R help - Jul 2003 - Looking to maximize a conditional likelihood

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.
          
-- 
Ross Boylan                                      wk:  (415) 502-4031
530 Parnassus Avenue (Library) rm 115-4          ross at biostat.ucsf.edu
Dept of Epidemiology and Biostatistics           fax: (415) 476-9856
University of California, San Francisco
San Francisco, CA 94143-0840                     hm:  (415) 550-1062

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.
>

Ross Boylan <ross at biostat.ucsf.edu> writes:
> 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.
Did you check out clogit from the same package?

-- 
   O__  ---- Peter Dalgaard             Blegdamsvej 3  
  c/ /'_ --- Dept. of Biostatistics     2200 Cph. N   
 (*) \(*) -- University of Copenhagen   Denmark      Ph: (+45) 35327918
~~~~~~~~~~ - (p.dalgaard at biostat.ku.dk)             FAX: (+45) 35327907

Can I ask if this method would be suitable for application to my problem?

I recently posted a question to which no one has replied:

https://www.stat.math.ethz.ch/pipermail/r-help/2003-July/034777.html

Basically I have multiple unique choice sets of various sizes on which I
want to apply a multinomial logit to optimise the attributes.

eg
Chosen  AttrQ   AttrW   Choices set size
0             8            0            3
1            20         34            3
0             7            2            3

0             5            3            4
0             3            5            4
1           25          18            4
0            4             9            4

1          30           12            2
0            2            4             2

Any help would be greatly appreciated - including any R code.


Thanks