Longitudinal tobit regression: a new approach to analyze outcome variables with floor or ceiling effects

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.

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).

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.

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.

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.