Re: [R] Regression model with proportional dependent variable

From: Achim Zeileis <Achim.Zeileis_at_uibk.ac.at>
Date: Tue, 12 Apr 2011 08:45:04 +0200 (CEST)

On Mon, 11 Apr 2011, ty ty wrote:

> Hello, dear experts. I don't have much experience in building
> regression models, so sorry if this is too simple and not very
> interesting question.
> Currently I'm working on the model that have to predict proportion of
> the debt returned by the debtor in some period of time. So the
> dependent variable can be any number between 0 and 1 with very high
> probability of 0 (if there are no payment) and if there are some
> payments it can very likely be 1 (all debt paid) although can be any
> number from 0 to 1.
> Not having much knowledge in this area I can't think about any
> appropriate model and wasn't able to find much on the Internet. Can
> anyone give me some ideas about possible models, any information
> on-line and some R functions and packages that can implement it.
> Thank you in advance for any help.

Beta regression is one possibility to model proportions in the open unit interval (0, 1). It is available in R in the package "betareg":

   http://CRAN.R-project.org/package=betareg    http://www.jstatsoft.org/v34/i02/

If 0 and 1 can occur, some authors have suggested to scale the response so that 0 and 1 are avoided. See the paper linked above for an example. If, however, there are many 0s and/or 1s, one might want to take a hurdle or inflation type approach. One such approach is implemented in the "gamlss" package:

   http://CRAN.R-project.org/package=gamlss
   http://www.jstatsoft.org/v23/i07/
   http://www.gamlss.org/

The hurdle approach can be implemented using separate building blocks. First a binary regression model that captures whether the dependent variable is greater than 0 (i.e., crosses the hurdle): glm(I(y > 0) ~ ..., family = binomial). Second a beta regression for only the observations in (0, 1) that crossed the hurdle: betareg(y ~ ..., subset = y > 0). A recent technical report introduces such a family of models along with many further techniques (specialized residuals and regression diagnostics) that are not yet available in R:

   http://arxiv.org/abs/1103.2372

Best,
Z

> Ihor.
>
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