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# Re: st: Truncated at zero count data with underdispersion

 From Steve Samuels <[email protected]> To [email protected] Subject Re: st: Truncated at zero count data with underdispersion Date Mon, 11 Oct 2010 14:36:42 -0400

```"> Does anyone know any stata command that i could use to model zero
> truncated count data with underdispersion?"

There are too possibilities:
or
2) The Poisson distribution doesn't fit your data-my best guess.

If the Poisson model doesn't fit, use -mlogit- or -ologit-,  with
categories being the numbers of cell phones.  You might have to
combine sparse categories.  Since your goal is prediction in an
external data set,  split the study data set into two parts; develop
the model on one part, and assess the predictive accuracy of the model
on the second.  (There are probably also -jackknife- or -boostrap-
possibilities for getting cross-validated "honest" assessments of
accuracy.)

Here's an example of assessing predictive accuracy from -mlogit-. The
predicted category is that with the highest probability, and
predictive criterion is the difference between observed and predicted
category and its root MSE.

***********CODE BEGINS*************
sysuse auto, clear
recode rep78 1/2 = 2
mlogit rep78 mpg trunk
forvalues i = 2/5{
predict p`i', outcome(`i')
}
egen pmax = rowmax(p2 p3 p4 p5)

gen p_class = 2
forvalues i =3/5{
replace p_class = `i' if pmax ==p`i'
}
label var p_class "Predicted Category"

gen diff = rep78 - p_class
tab diff
sum  diff
scalar mse = r(var) + r(mean)^2
di mse

***********CODE ENDS**************

On Sun, Oct 10, 2010 at 6:39 PM, Laurie Molina <[email protected]> wrote:
> Hi all,
>
> I have a question, i hope somebody  can help my.
>
> I am modelling count data truncated at zero: The number of cell phones
> of households with cells phone. The observed data goes from 1 to 9,
> with mean equals 1.89 and variance 1.14.
> I have done some underdispersion tests after running a poisson
> regression with the truncated data and i reject the one sided
> hypothesis of equidispersion with a p-value of cero. (the predicted
> values have mean 1.89 with variance equal .51).
>
> Regarding the latent variable, i have also availabre the number of
> cellphones of all the households, i.e. i have the data of the latent
> variable that goes from 0 to 9. Here the mean equals 1.15 and the
> variance equals 1.54. I have also done and underdispersion test after
> running a poisson regresion with all the data and i get
> underdispersion (the predicted values have mean 1.15 but variance
> equal .999).
>
> I am interested in the truncated regresion because i want to predict
> the number of cell phones of the HH who have cell phones. I mean, in
> addition to the data that i am using for this regresion,  i have
> another list of households and i know wheter they have or they dont
> have a cell phone. But among the HH in that list, who do have a cell
> phone, i do not know how many of them they have, and i am interested
> in that.
>
> To my understand if i use a poisson regression, given that my data is
> truncated i will get inconsistent estimates because the conditional
> expectation will not be correctly specified as an exponential function
> of xbeta.
> So i have to use the command:
> ****
> ztp depvar indep var
> ****
> But if the latent variable is not poisson i will get inconsistent estimates.
>
> I know stata has also availabre the zero truncated negative binomial
> regression, but since i get underdispersion in the latent variable i
> think the data is not negative binomial distributed so i will still
> get inconsistent estimates.
>
> Does anyone know any stata command that i could use to model zero
> truncated count data with underdispersion?
>
> Thank you all very much in advance.
>
> Regards,
>
> Laurie.
> *
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>

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```