%Beta_Regression Macro from "Inflated Beta Regression: Zero, One, and Everything in Between"

[markus24135]

Dear SAS Community,

I have recently run into a situation where my model requires a zero-one-inflated beta regression.

I have applied the macros created by Christopher Swearingen, Maria Melguizo Castro, and Zoran Bursac in their paper 325-2012 from the SAS Global Forum in 2012 (https://support.sas.com/resources/papers/proceedings12/325-2012.pdf) but I have a question.

The macro calls for:

%Macro Beta_Regression(Dataset,tech,details,mu_vars,phi_vars,zero_vars,one_vars,
depvar);

with - 

Dataset – the LIBNAME.DATA file
tech – allows for different optimization schemes to be used
details – allows for other options to be specified
mu_vars – variables modeling changes in mean
phi_vars – variables modeling changes in precision
zero_vars – variables predicting a response of zero
one_vars – variables predicting a response of one
depvar – the dependent variable scaled to a [0,1] interval

I can't figure out what they are referring to with the "mu_vars" and "phi_vars" though. From what I can gather from the paper and from Ospina et. al this could be referring to continuous independent variables and categorical independent variables, respectively, in the model. Is this correct?

Please explain as much as possible without jargon, I am not a statistician. Thank you very much in advance!!

Mark

[SteveDenham · Accepted solution]

mu_vars refer to model effects, whether continuous or categorical. In other words, the independent variables that have an effect on the mean of the dependent variable.  phi_vars refer to the reciprocal of the variance/deviance of the model.  There are several ways of parameterizing a beta distribution, and one is the "mean and precision" method. Here is a good introductory level presentation on the beta distribution:

http://quantdevel.com/public/CSP2017/ModelingProportionsAndProbabilities.pdf 

SteveDenham

[markus24135]

So you could have the same variables predicting both the mean and precision?

[SteveDenham]

Hi @markus24135 

I am not really familiar enough with the macro syntax to say for sure, but I would guess (and stress that it is only a guess) that the covariates associated with each of these could be identical, but may not be.  In the first example in the paper (Brazilian traffic accidents), they are identical. In the Barthel index examples where zero and one inflation are fit, it appears that they are not identical, with the phi_var as a subset of the mu_var.  I suppose if I tore into the coding I could give a better answer.

SteveDenham.