
Hi all,
 
I am trying to estimate a simple logit model.
By using MLE, I am maximizing the log likelihood, with optim().
The thing is, each observation has different set of choice options, so I need a loop inside the objective function,
which I think slows down the optimization process.
 
The data is constructed so that each row represent the characteristics for one alternative,
and CS is a variable that represents choice situations. (say, 1 ~ Number of observations)
cum_count is the “cumulative” count of each choice situations, i.e. number of available alternatives in each CS.
So I am maximizing the sum of [exp(U(chosen)) / sum(exp(U(all alternatives)))]
 
When I have 6,7 predictors, the running time is about 10 minutes, and it slows down exponentially as I have more predictors. (More theta’s to estimate)
I want to know if there is a way I can improve the running time.
Below is my code..
 
simple_logit = function(theta){
                realized_prob = rep(0, max(data$CS))
                theta_multiple = as.matrix(data[,4:35]) %*% as.matrix(theta)
                realized_prob[1] = exp(theta_multiple[1]) / sum(exp(theta_multiple[1:cum_count[1]]))
                for (i in 2:length(realized_prob)){
                                realized_prob[i] = exp(theta_multiple[cum_count[(i-1)]+1]) / sum(exp(theta_multiple[((cum_count[(i-1)]+1):cum_count[i])]))
                                }
                -sum(log(realized_prob))
}
 
initial = rep(0,32)
out33 = optim(initial, simple_logit, method="BFGS", hessian=TRUE)
 
 
 
Many thanks in advance!!! 		 	   		  
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