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st: Using -ml- for something other than a GLM


From   "Lacy,Michael" <Michael.Lacy@colostate.edu>
To   "'statalist@hsphsun2.harvard.edu'" <statalist@hsphsun2.harvard.edu>
Subject   st: Using -ml- for something other than a GLM
Date   Wed, 7 Sep 2011 22:15:58 +0000

Greetings,

I'm trying to use -ml- for the first time, but my particular
problem is different enough from any of the examples I have 
seen that I am even more puzzled than a new -ml- user
might be.  My problem does not involve a generalized linear
model, whereas all the examples I have found are for logit, probit etc.
or other regression models.

A description of my problem:

I am implementing an approach to modeling agreement among subjects 
giving answers to multinomial response items.  This approach models
agreement in terms of a subject's latent ability to know the "right" 
answer to any given question.  This vector of latent abilities
for the N subjects is what is to be estimated.

The likelihood is a function of the # of matches of the responses
among each of all possible pairs of subject, not the response
of any single subject:

For a pair of subjects the log likelihood has the form:

ln(a * P ) + (K-a)*ln(1-P)

where a is the observed  number of times a pair gave matching answers across all 
the questions, K is the number of questions, and P is the probability 
that the two subjects agreed on any given question. P is a linear function
 of the two subjects' latent abilities,D_i and D_j), and the number of answer 
options on each question, L:

P = (L -1)(D_i * D_j)/L + 1/L


I am fine as regards creating a program (Stata or Mata) that returns 
the log likelihood across all pairs of subjects as a function of the 
vector of unknowns D, but I don't see how to fit what I want into 
the framework of -ml-, which seems set up for regression models.  
At this point,  I can't,  for example, understand what would be the 
equation in an -ml model- statement.   Other things will doubtless
puzzle me as I get deeper into this :-}

Can someone point me to an example I might try to follow, or perhaps
sketch how this might fit in the framework of -ml- (or -moptimize-
or -optimize-).

Regards

Mike Lacy, Ph.D.
Assoc. Prof./Dir. Grad. Studies
Dept. of Sociology
Colorado State University
Fort Collins CO 80523-1784
970.491.6721 (voice)





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