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I read the user's guide and it seems that MLR in Mplus 7 can handle both missing data and nonnormal data. Am I correct? My understanding is that ML solution to missing data usually assumes a multivariate normal distribution. If MLR in Mplus can handle both missing data and nonnormal data, does it mean that MLR, though still assumes multivariate normal distribution, makes some adjustments such that even though the distribution is not so normal, it's results are robust to the deviation? If I want to know how robust MLR as implemented in Mplus is, are there simulation studies on its performance when both missing data and nonnormal data are present in a dataset, for various degrees of deviation from multivariate normal distribution? I would like to know to what extent I can trust the MLR results for my dataset. Thanks. 


Missing data modeling does indeed assume normality. MLR robustness does not necessarily hold for the combination of missing data and nonnormality. There have been simulation studies of this combination  see articles by Victoria Savalei in the SEM journal for instance (e.g. her 2010 article). See also Yuan et al (2012) in a recent issue of Sociological Methods & Research. 


Thanks for your prompt reply and the references. I am studying them. I am also interested in the technical details. May I know whether the section on MLR in the following web note in 2002 on MLR is still relevant to the Mplus 7? Muthén, B. and Asparouhov, T. (2002). Using Mplus Monte Carlo simulations in practice: A note on nonnormal missing data in latent variable models. Version 2, March 22, 2002. 


I forgot about that one. Section 5 is certainly relevant, showing that MLR can work quite well. So no theoretical guarantee, but it can do well in practice. So yes, still relevant for Version 7. 

Barbara O. posted on Monday, March 18, 2013  11:32 am



I am working on a paper examining longitudinal pathways predicting perpetration of dating violence in young adulthood. I'm using path analyses in mplus, accounting for the fact that dating violence is censored. There are three outliers in my dating violence variable. If I get rid of outliers (either by transforming or trimming), I get the same pattern of results regardless of whether I: (a) use MLR (even after transformation the variable has high kurtosis), (b) use ML without robust estimation, (c) don't account for censoring at all and just use ML. Thus, my results seem consistent. However, if I don't remove the outliers, and just use MLR to account for the nonnormal data, my pattern of results changes. Does MLR not take care of outlier problems? Thanks! 


MLR does not take care of outliers. 

John Plake posted on Thursday, September 19, 2013  10:06 am



I am trying to track down some documentation of the limits of MLM or MLR estimators in handling extremely nonnormal survey data, with and without MAR or MCAR data. In a recent pilot study with N = 65, itemlevel skew was common, with one extreme example showing skew = 8.307 and kurtosis = 69.000. Scalelevel nonnormality was 1.926 (skew) and 4.86 (kurtosis) in the worst case. Yuan and Bentler (2000) demonstrated that their approach (is it MLM in Mplus?) handled skew of 4.18 and kurtosis of 62.55 fairly well in MCAR. Can you help me know if the limits have been tested? 


Vika Savalei had a 2101 SEM article on that. Use MLR in Mplus. 

John Plake posted on Thursday, September 19, 2013  11:04 am



Great. Thanks! 

Yoosoo posted on Wednesday, January 28, 2015  4:58 pm



I am wondering how adequate MLR is in handling missing AND nonnormal data with categorical and continuous endogenous observed variables for a multilevel model. I read the references that Dr.Bengt Muthen suggested above(Savalei2010 and Yuan et al.2012), but I am unsure whether I'm understanding things correctly. Am I correct in saying that: 1. MLR assumes normality in missing data estimation? 2. MLR is robust in estimating nonnormal complete data and normal missing data? 3. EM algorithm and montecarlo() aid in fitting categorical data, but do not interfere with continuous data? And lastly, 4. If MLR is not as robust in fitting nonnormal missing data as we want, how do we gauge the validity of the results? is there a reference for it?) Thank you so much as always for your timely & succinct support. 


I don't think we know and a research study is probably called for regarding "how adequate MLR is in handling missing AND nonnormal data with categorical and continuous endogenous observed variables for a multilevel model. " 1. Yes, just like "FIML" does. 2. Yes. 3. They are not needed for continuous data for H0 models. 4. Don't know. I think it is a research topic. 

Yoosoo posted on Thursday, January 29, 2015  3:14 pm



Thank you for the response, Dr. Muthen. I have a follow up question: 1. You mentioned that MLR acts like FIML in assuming normality in missing data. Does it mean that my estimator 'switches' to FIML when it deals with missing data, or is there still a difference between MLR and FIML in missing data treatment? 2. You mentioned that it is unknown whether MLR is effective in dealing with nonnormal missing data. Does this apply to categorical missing data as well? 3. Would you advise if there is any other estimator that is known to effectively deal with complex (clustered) multilevel model with categorical outcome, with nonnormal missing data (which may not yet be offered in MPlus)? 


1. MLR is different from FIML only in how the SEs are computed, not the point estimates. 2. No, I don't think so since we only assume categorical, not a specific continuousvariable distribution. 3. None that I know of; we try to keep up with the latest. I should add that I don't worry much about the nonnormal missing data case  I don't expect much of a distortion acting as if normality is the case. 


Dear Bengt and Linda: Does MLR include cases with missing categorical data? We have some categorical outcomes and want to make sure that cases with missing data are not dropped from the model. Can MLR do this? Thanks! Seth Schwartz 


Yes. 


The tips above have been very useful. I was wondering what to do when you deal with nonnormal data, but also want to bootstrap (because of an indirect effect). This is not possible using MLR. Thank you in advance! Joyce 


Compared to ML, MLR just gives different SEs. I think bootstrapping would give some degree of robustness to nonnormality but I have not studied it. 

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