[R] Looking to maximize a conditional likelihood
Spencer Graves
spencer.graves at pdf.com
Thu Jul 17 23:27:37 CEST 2003
Have you considered "optim"?
spencer graves
Ross Boylan wrote:
> I want to maximize a conditional likelihood function that is basically
> logistic conditional on the number of successes within strata. What
> would be a good starting place for this? A complication is that the
> denominator includes a term that is the sum over all permutations.
>
> Although there is no time dimension to the problem, it's possible a
> degenerate use of the Cox proportional hazards model (in the survival
> package of 1.7) will do what I want.
>
> Here's a little more detail on the function, though this is still quite
> terse. Pseudo Tex notation:
>
> We have cases in clusters. y_ij is the outcome (0 or 1) for the j'th
> case in the i'th cluster It has vector covariates X_ij. c_ij is a
> transform of y_ij and is in (0, 1) (it's actually the probability of
> being in cluster j). It may be specified a priori or to be estimated.
>
> Maximize the product over i of
>
> c_ij exp(sum_j y_ij X_ij b)
> ----------------------------
> sum_K c_ij exp(sum_K y_ij X_ij b)
>
> Where sum_K means we are summing over all possible subsets of the strata
> that contain the observed number of successes.
> b, and perhaps c, are the parameters to estimate.
>
> The more vanilla case has no c_ij terms. That says we maximize the
> probability of the observed outcomes, given the total number of
> successes within strata--i.e., we condition out on strata-specific
> effects. I kind of expected there would already be a routine that does
> this, but I can't find it.
>
> Thanks for any help you can offer.
>
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