Tobit 1

[Florian Peitz]

Thisis fine. Now I want to run the "predict" function to get the fitted values. Ideally I am interested in the predicted values of the unobserved latent variable "y*" and the observed censored variable "y" [See Reference 1].

Generally predict-"response" results have been back-transformed to the original scale of data from whatever modeling transformations were used in a regression, whereas the "linear" predictions are the linear predictors on the link transformed scale. In the case of tobit which has an identity link, they should be the same.

The range ofpossible GRE scores is 200 to 800. This means that our outcome variable is both left censoredand right-censored. In other words, if two students score an 800, theyare equal according to our scale but might not truly be equal in aptitude.(In other words, we have a ceiling effect.) The same is true of two students scoring 200(a floor effect). Tobit regression generates a model thatpredicts the outcome variable to be within the specified range.

To generate a tobit model in Stata, list the outcome variable followed by thepredictors and then specify the lower limit and/or upper limit of the outcomevariable. The lower limit is specified in parentheses afterll and the upper limit isspecified in parentheses after ul.A tobit model can be used to predict an outcome that is censoredfrom above, from below, or both.

Hi, I'm doing a project for school. I'm trying to plot my tobit model. We didn't learn tobit in class but my professor said to write a strong report we'd have to use the tobit model. I've tried plotting it like I plotted my past glm and lm models but I receive an error message.

Ideally you'd give us a reproducible example (reprex) of your issue as a starting point. A reprex makes it much easier for others to understand your issue and figure out how to help. A lack of a reprex just makes it much less likely others will reply.

The function tobit is a convenience interface to survreg (for survival regression, including censored regression) setting different defaults and providing a more convenient interface for specification of the censoring information.

I understand that the coefficients given by a Tobit regression relate to an uncensored latent variable; however, since VMT actually cannot dip below zero, I'm interested in effects on the censored variable. I've found that typically the marginal effects are used to discuss Tobit results in this case vs. the regression coefficients.

For predicting values, I know one can make adjustments to generate expected values of the censored latent variable (as outlined here). In R, the VGAM package also allows you to specify type.fitted ="censored" for Tobit; when then fed into the predict function, it provides estimates for the censored latent variable as well.

My question is, is using these censored-variable estimates practical in generating real-world predictions, or is shifting the predicted values to reflect a censored latent variable more of an academic exercise? Hopefully that makes some sense -- I just haven't seen Tobit models used predictively anywhere, and I'm trying to generate how shifts in my independent variables will actually impact VMT from predicted values.

Yes, it is quite common to use tobit (and related) models for predictive modeling of non-negative variables with a point-mass at zero. Often probabilistic forecasts are used, e.g., the probability for a zero outcome or certain quantiles (median, 90% quantile, etc.).

Whether there really is an underlying latent variable that is actually censored is not so important. The "trick" of using a zero-censored Gaussian distribution for the model to accomodate the point mass at zero also works in many situations where an underlying uncensored variable is less plausible. For example, in our own work we often use tobit models for probabilistic forecasting of precipitation.

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Background: In many epidemiologic longitudinal studies, the outcome variable has floor or ceiling effects. Although it is not correct, these variables are often treated as normally distributed continuous variables.

Objectives: In this article, the performance of a relatively new statistical technique, longitudinal tobit analysis, is compared with a classical longitudinal data analysis technique (i.e., linear mixed models).

Study design and setting: The analyses are performed on an example data set from rehabilitation research in which the outcome variable of interest (the Barthel index measured at on average 16.3 times) has typical floor and ceiling effects. For both the longitudinal tobit analysis and the linear mixed models an analysis with both a random intercept and a random slope were performed.

Results: Based on model fit parameters, plots of the residuals and the mean of the squared residuals, the longitudinal tobit analysis with both a random intercept and a random slope performed best. In the tobit models, the estimation of the development over time revealed a steeper development compared with the linear mixed models.

Conclusion: Although there are some computational difficulties, longitudinal tobit analysis provides a very nice solution for the longitudinal analysis of outcome variables with floor or ceiling effects.

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