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Hello, I'm reporting SEM results that were calculated with the MLR estimator. While this may seem trivial, I haven't been able to find what the MLR acronym stands for. I'd guess that it stands for "Maximum Likelihood Robust", but I want to ensure that I cite it properly. If you could please let me know, I'd appreciate it. Thanks! 


I don't think MLR is an acronym. It is an Mplus option for maximum likelihood estimation with robust standard errors. 


I am running a two level MLSEM. I have slightly nonnormal continuous data and from what I understand, using a SatorraBentler x2 with robust standard errors should be used. Mplus has this under the MLM estimator. However, in a two level analysis, MLM is not available, but MLR is. In the manual, MLR also provides robust standard errors. My question is: how is MLR related to MLM (in short how do I write this up aside from saying that I used a maximum likelihood estimator with robust standard errors)? 


MLM – maximum likelihood parameter estimates with standard errors and a meanadjusted chisquare test statistic that are robust to nonnormality. The MLM chisquare test statistic is also referred to as the SatorraBentler chisquare. MLR – maximum likelihood parameter estimates with standard errors and a chisquare test statistic (when applicable) that are robust to nonnormality and nonindependence of observations when used with TYPE=COMPLEX. The MLR standard errors are computed using a sandwich estimator. The MLR chisquare test statistic is asymptotically equivalent to the YuanBentler T2* test statistic. See the Yuan and Bentler paper referenced in the user's guide. MLR is an extension of MLM that can include missing data. 


Thanks for the info. I have a follow up question. I am using MPLUS 5.2 and it displays the twotailed p value how is it possible that in the unstandardized output it is nonsignificant (p>.05) and then in the standardized results, it is significant (p<.05)? I am modeling achievement (ACHW and ACHB) defined by reading and math at two levels (student and school level) and I am using the presence of basic facilities at the school level as a predictor (i.e., presence of electricity, 1=yes, 0=no). Unstd ACHB ON ELECTRIC 1.438 0.864 1.664 0.096 STDY Standardization ACHB ON ELECTRIC 1.185 0.585 2.028 0.043 StdYX ACHB ON ELECTRIC 0.488 0.241 2.027 0.043 Thank you. 


The unstandardized and standardized values have different sampling distributions and can give somewhat different z values. 


If that is the case, which one should be 'trusted' and interpreted? 


I would go with the tests for the unstandardized coefficients, but I haven't seen this studied. It could be a good methods research project, simulating data to see for which type of coefficient the z tests behave best at different sample sizes. 


I was just wondering, if you use mlr as the estimator method on a regression or path analysis is it still helpful to center explanatory variables? 


I don't see that the MLR choice and centering choice are related. 


Thanks for your quick reply. 


Hello, If you use the estimator MLR without using the Type=Complex option, can you still get standard errors that are robust to nonnormality and nonindepenence of observations? Thanks Wayne 


No, without TYPE=COMPLEX MLR is robust only to nonnormality. 


hello, is the type=complex option required in the case of missing data (mcar or mar) or not. Thanks alex 


All missing data estimation using maximum likelihood assumes MAR. 

Till posted on Tuesday, September 13, 2011  11:47 am



Dear Mrs. or Mr. Muthén, I'm running a latent growth curve analysis. This is the Input: Variable: names= g1 e1 n1 g2 e2 n2 g3 e3 n3 l01 l02 l03 l04 l05 l06 l07 l08 l09; usevariable=all; missing=all(99); model: i s  l01@0 l02 l03 l04 l05@1 l06 l07 l08 l09; F1 by n1 n2 n3; F2 by e1 e2 e3; F3 by g1 g2 g3; i s on F1 F2 F3; Analysis: Estimator=MLR; output: samp standardized tech4; I would like to use the MLR estimator because the mardia coefficient shows me that I can't assume multivariate normal distribution for my data. Is the use of the MLR Estimator appropriate here or do I have to use the normal ML? Thank you in advance Till 


Dear Dr. Bengt and Dr. Linda In my model, I have 41 variables. 4 of them have kurtosis values > 3 (3.6, 3.6, 5.6 and 6.8). Do I need to run my model using MLM or MLV estimators? What is the rule of thumb to use the MLM/MLV instead of ML? What is the difference between MLM and MLV? Thanks 


There are three estimators that are robust to nonnormality. Following are brief descriptions. Only MLR is available with missing data. This is what I would recommend. • MLM – maximum likelihood parameter estimates with standard errors and a meanadjusted chisquare test statistic that are robust to nonnormality. The MLM chisquare test statistic is also referred to as the SatorraBentler chisquare. • MLMV – maximum likelihood parameter estimates with standard errors and a mean and varianceadjusted chisquare test statistic that are robust to nonnormality • MLR – maximum likelihood parameter estimates with standard errors and a chisquare test statistic (when applicable) that are robust to nonnormality and nonindependence of observations when used with TYPE=COMPLEX. The MLR standard errors are computed using a sandwich estimator. The MLR chisquare test statistic is asymptotically equivalent to the YuanBentler T2* test statistic. 


