Re: Constrain PD values using a logistic transformation
Hi Mahesh,
If you plan to use one of the approximate likelihood methods, e.g., FO or FOCE,
you may prefer to transform the data and use an additive model. In other words
transform the data according to Yobs = LOG(Xobs/(100-Xobs)) and use Y = 100 *
LOG(IPRE/(100-IPRE))+ERR(1) where Xobs is the observed data on the restricted
range.
Since you have some data at the extremes, you may want to extend the range used
for the extended logit to (-0.5, 100.5) or something similar. Otherwise you'll
end up with under- or over-flows.
Regarded other transformations, anything that transforms from a bounded
interval to the real line is potentially fair game. For example you could use
probit or complimetary log-log transformations extended to (0, 100). Another
approach would be to use an beta distribution extended to (0, 100) instead of
(0, 1) for the likelihood. Such an approach is described for a model of
ADAS-cog scores as a function of time (see the Alzheimer's disease progression
model at http://opendiseasemodels.org, specifically the model used for the
"raw" scores).
Cheers,
Bill Gillespie
Quoted reply history
On Jul 1, 2010, at 3:47 PM, Samtani, Mahesh [PRDUS] wrote:
> Dear NMusers,
> I am trying to model some PD data, which has a lower bound of zero and an
> upper bound of 100. I was wondering how to implement this restriction and if
> it was possible to use the general logistic transformation in the $ERROR
> block shown below:
>
> $ERROR
> IPRE=A(1)
> LT=LOG(IPRE/(100-IPRE))+ERR(1)
> Y=(100*EXP(LT))/(1+EXP(LT))
>
> If this is appropriate, do I understand correctly that this is NOT a
> transform both sides approach; i.e. DV stays in its original or natural form.
>
> Finally, the logistic transformation extends from -∞ to +∞. However, the
> dataset does have a small number of values that are zeros and 100 (Five zeros
> and a couple of 100s in a dataset of about 700 observations). Do these small
> number of extreme values in the dataset cause problem when the LT term is
> back transformed above.
>
> Any other method and references for papers that use these types of
> constraints would be greatly appreciated.
>
> Warm regards and thanks in advance...MNS
>