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Can I use probabilityweighted iterative generalized least square (PWIGLS) method with MPlus? Thank you in advance. 


Take a look at https://www.statmodel.com/download/webnotes/mplusnote72.pdf Table 11 in particular. To use probability weighted estimation in Mplus you simply use the command weight=. The estimation we use is technically not PWIGLS but is the superior PML. 


Thank you, Dr. Asparouhov. So can I say the method you mentioned there is a singlelevel pseudomaximum likelihood estimation method, even not a multilevel pseudomaximum likelihood estimation method? And it is not PWIGLS (proposed by Pfeffermann, et. al. 1998) either. So can I say so far I cannot run PWIGLS method in MPlus? Which software can I use for PWIGLS method? Only LISREL? Many thanks. 


As it is shown in the above article the PML and the PWIGLS are the same method  except that the way it is implemented in these software packages that are listed in the article the standard errors are incorrect in some packages. There is no option on what is right or wrong regarding that. Once the point estimates are set (identical point estimates in MplusPML and say MLwinPWIGLS) the standard error estimation is set and it amounts to correctly estimating the asymptotic distribution of these point estimates. That part is correct only in Mplus. The PWIGLS is not defined in twolevel models with two sets of weights. The twolevel models that Pfeffermann uses are equivalent to single level models since they have weights only on the between level. You can read more about probability weighting in twolevel models in https://www.tandfonline.com/doi/abs/10.1080/03610920500476598 


Just a correction actually. The Pfeffermann article that defines the PWIGLS is defined also for models with weights on both levels. http://www.bris.ac.uk/medialibrary/sites/cmm/migrated/documents/weightingforunequalselection.pdf Under Section 3 they point out that PML and PWIGLS are the same estimation methods essentially. 


Thank you so much, Dr. Asparouhov. I will work on these papers first. Respectfully, Bing 


Dear Dr. Asparouhov, First of all please forgive my shallow knowledge in using different estimation methods while incorporating sampling weights in HLM model. As you mentioned, if we use Mplus to run PWIGLS (based on my understanding, what you mean here is that they just used different terms referring to PWIGLS: in MPlus, the termed used for this is PML, PWIGLS in WlwiN.), we simply need to use one more WEIGHT statement compared with regular HLM in MPlus. But which level weight I should use? level 1 weight? or level 2 weight if I have a twolevel HLM model. Second, there are three scaling methods for level 1, and two scaling methods for level 2. If we use, for example, Weight=WSTUDENT; (studentlevel weight) Bweight =WSCHOOL;(schoollevel weight) Wtscale=cluster; bwtscale=sample; It seems it becomes multilevel pseudomaximum likelihood estimation (MPML) method with scaling method A (Pfeffermann, 1998). And there is scaing method B if we use different scaling method. Could you explain that to me? Thank you so much. Respectfully, Bing 


Dear Dr. Asparouhov, For my first concern in the previous post, maybe I should put it in this way. You used PML estimator in Asparouhov (2005), in which only individuallevel weight was used for a latent growth curve model. If I have a crosssectional data set with individual as first level and school second level. And I have weights for both levels. If I would like to use PWIGLS to estimate my parameters in MPLUS, how to code them? Could you show me an example of this? How would it be different from MULTILEVEL PSEUDOMAXIMUM LIKELIHOOD ESTIMATION (MPML) method (which was metioned in my second concern in the previous post) in codes? Thank you. Best regards, Bing 


The scaling methods are described here and generally we recommend that you use our default methods (which is method A) http://statmodel.com/download/Scaling3.pdf I would also recommend this article https://www.tandfonline.com/doi/abs/10.1207/s15328007sem1301_2 


Thank you, Dr. Asparouhov. All I know is that we can use different scaling methods in both levels for MPML in MPlus. For PWIGLS, LISREL can handle it with scaling method B (Pfeffermann, 1998).Maybe WLwin can handle PWIGLS as well. But my question is: can I use MPlus to run PWIGLS? If I can, could you show me the example? I really appreciate your help. Thanks.] Bing 


I don't have anything new to add to what is in these papers. I will reiterate however that if you are being advised to pursue PWIGLS that is a poor advice in my point of view since we have documented that there are errors there. Mplus will probably never be implementing PWIGLS for two reasons: the errors we have found and the fact that it only applies to a much more limited number of models. 


Thank you very much, Dr. Asparouhov. Best wishes, Bing 


Dear Dr. Asparouhov, I have a question about how to evaluate the estimates. I know usually we may use relative bias, MSE, and coverage rate to evaluate the estimates if we have simulation data (thus we have true values of estimates). But if I just use empirical data, which method(s) can I use to evaluate the estimates (since I don't have population estimates)? Thank you in advance. Best regards, Bing 


You can do bias/MSE/coverage evaluation only in simulation studies. 


Yes, you are right. But what if I use empirical data? What methods can I use to evaluate the estimates if I use empirical data? Thank you. Best wishes, Bing 


Your best option is to make a simulation study that resembles the conditions in the empirical data. You have to be careful though regarding the weights. You can see how that is done here https://www.statmodel.com/download/webnotes/mplusnote72.pdf 


Thank you so much, Dr. Asparouhov. Best wishes, Bing 

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