Re: st: use -predictnl- to construct confidence intervals

[Stas Kolenikov <skolenik@gmail.com>]

-predictnl- is not aware of your interpretation of [whatever
complicated nonlinear expression you feed it] as a probability. To get
more appropriately bounded, although asymmetric, prediction intervals
(technically, those are not confidence intervals, by the way, since
you are not talking about a population parameter), you might want to
run the prediction on the logit scale, and then manually transform the
prediction and the confidence limits.

On Tue, Aug 31, 2010 at 4:50 PM, J. Li <lij53@univmail.cis.mcmaster.ca> wrote:
> Dear all,
>
> I am using a random effects ordered probit model to estimate the
> transition of health status over time. There are four health states:
> poor, fair, good and excellent. After using -reoprob- estimation, I
> used -predictnl- to construct 95% intervals of the predicted
> probabilities of reporting each health status. I specified the
> expression to -predictnl- for reporting the poor health status as
> following:
>
> predictnl prob1=
> normprob((_b[_cut1:_cons]/sqrt(1+(_b[rho:_cons]/(1-_b[rho:_cons])))) -
> (predict(xb)/sqrt(1+(_b[rho:_cons]/(1-_b[rho:_cons]))))), ci(p1lower
> p1upper)
>
> in which    _b[_cut1:_cons]    is the estimate of the lowest cut-point
>  and      sqrt(1+(_b[rho:_cons]/(1-_b[rho:_cons])))    is a scale
> representing the square root of (1+ &#963;^2). In Wooldridge 2005
>  “SIMPLE SOLUTIONS TO THE INITIAL CONDITIONS PROBLEM IN DYNAMIC,
> NONLINEAR PANEL DATA MODELS WITH UNOBSERVED HETEROGENEITY”, it is
> suggests that the original parameters should be divided by this scale
> to construct the expected probability function in order to calculate
> the average partical effects.
>
> After the prediction, I got two variables for the upper and lower
> bounds of the 95% confidence interval for each observation. But
> strangely, for some of the observations, the left endpoint is a
> negative value. This is supposed to be a predicted probability, so I am
> not sure why -predictnl- is generating a negative value here. Did I do
> something wrong with the expression in -predictnl- ? Many thanks!
>
> Daisy
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-- 
Stas Kolenikov, also found at http://stas.kolenikov.name
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