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I am running a series of CFAs with censored variables and would like to use the MLR estimator due to missing data. I am not getting regular fit indices (chisquare, CFI, TLI, RMSEA) when I use this estimator. Do these need to be requested? 


Maximumlikelihood estimation with censored variables does not have means, variances and covariances as sufficient statistics, but instead raw data, and therefore does not do the usual model test of fit. If you want a test of the fit to the covariance matrix you can use WLSMV. You can also use MLR and create your own unrestricted covariance matrix model in Mplus to test against, that is do a second run, and then compute chisquare as 2 times the log likelihood difference. 


I spoke too quickly in my last sentence above. To do what I suggested one must allow a factor behind each censored variable which will lead to too many dimensions of integration with MLR. Instead, you can either use WLSMV for such testing and hope that the missing data handling in WLSMV is sufficient. Or, better still, use MLR and work with likelihoodratio chisquare testing of nested neighboring models to see if specific restrictions in your model are well fitting or not. 


Dr. Muthen. Thank you for your prompt response. I had originally used the censored with WLSMV, but after reading more about estimators it seemed that MLR might be more appropriate. I appreciate your suggestions. 

Cassie Suh posted on Monday, January 25, 2016  6:46 am



Hello, I am running a SEM model with a categorical variable as the final outcome and with weights. USEVARIABLES ARE A B c1c5 D weights; CATEGORICAL = D; WEIGHT IS weights; ANALYSIS: type=general; INTEGRATION = MONTECARLO(500); ESTIMATOR=MLR; MODEL: C by c1 c2 c3 c4 c5; D ON C B A; C ON B A; B ON A ; I used the estimator MLR because of issues of nonnormality and because my model uses weights. I was wondering if 1) The use of MLR is appropriate for my measurement and structural model with a categorical outcome (I think it is based on other posts I've been) 2) And if so, how would I proceed to explain the results for my measurement model as the MLR estimator with categorical outcomes does not give model fit indices such as CFI, TLI, RMSEA ( I am not comparing my model with any other models). Do you think it would be enough to give results of CFA for just the one variable that is latent? 3) Also, for my structural model (I am not comparing this with any other models), is there any reference that I can use that what I am doing is correct and that no model indices of CFI, TLI and RMSEA are natural? Thank you very much. 


1. Yes. The default for MLR and the CATEGORICAL option is logistirc regression. 23. When numerical integration is required, means, variances, and covariances are not sufficient statistics for model estimation and chisquare and related fit statistics are not available. Which nonnormality are you concerned with? Is it your categorical factor indicators? 

Cassie Suh posted on Tuesday, January 26, 2016  7:23 am



Thank you so much for your prompt reply I meant that MLR gives robust standard errors. I had two follow up questions as well. 1) just to clarify your answer to question above regarding the measurement mode, I would say that model fit indices are not available and move on. 2) I want to run a lagged effects model as well by including the same variables from previous time points as controls where BB cc1cc5 DD corresponds to B c1c5 D The model would be USEVARIABLES ARE A B c1c5 D BB cc1cc5 DD weights; CATEGORICAL = D; WEIGHT IS weights; ANALYSIS: type=general; INTEGRATION = MONTECARLO(500); ESTIMATOR=MLR; MODEL: C by c1 c2 c3 c4 c5; CC by cc1 cc2 cc3 cc4 cc5; D ON C B A DD; C ON B A CC; B ON A BB ; My concern is the effects of A and my final dependent variable is D. 2)1 Is a latent variable(CC in this case) able to be used solely as a control variable like above. Or should I use CC as a observed variable(by adding/averaging cc1cc5) and then add it to the model? 2)2 Also, as I have a lagged effects model, I have compared it with the model with no lagged effects and got better model fot. Do you think this is nessasary as sort of a robustness check or if I should just report the results of the lagged effects models as that is the model with stronger controls and thus more appropriate? Thank you! 


1) Check if you get TECH10. 2) Ask on SEMNET. 

Nagwan zahry posted on Thursday, September 28, 2017  9:49 am



Hi, When I used the MLR estimator to correct for violations of normality, should I report of the goodnesfitindices without doing further analysis? i read in your comments that "we can also use MLR and create your own unrestricted covariance matrix model in Mplus to test against, that is do a second run, and then compute chisquare as 2 times the log likelihood difference." Please advise. Thank you Nogag 


Q1: Yes. The alternative gives the same result. 


What does a value of MODEL FIT INFORMATION below indicate for a CFA with 20 dependent categorical (binary)variables and 4 latent varaiables : Number of Free Parameters 61 Loglikelihood H0 Value 44991.437 H0 Scaling Correction Factor 1.0179 for MLR Information Criteria Akaike (AIC) 90104.874 Bayesian (BIC) 90498.532 SampleSize Adjusted BIC 90304.697 (n* = (n + 2) / 24) How should I interpret and report it? 2)Is something wrong in my model with Ho in negative? If yes what is it and how can it be corrected? 3) what can be done to correct it? 


Big topic. You may want to study our Topic 2 course on the web. These are relative fit measures, useful for comparing models. You don't get absolute fit with ML for categorical. You get it with WLSMV and Bayes. 


Hello, Why do we not obtain fit statistics when using MLR? Also, under what circumstances would you not obtain fit statistics using WLSMV? I ran a growth curve analysis using WLSMV (assessing mediation) and did not obtain fit statistics. I also did not obtain fit stats when running a growth curve analysis using WLSMV assessing moderation. Thanks! Hillary 


Q1: When a sample mean vector and covariance matrix are not sufficient statistics but you need to work with raw data. For instance, when all DVs are continuous, normality is assumed and you have those sufficient statistics and therefore overall model fit statistics. When at least one of the DVs is not continuous, you don't have them. Q2: WLSMV should always give fit statistics unless the model is justidentified, that is, has zero degrees of freedom (no restriction such as a leftout path is present in the model). 


Hello Dr. Muthen, Thank you for your response! With regard to Q2, in the model with the categorical indicator (WLSMV estimation), I used a mediation model (MODEL INDIRECT statement). Also, I had to use monte carlo integration. Could either of these specifications get in the way of the model providing fit statistics? My model is not justidentified. Thanks! Hillary 


WLSMV doesn't use monte carlo integration  that is only with ML. When ML needs montecarlo integration, the regular fit indices are not available because you no longer fit the model to means, variances, and covariances but need to work with raw data. 


If there are no model fit indices available when using MLR with numerical integration with categorical dependent variables, is it impossible to assess model fit? Do you just assume the parameter estimates are acceptable? 


Try TECH10 which gives you fit to univariate and bivariate distributions among your variables. 


What if you are using MLR with numerical integration with continuous variables? Are there any options for assessing model fit in that case? 


Like with XWITH? No totally satisfactory options> 


I have hypotheses with and without XWITH. One is a Level 1 to Level 2 direct effect. Does that make a difference? 


Perhaps you can work with "neighboring models". That is, compare the model of interest to you with a less restricted model with more parameters (such as a direct effect) and see of those extra parameters are significant (using Model Test). 

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