Hi all SAS users, I'm trying to model loss-given-default data on the basis of the SAS paper n. 1593-2014 (see http://support.sas.com/resources/papers/proceedings14/1593-2014.pdf). Particularly, the third model proposed by the authors in such paper is based on the inflated beta regression model, that is explained with the following SAS program: proc nlmixed data=MyData tech=quanew maxiter=3000 maxfunc=3000 qtol=0.0001;
parms b0-b14=0.0001
pie=0.2
kesai=0.3
phi=2;
cov_mu=b0+b1*Var1+b2*Var2+…+b14*Var14;
mu=logistic(cov_mu);
if RR=0
then loglikefun=log(pie)+log(1-kesai);
if RR>=1
then loglikefun=log(pie)+log(kesai);
if 0<RR<1
then loglikefun=log(1-pie)+lgamma(phi)-lgamma(mu*phi)-lgamma((1-mu)*phi)
+(mu*phi-1)*log(RR)+((1-mu)*phi-1)*log(1-RR);
predict pie*kesai+(1-pie)*mu out=Inf_beta_output (keep=instrument_id RR pred);
model RR~general(loglikefun);
run; I would like to understand what are the parameters pie, kesai and phi and how they can be computed/estimated. Indeed, I know that the beta distribution has 2 shape parameters, usually named alpha and beta, that can be computed on the basis of the sample mean and variance by using the method of moments, but I do not know how to to relate such parameters with ones used in the program (pie, kesai and phi). Could you suggest some solution or explanation about such parameters? Thanks all!
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