Hi Linda, I just follow some of your previous suggestions about using WLSMV for a combination of continuous and categorical variables, in non normal distribution data. However, I´m not sure how to interpret the results as I didn´t get RMSEA, CFI,TLI or SRMR as I use to see using MLR estimate. Thanks for your help! Susana 


WLSMV gives you chi2, RMSEA, CFI, TLI. Perhaps you have an older version, or perhaps the run had a problem. 


Hi Linda, Thanks for your response. I´m trying another versión of the program, but I had this warning message: *** ERROR in VARIABLE command The CATEGORICAL option is used for dependent variables only. The following variable is an independent variable in the model. Problem with: NSE *** ERROR in VARIABLE command The CATEGORICAL option is used for dependent variables only. The following variable is an independent variable in the model. Problem with: EDUCA I´m using some demographics as education, sex and age to predict physical activity levels in my model. I don´t understand why categorical variables can only be dependent variables. Many many thanks for your help! Susana 


It is not that categorical variables can only be dependent variables. It is that the scale is only an issue for dependent variables. In regression, covariates can be binary or continuous. In all cases, they are treated as continuous and the model is estimated conditioned on them so that no distributional assumptions are made about them. 


But I didn´t get any results with this data, only the warning message. That means that I should treat my categorical variables as continuous? In that sense, use MLR and do not introduce them as categorical? Many thanks! Susana 


If you remove the CATEGORICAL option that has covariates on it, I think you will then get results. You cannot use WLSMV if you have no categorical dependent variables. Then you should use MLR. 

Daniel Lee posted on Thursday, September 29, 2016  10:54 am



Hi, I am conducting a latent growth model with 4 time points. At each time point, the the observed variables are skewed and departs from normality. In such a case, would you recommend I use MLR instead of ML? Thank you! 


Yes. 


Dear Linda and Bengt, My sample is 508, and I am running a full mediation model: P>B>D. When estimating an indirect effect, bootstrapping cannot be used with MLR. Since it is known that MLR is robust to nonnormality, I was wondering if MLR or MLM are also robust to the nonnormality of the product term (PB * BD) in this case? In other words, can I be confident that a p value associated with an indirect effect is accurate when MLR or MLM are used? If so, is there any reference to back this up? Thanking you in advance Alex 


To get bootstrapped SEs and CIs, you should use Estimator = ML. The acronym MLR is reserved for another type of SEs. 


Dear Linda and Bengt, For my PhD, I am performing multigroup analysis, as I want to test a model in two different countries. The dependent variable of my model is categorical. Firstly, I checked the invariance for each construct and now I am examining the invariance of regression coefficients and of one mediation. Because my data is not normal, and I have some missing values, for checking the invariance of my independent variables (which are continuous), I used the MLR estimator, and I used the WLMSV for the dependent variable. Could you please tell me if I can use the MLR with individual data (and not only with mixture models, which is the default estimator)? Secondly, I also checked the full SEM model in each group, and I used the WLMSV and the bootstrap (because I have a mediation). Thus, could you please tell me if it is correct to use the MLR for examining the measurement invariance in each independent variable, and then in a later stage of my analysis, use the bootstrap procedure (for assessing if the mediation is significant)together with other estimator? I am asking this, because I know that the MLR estimator could not be run with bootstrap. Once again, many thanks for your help, 


You can use MLR. MLR can also be used with bootstrapping unless you have multilevel data or sampling weights. 


Thank you so much Bengt. 


Hi Bengt, I have a quick follow up question to your response from Filipa. I am trying to run a mediated GMM, with a 3 class nominal outcome. I'm using dummy variables to account for school level clustering as I only have 7 total clusters. When I try to add boostrap to my Analysis command, I get an error that "Bootstrap is not available for estimators MLM, MLMV, MLF and MLR", but your comment above makes it sound like it is? Any help would be wonderful. Best, Katie 


Use ML. The other estimators have the same ML parameter estimates. ML with bootstrap gives you ML parameter estimates and bootstrapped standard errors. 

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