RE: st: which -cmp- option to use for poisson model with count data?

[Cameron McIntosh <cnm100@hotmail.com>]

Laura,
Yes, the "independence of observations" assumption that Nick mentions below could be violated due to a complex survey design with stratification and clustering (or clustering of cases due to any number of possible reasons).  This can be dealt with: 
Lu, M., & Yang, W. (2012). Multivariate Logistic Regression Analysis of Complex Survey Data with Application to BRFSS Data. Journal of Data Science 10, 157-173.

Moore, C.G., Lipsitz, S.R., Addy, C.L., Hussey, J.R., Fitzmaurice, G., & Natarajan, S. (2009). Logistic regression with incomplete covariate data in complex survey sampling: application of reweighted estimating equations. Epidemiology, 20(3), 382-390.

If you want to use an ordered regression model with count data, you can consider the counts as thresholds on a latent response variate (i.e., propensity to consult experts in this case):

Kasteridis, P.P., Munkin, M.K. ,& Yen, S.T. (2010). Demand for cigarettes: a mixed binary-ordered probit approach. Applied Economics, 42(4), 413-426. 

Cam----------------------------------------> From: n.j.cox@durham.ac.uk
> To: statalist@hsphsun2.harvard.edu
> Date: Mon, 7 May 2012 18:16:49 +0100
> Subject: RE: st: which -cmp- option to use for poisson model with count data?
>
> For the record, that's close to what I said.
>
> On dependence: I don't think it is crucial that you can't ask 3 experts without asking 2 first, and so forth. How you get to what is recorded as an outcome of 3 is a separate issue. Dependence would mean that my chance of asking so many experts would depend on somebody else's chances, somehow.
>
> Nick
> n.j.cox@durham.ac.uk
>
> Maarten Buis
>
> On Mon, May 7, 2012 at 4:58 PM, Laura R. wrote:
> > the distribution of the variable "number of experts" consulted is not
> > "zero-inflated", but rather follows a normal distribution from 0 to 5.
>
> That is very implausibly, if not impossible (assuming that with
> "normal distribution" you mean the Gaussian distribution that is often
> called "bell shaped" in introductory statistics books).
>
> > As there theoretically can be more than 5 experts, Nick sais, if I
> > understand correctly, that this would be a hint to use Poisson model,
> > as I would have to label the highest "category" "5 or more" in ordered
> > probit.
>
> Neither Poisson nor ordered probit/logit care (and thus ignore) how
> you label values, so your summary of Nick's reasoning is not true.
> Based on the information you have given us I would lean towards
> Poisson, but to make this kind of choice you really need to have
> detailed knowledge of the data, the exact question that was asked and
> the possible answer categories (don't trust the variable label, look
> in the codebook and the original questionnaire), the process that is
> being measured, etc. etc.
>
> > However, I have read that the events have to be independent of each
> > other in the Poisson model, e.g. emergency room admission (taking
> > David Roodman's example). This would be a reason for not using
> > Poisson. E.g., deciding on getting a third child probably depends on
> > how life is with 2 children --> ordered probit model. COnsulting
> > another expert can also depend on what the last one had said.
> >
> > I think I will try the ordered probit model again, as this can be used
> > within -cmp-, while the Poisson model cannot. If the parallel
> > regression assumption or other assumptions for ordered probit models
> > turn out to be violated, I will try the Poisson model, but then I have
> > to come up with an idea similar to -cmp- that can be used with
> > Poisson.
>
>
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