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 Anonymous posted on Wednesday, August 17, 2005 - 10:53 am
In a couple of discussion threads I've noticed questions about regression with censored, nonnormal dependent variables...

I was wondering what the underlying assumptions are for CR in MPlus? I saw it said in one thread that there were some shortcomings in the Tobit estimator and it is not used in the current version of MPlus.

We have a censored, nonnormal dependent variable which is an offending diversity index based on Agresti and Agresti (1978) and are reluctant to transform it to use some type of ordered or binary regression for fear of losing a lot of the value of this measure.

Is there an approach in MPlus that would help in ensuring that our estimates are not biased? Is there a particular estimator (s) that we could use with the MPlus censored regression?
 bmuthen posted on Wednesday, August 17, 2005 - 10:59 am
Censored-normal regression can be done by ML or WLS(MV) in Mplus. This is the standard Tobit model assuming an underlying normal (uncensored) dependent variable that is censored from below or above at a known point. Earlier versions of Mplus didn't have the censored option. There is also censored-inflated modeling available in line with zero-inflated Poisson regression. And this can be incorporated in a larger model.
 Anonymous posted on Friday, August 19, 2005 - 4:51 am
Thank you Dr. Muthen.

Just to clarify--there aren't any estimators associated with the MPlus censored reg models that are appropriate for nonnormal data?

Are there any other options available in MPlus for dealing with that type of limited DV?
 Linda K. Muthen posted on Friday, August 19, 2005 - 8:23 am
Censored variables are non-normal and this is taken into account in the estimation of the model. Robust estimators are available with censored outcomes. If you look up ESTIMATOR in the index of the Mplus User's Guide, it will take you to a table where analysis type and scale of the dependent variables are crossed. The entries in the table are the estimators available.

Two-part modeling may be another approach for censored data. See what the following paper says about that:

Olsen, M. K, & Schafer, J., L. (2001). A two-part random effects model for semicontinuous longitudinal data. Journal of the American Statistical Association, 96, 730-745.
 Michael posted on Wednesday, October 12, 2005 - 10:40 am
I'm considering using my Mplus software to do SEM with censored variables, using ordinary TOBIT analysis.

Can you recommend a user-friendly paper on what it is that TOBIT does, hopefully written for a nonstatistician?

I've seen folks like Stoolmiller use it, but still don't have a great idea about what it actually does.

Thanks.
 bmuthen posted on Wednesday, October 12, 2005 - 11:26 am
Here are some references for Tobit regression, which is a building block for censored SEM. The Long book may be the more accessible for a nonstatistician. Tobin's article is the origin of this.

Long, S. (1996). Regression models for categorical and limited dependent variables. Thousand Oaks: Sage.

Maddala, G.S. (1983). Limited-dependent and qualitative variables in econometrics. Cambridge: Cambridge University Press.

Tobin, J (1958). Estimation of relationships for limited dependent variables. Econometrica, 26, 24-36.

I have a paper on censored factor analysis referenced on the Mplus web site but it si more technical.
 J.W. posted on Tuesday, March 18, 2008 - 11:46 am
The Tobit model assumes that the variance of the conditional distribution is uniform. Maddala (1983) comments that in the presence of heteroscedasticity, the usual Tobit estimates are inconsistent, and that there is only limited information about the direction of the bias. Maddala (1983) extends the Tobit model to cases where heteroscedasticity is present, and where one is able to specify the functional form of the variance (e.g. variance increases linearly as a function of a specific covariate). Methods for estimating the Tobit model in the presence of heteroscedasticity have been implemented in statistics/econometric software packages such as Limdep. Is it possible to run censored regression or censored-inflated regression in Mplus without bias in the presence of heteroscedasticity? Your help will be appreciated.
 Bengt O. Muthen posted on Saturday, March 22, 2008 - 12:58 pm
I am not sure, but I wonder if you can use the constraint = z option of the variable command in conjunction with Model Constraint in line with UG ex 5.23 ("QTL" example) to model the Tobit residual variance as a function of an observed z variable.
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