In this paper, I show how to estimate the parameters of the beta-binomial distribution and its multivariate generalization, the Dirichlet-multinomial distribution. This approach involves no additional programming, as it relies on an existing Stata command used for overdispersed count panel data. Including covariates to allow for regression models based in these distributions is straightforward.
AgrestiA.2002. Categorical Data Analysis.2nd ed. Hoboken, NJ: Wiley.
2.
GuimarãaesP.2004. Understanding the multinomial-Poisson transformation. Stata Journal4: 265–273.
3.
GutierrezR. G., CarterS., and DrukkerD.M.2001. sg160: On boundary-value likelihood-ratio tests. Stata Technical Bulletin60: 15–18. In Stata Technical Bulletin Reprints, vol. 10, 269–273. College Station, TX: Stata Press.
4.
HeckmanJ., and WillisR.1977. A beta-logistic model for the analysis of sequential labor force participation by married women. Journal of Political Economy85: 27–58.
5.
JohnsonN., KotzS., and BalakrishnanN.1997. Discrete Multivariate Distributions.New York: Wiley.
6.
MosimannJ.1962. On the compound multinomial distribution, the multivariate betadistribution, and correlations among proportions. Biometrika49: 65–82.
7.
NeerchalN., and MorelJ.2005. An improved method for the computation of maximum likelihood estimates for multinomial overdispersion models. Computational Statistics and Data Analysis49: 33–43.
