[R] Modeling Dependent Bernoulli Trials?

Spencer Graves spencer.graves at pdf.com
Fri Jul 23 04:55:09 CEST 2004

      Is there any software to estimate dependence between Bernoulli 

      I have N observations on k-vectors of 0s and 1s, and I need to 
model the dependence.  Consider the simple case with k = 2.  There are 4 
possible outcomes:  (0, 0), (0, 1), (1, 0), and (1, 1).  I assume 0 = 
"failure" and 1 = "success".  I assume further that there are 3 
independent failure mechanisms, one that makes the first outcome 0 with 
probability (1-q1), another that makes the second outcome 0 with 
probability (1-q2), and a third that make them both 0 with probability 
(1-q12).  I compute the probabilities of these 4 outcomes as follows: 

      P00 = Pr(0, 0) = q1*q2*q12 = probability of no failures. 

      P01 = Pr(0, 1) = q1*(1-q2)*q12 = probability of a failure from the 
second mechanism and none from the other 2. 

      P10 = Pr(1, 0) = (1-q1)*q2*q12 = probability of a failure from the 
first mechanism and none from the other 2. 

      P11 = Pr(1, 1) = 1-Pr(0,0)-Pr(0,1)-Pr(1,0). 

      With this setup, I can write a likelihood function, parameterize 
it appropriately, and estimate what I need.  However, I wonder if 
something already exists. 

      Best Wishes,
      Spencer Graves

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