus. You should post your question on a general discussion forum like SEMNET. 


Hello Mplus Team, In the Multilevel CFA anlaysis, I got the following results: ChiSquare Test of Model Fit Value 4.338 Degrees of Freedom 4 PValue 0.3623 RMSEA 0.008 CFI 1.000 TLI 1.000 SRMR Value for Within 0.004 Value for Between 0.002 Other than Pvalue of "ChiSquare", all other fit Indices are within the range. Is my model fit? 


A large pvalue like this indicates that you can't reject the model  so the model fit is good. 


Thank you Sir. But, usually it is said that, "Pvalue" should be less than "0.05". So, how can a large "Pvalue (0.3623)" indicate a Good Model fit? 


I see where you are coming from. It all depends on the hypothesis. Regular statistics and SEM have the opposite starting point in this regard. Usually, in statistics you hope to reject your null hypothesis that there is no effect because you hope there is an effect (of the treatment that you've come up with for example). In contrast, in a SEM setting, you hope to not reject your null hypothesis because the null refers to the model you have specified. So with SEM, you want large pvalues because a pvalue less than say 0.05 would say that you reject your null. 


I am a bit confused Sir. Some articles report that, "ChiSquare Test of Model Fit" is determined only if the Pvalue is less than "0.05" But here, "ChiSquare Test of Model Fit" of my results have the Pvalue = 0.3623. So, should I understand the "Chisquare Test of Model fit" as statistically significant or not? 


Simply put, in SEM testing of overall test of model fit, p less than 0.05 is taken as poor fit (model can be rejected) and p greater than 0.05 is taken as good fit. If you have seen the opposite, I'd like to hear what the reference is. It doesn't make sense to take a low pvalue as an indication of model fit because the hypothesis is that the H0 model is correct so we don't want it to have a low pvalue. 


Sorry, Sir. I was mistaken. I have rechecked the references, the "Pvalue of Chisquare model fit" should be greater than "0.05". Thank you. 

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