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RE: st: Model for Poisson-shaped distribution but with non-count data


From   Cameron McIntosh <cnm100@hotmail.com>
To   STATA LIST <statalist@hsphsun2.harvard.edu>
Subject   RE: st: Model for Poisson-shaped distribution but with non-count data
Date   Wed, 7 Dec 2011 22:43:32 -0500

Following from Nick's emphasis on the behaviour/shape of conditional distributions in multivariate modeling rather than just the marginal distribution of the DVs (a point that is often not appreciated) -- in some modeling contexts, this is taken into account explicitly and one can capitalize on the presence of covariates to tame the distributions of the DVs. For example, certain weighted least squares approaches to path analysis, factor analysis and structural equation modeling will begin with conventional linear and/or non-linear regressions of all observed DVs on observed IVs (covariates/background variables), as well as regressing pairs of DVs on the IVs. The intercepts, slopes, and residual correlations from these first-stage regressions are saved and then used as the input data for estimating the the target model using robust weighted least squares, effectively directly invoking the assumption of "normality of y conditional on x".  This approach relaxes the normality as!
 sumption typically needed for computing sample moments and fitting structural models. See:

Muthén, B., du Toit, S.H.C., & Spisic, D. (November 18, 1997). Robust inference using weighted least squares and quadratic estimating equations in latent variable modeling with categorical and continuous outcomes. Unpublished technical report.http://www.gseis.ucla.edu/faculty/muthen/articles/Article_075.pdf

Muthen, B., & Satorra, A. (1995). Technical Aspects of Muthen's LISCOMP Approach to Estimation of Latent Variable Relations With a Comprehensive Measurement Model. Psychometrika, 60(4), 489-503.http://pages.gseis.ucla.edu/faculty/muthen/articles/Article_062.pdf

and further references therein. I am not sure what is currently available in Stata in this regard. 

Cam
----------------------------------------
> From: n.j.cox@durham.ac.uk
> To: statalist@hsphsun2.harvard.edu
> Date: Wed, 7 Dec 2011 19:47:28 +0000
> Subject: RE: st: Model for Poisson-shaped distribution but with non-count data
>
> Thanks.
>
> I did not spell out another key limitation, namely that -lnskew0- just works on the marginal distribution of the response and takes no account of the information in the predictors.
>
> Nick
> n.j.cox@durham.ac.uk
>
> -----Original Message-----
> From: owner-statalist@hsphsun2.harvard.edu [mailto:owner-statalist@hsphsun2.harvard.edu] On Behalf Of Owen Gallupe
> Sent: 07 December 2011 19:33
> To: statalist@hsphsun2.harvard.edu
> Subject: Re: st: Model for Poisson-shaped distribution but with non-count data
>
> Point taken...thank you for the advice, Nick. Very much appreciated.
>
> Owen
>
>
>
> On Wed, Dec 7, 2011 at 1:13 AM, Nick Cox <njcoxstata@gmail.com> wrote:
> > -lnskew0-  is a transformation command rather than a modelling
> > command. Its use would, in my view, create two key problems even if it
> > "worked".
> >
> > 1. You still have to explain to whoever you are writing for why using
> > ln(y - k) (in the most common case) makes scientific sense. Of course,
> > you may have a rationale for that. The usual rationale is that this is
> > in effect fitting a three-parameter lognormal distribution and there
> > is some clearcut reason why there is a definite lower limit to values
> > and also that it needs to be estimated from the data. Conversely if
> > you know k as a fixed minimum, there is no need to estimate it. No
> > covariates appear in this story.
> >
> > 2, The estimation of k and the estimation of whatever parameters you
> > use in any subsequent modelling command (in which covariates are now
> > introduced) are uncoupled, which is at best statistically awkward. If
> > you feed the results of -lnskew0- to a modelling command, you are
> > neglecting the uncertainty about k.
> >
> > In short, I would never use -lnskew0- unless it was _exactly_ what I wanted.
> >
> > Nick
> >
> > On Tue, Dec 6, 2011 at 8:48 PM, Owen Gallupe <ogallupe@gmail.com> wrote:
> >> Thank you for the input, Cam, Paul, Paul, Nick, David, and Bill.
> >>
> >> You have given me some very good options to consider.
> >>
> >> Regarding Cam's earlier question, the multimodality only surfaces when
> >> the DV is transformed using lnskew0. It is not an issue using the raw
> >> version.
> >>
> > *
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