Anonymous posted on Thursday, April 15, 2004 - 7:31 pm
I recently received the new version of M+, and noticed, to my dismay, that the actual models being fitted are not included in the User's Guide.
My question is about parameterization of models with categorical observed variables, vis-a-vis the models containing either continuous or categorical latent variables.
Is model parameterization with categorical variables the same regardless of whether or not the latent variables are categorical or continuous? E.g., are they both treated in the same logit framework, or is the model a threshold model for latent continuous variables, and a logit model for latent categorical variables?
It seems that the model framework is the same for continuous observed variables--e.g., the same multivariate normal model family is being fit when the obs. variables are continuous, and the lat. variables are either continuous or categorical. However, when the observed variables are categorical, it's not clear whether or not latent continuous and latent categorical models are being treated in the same model family, and if so, what that family is.
bmuthen posted on Thursday, April 15, 2004 - 8:11 pm
The User's Guide focuses on the use of the program, avoiding mixing technical-statistic matters with program language matters, instead focusing on examples which is more accessible to many. Technical-statistical aspects of the modeling in Mplus is given in the series of papers on the Mplus web site and in technical appendices (the latter to be uploaded shortly). Your questions are to the point and have answers in the examples sections of the User's Guide as follows. With categorical latent variables, categorical observed variables are modeled using logistic regression (proportional odds if ordered polytomous outcomes and multinomial logistic regression with unordered outcomes) using maximum-likelihood estimation. With continuous latent variables, maximum-likelihood uses logistic regression while weighted least-squares uses probit regression (threshold model).
I have a question about your last statement: "With continuous latent variables, maximum-likelihood uses logistic regression while weighted least-squares uses probit regression (threshold model)."
Is there any way to get a probit regression using maximum likelihood estimation? I believe that other programs such as SAS and SPSS use ML in their probit regressions. If this is not available, is there an article/reference that explains why WLSMV is used instead of ML?
Also, I have a related question about standard errors. Comparing probit regressions between SPSS and MPlus, the standard errors are consistently larger in MPlus. Is this solely because errors are estimated under non-normality in WLSMV? I also have noticed that the difference in errors increases as more variables are added to the regression. Again, is this solely because of multivariate non-normality?
Mplus does not provide probit regression with maximum likelihood except when there is a single dependent variable. With a single dependent variable, the sample statistics are the maximum likelihood estimates. We chose to use weighted least square for probit regression with more than one dependent variable because a more general model can be supported, for example, residual covariances. You can look at Bengt's 1979 JASA article and 1984 Psychometika article which are listed on our website. If you can send output from SPSS and Mplus illustrating what you report in your last paragraph, I can try to offer an explanation.
Thank you for sending your output. The differences between SPSS and Mplus are most likely due to different ways of computing the information matrix that is used for the standard errors. The differences are within acceptable limits for your relatively small sample size. Mplus uses a sandwich like information matrix calculation. We don't know what SPSS uses. We expect these different approaches closer and closer results as the sample size increases.
Regarding the change in standard errors when you add more x variables, this can happen because the models are different.
Anonymous posted on Thursday, January 13, 2005 - 9:05 am
Can you please let me know the complete ISBN and price of the M+ User's Guide. Do you have a European Distributor for this publication ? Thanks a lot !