R vs SAS Tobit Regression
Tobit Regression Comparison
The following table shows the tobit regression analysis, the capabilities of each language, and whether or not the results from each language match.
| Analysis | Supported in R | Supported in SAS | Results Match | Notes |
|---|---|---|---|---|
| Tobit Regression (normal distributed data assumption) | Yes | Yes | Yes | The results from censReg::censReg and survival::survreg match the SAS PROC LIFEREG results |
Comparison Results
Normally distributed data assumption
Here is a table of comparison values between the R functions censReg::censReg, survival::survreg, VGAM::vglm, and SAS PROC LIFEREG for the dataset used. The statistics around the treatment effect (difference between group A and B, B-A) are provided. Further we also present the estimate of \(\sigma\). All numbers are rounded to 4 digits
| Statistic | censReg() | survreg() | vglm() | LIFEREG | Match | Notes |
|---|---|---|---|---|---|---|
| Treatment effect | 1.8225 | 1.8225 | 1.8226 | 1.8225 | Yes | see below |
| Standard error | 0.8061 | 0.8061 | 0.7942 | 0.8061 | Yes | see below |
| p-value | 0.0238 | 0.0238 | 0.0217 | 0.0238 | Yes | see below |
| 95% CI (Wald based) | 0.2427 ; 3.4024 | 0.2427 ; 3.4024 | 0.2661 ; 3.3791 | 0.2427 ; 3.4024 | Yes | see below |
| \(\sigma\) | 1.7316 | 1.7316 | 1.7317 | 1.7316 | Yes | see below |
Note: The results of VGAM::vglm() are slightly different since an iteratively reweighted least squares (IRLS) algorithm is used for estimation.
Summary and Recommendation
Comparison between SAS PROC LIFEREG and R functions censReg::censReg and survival::survreg show identical results for the dataset tried.
Historically and typically the Tobit model is based on the assumption of normal distributed data. Within SAS PROC LIFEREG and R survival::survreg multiple other different distributional assumption are possible. These include weibull, exponential, gaussian, logistic, lognormal and loglogistic for survival::survreg. These include EXPONENTIAL, GAMMA, LLOGISTIC, LOGISTIC, LOGNORMAL, NORMAL, WEIBULL for PROC LIFEREG.
References
Breen, R. (1996). Regression models. SAGE Publications, Inc., https://doi.org/10.4135/9781412985611
Tobin, James (1958). “Estimation of Relationships for Limited Dependent Variables”. Econometrica. 26 (1): 24-36. doi:10.2307/1907382