Hallo. Many thanks for your answer. Let me check please that I do understand it correctly. Does it mean that the estimated log-likelyhood function is (in the Gaussian case)
sum y * log F(x'b / exp(z'g)) + sum (1 - y) * log(1 - F(x'b / exp(z'g)) where F is standard normal CDF, and the rest is as in your mail? Many thanks once more. Best wishes Michal P.S. Sorry if you get this mail twice -- I'm not yet certain with this mailing list to what mail address I should reply. 2013/5/31 Achim Zeileis <achim.zeil...@uibk.ac.at>: > On Fri, 31 May 2013, Michal Kvasni?ka wrote: > >> Hallo. >> >> First many thanks to its authors for glmx package and hetglm() >> function especially. It is absolutely great. > > > Glad it is useful for you! > > >> Now, let me ask my question: what model of heteroskedasticity hetglm() >> uses? Is the random part of the Gaussian probit model >> >> norm(0, sd = exp(X2*beta2)) >> >> where norm is the Gaussian distribution, 0 is its zero mean, and sd is >> its standard deviation modelled as a linear model with explanatory >> variables X2 (a matrix) and some unknown parameters beta2? > > > In the hetglm model the response y is distributed with mean mu and from some > exponential family (default: binomial). And the following equation holds: > > mu = h( x'b / exp(z'g) ) > > where h() is the inverse link function. Thus if h() is the normal > distribution function (inverse probit link), then > > mu = P(X > 0) > > where X is normally distributed with mean x'b and standard deviation > exp(z'g). > > Hope that helps, > Z > >> I'm asking because after estimating a heteroskedastic probit, I want >> to estimate a Heckit. I plan to use two-stage estimation procedure. In >> the first step I want to estimate the heteroskedastic probit, and in >> the second step the linear part (with bootstrapped confidence >> intervals of parameters). The linear part includes inverse Mill's >> ration lambda where >> >> lambda = dnorm(X1*beta1, sd=?) / pnorm(X1*beta1, sd=?) >> >> where X1 are the explanatory variables of the probit model, and beta1 >> are their parameters. (I hope I can tweak the homoskedastic model this >> way.) (I plan to use two-step estimation to avoid further distribution >> assumptions on the linear part of the model.) >> >> Many thanks for your answer to my question (and also for any comment >> on the overall estimation procedure). >> >> Best wishes, >> Michal >> >> ______________________________________________ >> R-help@r-project.org mailing list >> https://stat.ethz.ch/mailman/listinfo/r-help >> PLEASE do read the posting guide >> http://www.R-project.org/posting-guide.html >> and provide commented, minimal, self-contained, reproducible code. >> > ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
