R help - May 2013 - glmx specification of heteroskedasticity (and its use in Heckit)

Hallo.

First many thanks to its authors for glmx package and hetglm()
function especially. It is absolutely great.

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?

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

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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