scholarly journals The use of heuristic optimization algorithms to facilitate maximum simulated likelihood estimation of random parameter logit models

2017 ◽  
Vol 66 (5) ◽  
pp. 997-1013 ◽  
Author(s):  
Arne Risa Hole ◽  
Hong Il Yoo
Keyword(s):  
Optimization Algorithms ◽  
Likelihood Estimation ◽  
Random Parameter ◽  
Heuristic Optimization ◽  
Logit Models ◽  
Maximum Simulated Likelihood ◽  
Simulated Likelihood ◽  
Random Parameter Logit ◽  
Maximum Simulated Likelihood Estimation

Biases in Maximum Simulated Likelihood Estimation of Bivariate Models

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Maksat Jumamyradov ◽  
Murat K. Munkin
Keyword(s):  
Maximum Likelihood ◽  
Likelihood Estimation ◽  
Random Parameter ◽  
Bivariate Normal Distribution ◽  
Maximum Simulated Likelihood ◽  
Bivariate Normal ◽  
Simulated Likelihood ◽  
Bivariate Normal Model ◽  
Variance Parameters ◽  
Maximum Simulated Likelihood Estimation

Abstract This paper finds that the maximum simulated likelihood (MSL) estimator produces substantial biases when applied to the bivariate normal distribution. A specification of the random parameter bivariate normal model is considered, in which a direct comparison between the MSL and maximum likelihood (ML) estimators is feasible. The analysis shows that MSL produces biased results for the correlation parameter. This paper also finds that the MSL estimator is biased for the bivariate Poisson-lognormal model, developed by Munkin and Trivedi (1999. “Simulated Maximum Likelihood Estimation of Multivariate Mixed-Poisson Regression Models, with Application.” The Econometrics Journal 2: 29–48). A simulation study is conducted, which shows that MSL leads to serious inferential biases, especially large when variance parameters in the true data generating process are small. The MSL estimator produces biases in the estimated marginal effects, conditional means and probabilities of count outcomes.

scholarly journals Designed quadrature to approximate integrals in maximum simulated likelihood estimation

2021 ◽  
Author(s):  
Prateek Bansal ◽  
Vahid Keshavarzzadeh ◽  
Angelo Guevara ◽  
Shanjun Li ◽  
Ricardo A Daziano
Keyword(s):  
Monte Carlo ◽  
Likelihood Estimation ◽  
Latin Hypercube Sampling ◽  
Polynomial Space ◽  
Integral Approximation ◽  
Maximum Simulated Likelihood ◽  
Quasi Monte Carlo ◽  
Simulated Likelihood ◽  
Multidimensional Integral ◽  
Maximum Simulated Likelihood Estimation

Abstract Maximum simulated likelihood estimation of mixed multinomial logit models requires evaluation of a multidimensional integral. Quasi-Monte Carlo (QMC) methods such as Halton sequences and modified Latin hypercube sampling are workhorse methods for integral approximation. Earlier studies explored the potential of sparse grid quadrature (SGQ), but SGQ suffers from negative weights. As an alternative to QMC and SGQ, we looked into the recently developed designed quadrature (DQ) method. DQ requires fewer nodes to get the same level of accuracy as of QMC and SGQ, is as easy to implement, ensures positivity of weights, and can be created on any general polynomial space. We benchmarked DQ against QMC in a Monte Carlo and an empirical study. DQ outperformed QMC in all considered scenarios, is practice-ready and has potential to become the workhorse method for integral approximation.

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