Robit regression in Stata

Abstract

Logistic and probit models are the most popular regression models for binary outcomes. A simple robust alternative is the robit model, which replaces the underlying normal distribution in the probit model with a Student’s t distribution. The heavier tails of the t distribution (compared with the normal distribution) mean that model outliers are less influential. Robit regression models can be fit as generalized linear models with the link function defined as the inverse cumulative t distribution function with a specified number of degrees of freedom; they have been advocated as being particularly suitable for estimating inverse-probability weights and propensity scoring more generally. Here we describe a new command, robit, that implements robit regression in Stata.

Keywords

st0724 robit xlink robit regression binary regression generalized linear models inverse-probability weights

Get full access to this article

View all access options for this article.

References

Albert

J. H.

Chib

. 1993. Bayesian analysis of binary and polychotomous response data. Journal of the American Statistical Association 88: 669–679. https://doi.org/10.2307/2290350.

Buis

M. L.

2007. Stata tip 48: Discrete uses for uniform(). Stata Journal 7: 434–435. https://doi.org/10.1177/1536867X0700700309.

Cattaneo

M. D.

2010. Efficient semiparametric estimation of multi-valued treatment effects under ignorability. Journal of Econometrics 155: 138–154. https://doi.org/10.1016/j.jeconom.2009.09.023.

Gelman

Hill

Vehtari

. 2021. Regression and Other Stories. Cambridge University Press: Cambridge. https://doi.org/10.1017/9781139161879.

Kang

J. D. Y.

Schafer

J. L.

. 2007. Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data. Statistical Science 22: 523–539. https://doi.org/10.1214/07-STS227.

Lange

K. L.

Little

R. J. A.

Taylor

J. M. G.

. 1989. Robust statistical modeling using the t distribution. Journal of the American Statistical Association 84: 881–896. https://doi.org/10.2307/2290063.

Nadarajah

. 2020. A review of Student’s t distribution and its generalizations. Empirical Economics 58: 1461–1490. https://doi.org/10.1007/s00181-018-1570-0.

Liu

C. H.

2004. Robit regression: A simple robust alternative to logistic and probit regression. In Applied Bayesian Modeling and Causal Inference from Incomplete-Data Perspectives, ed. Gelman

Meng

X.-L.

, 227–238. Chichester, U.K.: Wiley. https://doi.org/10.1002/0470090456.ch21.

Liu

C. H.

2006. Robit regression: A simple robust alternative to logistic and probit regression. https://www.stat.purdue.edu/∼/chuanhai/teaching/Stat598A/robit.pdf.

10.

Lunt

2017. Propensity analysis. https://personalpages.manchester.ac.uk/staff/mark.lunt/propensity.html.

11.

McCullagh

Nelder

J. A.

. 1989. Generalized Linear Models. 2nd ed. London: Chapman and Hall/CRC. https://doi.org/10.1201/9780203753736.

12.

Mudholkar

G. S.

George

E. O.

. 1978. A remark on the shape of the logistic distribution. Biometrika 65: 667–668. https://doi.org/10.1093/biomet/65.3.667.

13.

Newson

R. B

. 1998a. parmest: Stata module to create new data set with one observation per parameter of most recent model. Statistical Software Components S352601, Department of Economics, Boston College. https://ideas.repec.org/c/boc/bocode/s352601.html.

14.

Newson

R. B

. 1998b. somersd: Stata module to calculate Kendall’s tau-a, Somers’ D and median differences. Statistical Software Components S336401, Department of Economics, Boston College. https://ideas.repec.org/c/boc/bocode/s336401.html.

15.

Newson

R. B

. 2002a. lincomest: Stata module to generate linear combinations of estimators saved as estimation results. Statistical Software Components S430901, Department of Economics, Boston College. https://ideas.repec.org/c/boc/bocode/s430901.html.

16.

Newson

R. B

. 2002b. Parameters behind “nonparametric” statistics: Kendall’s tau, Somers’ D and median differences. Stata Journal 2: 45–64. https://doi.org/10.1177/1536867X0200200103.

17.

Newson

R. B

. 2006. Confidence intervals for rank statistics: Somers’ D and extensions. Stata Journal 6: 309–334. https://doi.org/10.1177/1536867X0600600302.

18.

Newson

R. B

. 2009a. haif: Stata module to compute Homoskedastic Adjustment Inflation Factors for model selection. Statistical Software Components S457016, Department of Economics, Boston College. https://ideas.repec.org/c/boc/bocode/s457016.html.

19.

Newson

R. B

. 2009b. listtab: Stata module to list variables as rows of a T_EX, HTML or word processor table. Statistical Software Components S457088, Department of Economics, Boston College. https://ideas.repec.org/c/boc/bocode/s457088.html.

20.

Newson

R. B

. 2016. The role of Somers’ D in propensity analysis. Presented at the U.K. Stata Users Group meeting, London, U.K., September 8–9. https://www.stata.com/meeting/uk16/slides/newson_uk16.pdf.

21.

Newson

R. B

. 2021. xlink: Stata module to provide extra link functions for use with glm. Statistical Software Components S458996, Department of Economics, Boston College. https://econpapers.repec.org/software/bocbocode/s458996.htm.

22.

Ridgeway

McCaffrey

D. F.

. 2007. Comment: Demystifying double robustness: A comparison of alternative strategies for estimating a population mean from incomplete data. Statistical Science 22: 540–543. https://doi.org/10.1214/07-STS227C.

23.

Rubin

D. B.

2008. For objective causal inference, design trumps analysis. Annals of Applied Statistics 2: 808–840. https://doi.org/10.1214/08-AOAS187.

24.

Seaman

S. R.

White

I. R.

. 2013. Review of inverse probability weighting for dealing with missing data. Statistical Methods in Medical Research 22: 278–295. https://doi.org/10.1177/0962280210395740.

25.

Seber

G. A. F.

Lee

A. J.

. 2003. Linear Regression Analysis. 2nd ed. New York: Wiley. https://doi.org/10.1002/9780471722199.

26.

Zellner

1976. Bayesian and non-Bayesian analysis of the regression model with multivariate Student-t error term. Journal of the American Statistical Association 71: 401–405. https://doi.org/10.1080/01621459.1976.10480357.

Supplementary Material

Please find the following supplemental material available below.

For Open Access articles published under a Creative Commons License, all supplemental material carries the same license as the article it is associated with.

For non-Open Access articles published, all supplemental material carries a non-exclusive license, and permission requests for re-use of supplemental material or any part of supplemental material shall be sent directly to the copyright owner as specified in the copyright notice associated with the article.

0.00 MB