Re: st: RE: new package margdistfit available on SSC

[Austin Nichols <austinnichols@gmail.com>]

Maarten--
This is an interesting exercise, though I would think only relevant
for ML since no theoretical distribution is assumed for OLS etc.

Minor points:

1. A parametric regression typically does not allow parameters to
change as X changes, contrary to your text describing the command:
"The idea behind a parametric regression model is that it assumes a
distribution for the dependent variable, but lets one or more
parameters, typically the mean, change whenever the explanatory
variables change."

That (allowing parameters to change as X changes) is in fact what
(say) -lpoly- does, or other semi- or nonparametric methods.

Parametric regression models do not need to assume a distribution for
the dependent variable.
The conditional mean changes with X, but the parameters b multiplying
X do not change with X, by assumption.
And a linear regression need not be linear in variables, only linear
in parameters b.

This is easily fixed if you write instead of:

"The key concept in this command is the marginal distribution. The
idea behind a parametric regression model is that it assumes a
distribution for the dependent variable, but lets one or more
parameters, typically the mean, change whenever the explanatory
variables change. So, the marginal distribution of the dependent
variable implied by the model is a mixture distribution of N
distributions, such that each component distribution gets the
parameters of one of the observations in the data."

something like:

"The key concept in this command is the marginal distribution. The
idea behind a parametric regression model is that the conditional mean
of the dependent variable changes whenever the explanatory variables
change. So, the marginal distribution of the dependent variable
implied by the model is a mixture distribution of N distributions,
such that each component distribution gets the conditional mean of one
of the observations in the data."

2. What effect do heteroskedasticity or clustering of errors have on
your examples?   Must you assume i.i.d. errors?

3. The link to "helpfile" at http://www.maartenbuis.nl/software/margdistfit.html
pointing to http://repec.org/bocode/m/margdistfit.html
seems to be broken.

On Fri, Nov 18, 2011 at 8:53 AM, Feiveson, Alan H. (JSC-SK311)
<alan.h.feiveson@nasa.gov> wrote:
> Maarten - Thank you! I have been doing this "by hand" for years!
>
> Al
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Maarten Buis
> Sent: Friday, November 18, 2011 3:48 AM
> To: statalist@hsphsun2.harvard.edu
> Subject: st: new package margdistfit available on SSC
>
> Thanks to Kit Baum a package, -margdistfit-, is now available from
> SSC. -margdistfit- displays graphs that can help determine how well a
> distributional assumption made in a parametric regression model fits
> to the data. It does so by comparing the distribution of the dependent
> variable with the marginal distribution implied by the model. To
> install -margdistfit- type in Stata: -ssc install margdistfit-.
>
> In parametric regression models a distribution is assumed for the
> dependent variable, but its parameters, typically the mean,  is
> allowed to change from observation to observation depending on the
> values of the explantory variables. So the distribution of the
> dependent variable implied by the model is a mixture of N
> distributions, such that each component distribution has the
> parameters of one of the observations. This is the called the marginal
> distribution. If the distributional assumption is correct than this
> marginal distribution should correspond with the distribution of the
> dependent variable. -margdistfit- compares the two distribution with a
> probabiltiy-probability plot (to investigate the middle of the
> distribution) and a quantile-quantile plot (to investigate the tails).
> It can also show the two cumulative density functions. Examples can
> be found at <http://www.maartenbuis.nl/software/margdistfit.html>.
>
> The current version of -margdistfit- can be used after -regress- and
> -betafit-, the latter is available from SSC.
>
> I hope some of you will find it useful,
> Maarten

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