I read the user's guide and it seems that MLR in Mplus 7 can handle both missing data and non-normal 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 non-normal 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 non-normal 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 non-normality. 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 non-normal 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 non-normal data, my pattern of results changes.
Does MLR not take care of outlier problems? Thanks!
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 non-normal survey data, with and without MAR or MCAR data.
In a recent pilot study with N = 65, item-level skew was common, with one extreme example showing skew = -8.307 and kurtosis = 69.000. Scale-level non-normality 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
Yoosoo posted on Wednesday, January 28, 2015 - 4:58 pm
I am wondering how adequate MLR is in handling missing AND non-normal 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 non-normal complete data and normal missing data? 3. EM algorithm and montecarlo() aid in fitting categorical data, but do not interfere with continuous data?
4. If MLR is not as robust in fitting non-normal 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 non-normal data with categorical and continuous endogenous observed variables for a multilevel model. "
1. Yes, just like "FIML" does.
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 non-normal 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 non-normal 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 continuous-variable 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 non-normal missing data case - I don't expect much of a distortion acting as if normality is the case.
I was wondering if the robust two stage procedure for incomplete non-normal data used in Savalei & Falk (2014) was available in Mplus of if there may be a way to implement it.
Savalei, V., & Falk, C. F. (2014). Robust two-stage approach outperforms robust full information maximum likelihood with incomplete nonnormal data. Structural Equation Modeling: A Multidisciplinary Journal, 21(2), 280-302.