Thank you, Dr. Asparouhov. So can I say the method you mentioned there is a single-level pseudo-maximum likelihood estimation method, even not a multilevel pseudo-maximum 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?
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 Mplus-PML and say MLwin-PWIGLS) 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 two-level models with two sets of weights. The two-level 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 two-level models in https://www.tandfonline.com/doi/abs/10.1080/03610920500476598
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 two-level HLM model.
Second, there are three scaling methods for level 1, and two scaling methods for level 2. If we use, for example,
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 individual-level weight was used for a latent growth curve model. If I have a cross-sectional 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 PSEUDO-MAXIMUM LIKELIHOOD ESTIMATION (MPML) method (which was metioned in my second concern in the previous post) in codes?
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 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.
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.