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  • Tobit model and multiple imputation

    Hi, I am using a Tobit model. But my data have a lot of missing values. So I have to create 5-20 imputed data sets. However, the Stata command "mi estimate:" does not support commands such as "tobit" or "craggit" (Cragg's Tobit). My questions are:
    (1) Is there any command that can be used to calculate coefficients, standard errors, and p-values for Tobit models based on imputed data sets?
    (2) More generally, for any regression models not supported by the command "mi estimate," how can I get the coefficients and standard errors by hand calculation? Do I simply "average" the coefficients and standard errors across my imputed data sets, or is there any formula?

  • #2
    as far as your question #(2) is concerned, you may find some enlightening stuff via - help mi estimate- and related entry in Stata 13.1 .pdf manual, page 64-67.
    Kind regards,
    (Stata 16.0 SE)


    • #3
      I just ran into this problem, and I wanted to follow up.

      In theory, you can force Stata to MI estimate a Tobit model like this:

      mi estimate, cmdok: tobit y x, ul(5)
      I just did this, and the command ran. Programming-wise, Stata has some simple requirements listed below, and many estimation commands meet these requirements.

      Per Rubin's rules, which form the theoretical underpinning of multiple imputation, the statistic that you are estimating must have an asymptotic normal distribution for the results from MI to be theoretically valid. People interested in the math can go Google Rubin's reference (listed in the link), and then calculate any statistics involved by hand.

      That leaves open the question of whether the Tobit model's coefficients have an asymptotic normal distribution. I would be interested to hear if anyone knows anything on the theoretical side. If the Tobit model's properties are too ill-behaved to work, is there another way to handle missing data in a censored regression model that is also theoretically justified?
      Please use the code delimiters to show code and results - use the # button on the formatting toolbar, between the " (double quote) and <> buttons.

      Please use the command -dataex- to show a representative sample of data; it is installed already if you have Stata 14.2 or 15.1, else you can install it by typing

      ssc install dataex


      • #4
        Hi - I am also interested in this question, and have been unable to find an answer - can anybody clarify whether/under what conditions the parameters from the tobit model are asymptotic normal, and therefore suitable for use with Rubin's rules?

        I have also asked the same question here: