Parameter Estimation in Probit Model for Multivariate Multinomial Response Using SMLE

Abstract

In  the  research  field  of  transportation,  market  research and  politics,  often involving  the  response  of  the multinomial multivariate  observations.  In  this  paper, we discused  a  modeling  of  multivariate  multinomial  responses  using  probit  model.  The estimated  parameters  were  calculated  using Maximum  Likelihood  Estimations  (MLE) based  on  the  GHK  simulation.  method  known  as Simulated  Maximum  Likelihood Estimations (SMLE). Likelihood function on the Probit model contains probability values that must be resolved by simulation. By using  the GHK simulation algorithm,  the estimator equation has been obtained for the parameters in the model Probit
 
Keywords : Probit Model, Newton-Raphson Iteration,  GHK simulator, MLE, simulated log-likelihood