Performance Analysis of Mixed Logit Models for Discrete Choice Models

Jaka Nugraha

Abstract


Mixed Logit model  (MXL) is generated from Multinomial Logit model (MNL) for discrete, i.e. nominal, data. It eliminates its limitations particularly on estimating the correlation among responses.  In the MNL, the probability equations are presented in the closed form and it is contrary with in the MXL. Consequently, the calculation of the probability value of each alternative get simpler in the MNL, meanwhile it needs the numerical methods for estimation in the MXL.  In this study, we investigated the performance of maximum likelihood estimation (MLE) in the MXL and MNL into two cases, the low and high correlation circumstances among responses. The performance is measured based on differencing actual and estimation value.  The simulation study and real cases show that the MXL model is more accurate than the MNL model. This model can estimates the correlation among response as well. The study concludes that the MXL model is suggested to be used if there is a high correlation among responses.

 


Keywords


Logit; Maximum Likelihood; Monte Carlo simulation; Utility model

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DOI: http://dx.doi.org/10.18187/pjsor.v15i3.2313

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Title

Performance Analysis of Mixed Logit Models for Discrete Choice Models

Keywords

Logit; Maximum Likelihood; Monte Carlo simulation; Utility model

Description

Mixed Logit model  (MXL) is generated from Multinomial Logit model (MNL) for discrete, i.e. nominal, data. It eliminates its limitations particularly on estimating the correlation among responses.  In the MNL, the probability equations are presented in the closed form and it is contrary with in the MXL. Consequently, the calculation of the probability value of each alternative get simpler in the MNL, meanwhile it needs the numerical methods for estimation in the MXL.  In this study, we investigated the performance of maximum likelihood estimation (MLE) in the MXL and MNL into two cases, the low and high correlation circumstances among responses. The performance is measured based on differencing actual and estimation value.  The simulation study and real cases show that the MXL model is more accurate than the MNL model. This model can estimates the correlation among response as well. The study concludes that the MXL model is suggested to be used if there is a high correlation among responses.

 


Date

2019-09-07

Identifier


Source

Pakistan Journal of Statistics and Operation Research; Vol. 15 No. 3, 2019



Print ISSN: 1816-2711 | Electronic ISSN: 2220-5810