I'm estimating an ICLV mode including two latent variables. Both random error term of each latent variable is normally distributed. I want to know that if I need to use Monte-Carlo integration (loglike = log(MonteCarlo(condprob))) rather than numerical integration (loglike = log(Integrate(condprob * density, 'omega')))?
In addition, I'm confused about the function of the parameter, numberOfDraws. When I set it equal to 20000, I found that the solution time is particularly long. However, when I remove this parameter, just use biogeme = bio.BIOGEME(database, loglike) in my code, the solution time will be shorter. But I'm not sure that whether the results in this way is reliable or not. Is the numberOfDraws related to the accuracy of the results?
In my research, there are about 30 variables to be estimated and the total number of data is N=3905. What is the appropriate setting for the numberOfDraws?
I'm looking forward to your reply.
Best wishes for you.