Shrinkage Estimation in the Random Parameters Logit Model

Abstract

In this paper, we explore the properties of a positive-part Stein-like estimator which is a stochastically weighted convex combination of a fully correlated parameter model estimator and uncorrelated parameter model estimator in the Random Parameters Logit (RPL) model. The results of our Monte Carlo experiments show that the positive-part Stein-like estimator provides smaller MSE than the pretest estimator in the fully correlated RPL model. Both of them outperform the fully correlated RPL model estimator and provide more accurate information on the share of population putting a positive or negative value on the alternative attributes than the fully correlated RPL model estimates. The Monte Carlo mean estimates of direct elasticity with pretest and positive-part Stein-like estimators are closer to the true value and have smaller standard errors than those with fully correlated RPL model estimator.

Economic valuation of attributes of Lake Tana: random parameter model

“…The odds of probabilities of two alternatives could not beaffected by adding or removal of other alternative. Random part of utility in this model can be categorized into two; the first one is independent and identically distributed that is gamble and the second one is preference of individuals can take any distribution (Zeng, 2011). Given two alternatives presented to respondents that are j & i, the probability to choose alternative j:…”

Can I Trust You? Estimation Models for e-Bikers Stop-Go Decision before Amber Light at Urban Intersection

“…However, the base logit model has drawbacks which cannot analyze the potential effects of unobserved heterogeneity in riders' individual characteristics and cannot allow unobserved environment factors of utility to be correlated. All these random effects may result in erroneous parameter estimation and prejudices in estimation of the model, and the heterogeneity (i.e., some riders are prone to stop at the amber light interval and have lower risk propensity) may damage the Independence from Irrelevant Alternatives (IIA) assumption [15,19,24,37,40,46]. To obtain an accurate estimation of variables, we proposed a random parameter logit model to analyze e-bikers' YLR behavior.…”

“…e probability of the rider i's infringement of the amber light estimated by equation ( 7) cannot be calculated exactly because of involving a multidimensional integral which is not close to solution. Quasirandom numbers generated by Halton, also called Halton's draws, were proved to be an efficient alternative to pseudorandom numbers by Bhat and Train [37]. In this study, we used Halton's draws to draw the values of β i from f(β i |ϕ).…”

“…However, the violation behaviour might occur under distinct conditions and influencing by other unobserved influential factors of individuals, which may lead to omitting the unobserved heterogeneity and making the wrong analysis for the results [24,36]. To provide some insights into this problem, some researchers established random parameter logit model (RPLM) which is also called mixed logit model [19,24,37] to eliminate the effects of unobserved heterogeneity. Wang et al identified variables contributing to RLR behavior of pedestrians and e-bikers using the RPLM [24].…”

Estimation strategy of multilevel model for ordinal longitudinal data

“…Hossain et al (2016) developed the pretest and shrinkage estimation methods for the analysis of longitudinal data under a partial linear model when some parameters are subject to certain restrictions. Zeng and Hill (2016) explored the properties of pretest and shrinkage estimators for random parameters logit models. Many articles have been devoted to the study of pretest and shrinkage estimators in parametric and semi-parametric linear models for uncorrelated data, including Thomson et al (2016), Hossain et al (2015), Lian (2012), and among others.…”