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
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