betafit

Authors: Maarten L. Buis, Nicholas J. Cox, and Stephen P. Jenkins

Stata program fitting a two parameter beta distribution, optionally dependent on covariates. The beta distribution is a flexible model for a dependent variable that is bounded between zero and one, for example a proportion. betafit allows two parameterizations, besides the traditional parameterization in terms of two shape parameters it also alows a more interpretable alternative (regression-like) parameterization in terms of a location and scale parameter, which was independently proposed by Philip Paolino (2001), Silvia Ferrari and Francisco Cribari-Neto (2004), and Michael Smithson and Jay Verkuilen (2006).

This package can be installed by typing in Stata: ssc install betafit

Supporting materials

Presentation held at the 2010 German Stata Users' meeting on analyzing proportions with betafit, zoib, the fractional logit, dirifit, and fmlogit.
Presentation held at the London Stata Users' meeting 2006 on analyzing proportions with betafit, dirifit, and other Stata programs.
Short technical text on how to get from the probability density function shown in the above presentation to the likelihood function used in betafit.
summary on ssc
helpfiles:
- helpfile betafit, and
- helpfile betafit post-estimation commands
certification script used for version 1.1.7 (April 08, 2011).
Announcement on statalist of update including the alternative parameterizations.
Announcement on Statalist of update including dbetafit which calculates various marginal effects.
Resources for estimating beta regression in SPSS, R, and SAS, by Michael Smithson and Jay Verkuilen.

References

Ferrari, S.L.P. and Cribari-Neto, F. (2004). Beta regression for modelling rates and proportions. Journal of Applied Statistics 31(7): 799-815.

Paolino, P. (2001). Maximum likelihood estimation of models with beta-distributed dependent variables. Political Analysis 9(4): 325-346. link

Smithson, M. and Verkuilen, J. (2006) A better lemon squeezer? Maximum likelihood regression with beta-distributed dependent variables. Psychological Methods 11(1): 54-71.

Example

. use http://fmwww.bc.edu/repec/bocode/c/citybudget.dta, clear (Spending on different categories by Dutch cities in 2005)

. betafit governing , mu(minorityleft noleft )

initial: log likelihood = 718.24584 rescale: log likelihood = 718.24584 rescale eq: log likelihood = 718.24584 Iteration 0: log likelihood = 718.24584 Iteration 1: log likelihood = 732.19835 Iteration 2: log likelihood = 738.15983 Iteration 3: log likelihood = 738.1705 Iteration 4: log likelihood = 738.1705

ML fit of beta (mu, phi) Number of obs = 394 Wald chi2(2) = 40.19 Log likelihood = 738.1705 Prob > chi2 = 0.0000

------------------------------------------------------------------------------ | Coef. Std. Err. z P>|z| [95% Conf. Interval] -------------+---------------------------------------------------------------- minorityleft | -.0407548 .0639882 -0.64 0.524 -.1661693 .0846598 noleft | .2520844 .0631474 3.99 0.000 .1283178 .375851 _cons | -2.332194 .0539375 -43.24 0.000 -2.43791 -2.226479 -------------+---------------------------------------------------------------- /ln_phi | 4.013526 .0715673 56.08 0.000 3.873256 4.153795 -------------+---------------------------------------------------------------- phi | 55.34165 3.960652 48.09876 63.6752 ------------------------------------------------------------------------------

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