scholarly journals A Microeconomic Interpretation of the Maximum Entropy Estimator of Multinomial Logit Models and Its Equivalence to the Maximum Likelihood Estimator

Entropy ◽  
2010 ◽  
Vol 12 (10) ◽  
pp. 2077-2084 ◽  
Author(s):  
Pedro Donoso ◽  
Louis de Grange
Keyword(s):  
Maximum Likelihood ◽  
Maximum Entropy ◽  
Maximum Likelihood Estimator ◽  
Multinomial Logit ◽  
Logit Models ◽  
Likelihood Estimator ◽  
Multinomial Logit Models ◽  
Entropy Estimator

scholarly journals A warning on separation in multinomial logistic models

2018 ◽  
Vol 5 (2) ◽  
pp. 205316801876951 ◽  
Author(s):  
Scott J. Cook ◽  
John Niehaus ◽  
Samantha Zuhlke
Keyword(s):  
Political Science ◽  
Empirical Analysis ◽  
Penalized Likelihood ◽  
Logistic Models ◽  
Multinomial Logit ◽  
Logit Models ◽  
Red Flags ◽  
Binary Outcome ◽  
Likelihood Estimator ◽  
Multinomial Logit Models

Oppenheim et al. (2015) provides the first empirical analysis of insurgent defection during armed rebellion, estimating a series of multinomial logit models of continued rebel participation using a survey of ex-combatants in Colombia. Unfortunately, many of the main results from this analysis are an artifact of separation in these data – that is, one or more of the covariates perfectly predicts the outcome. We demonstrate that this can be identified using simple cross tabulations. Furthermore, we show that Oppenheim et al.’s (2015) results are not supported when separation is explicitly accounted for. Using a generalization of Firth’s (1993) penalized-likelihood estimator – a well-known solution for separation – we are unable to reproduce any of their conditional results. While our (re-)analysis focuses on Oppenheim et al. (2015), this problem appears in other research using multinomial logit models as well. We believe that this is both because the discussion on separation in political science has primarily focused on binary-outcome models, and because software (Stata and R) does not warn researchers about seperation in multinomial logit models. Therefore, we encourage researchers using multinomial logit models to be especially vigilant about separation, and discuss simple red flags to consider.

Efficiently Estimating Nested Logit Models with Choice-Based Samples

2005 ◽  
Vol 1921 (1) ◽  
pp. 63-69 ◽  
Author(s):  
Frank S. Koppelman ◽  
Laurie A. Garrow
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Estimation Procedure ◽  
Multinomial Logit Model ◽  
Nested Logit ◽  
Logit Models ◽  
Likelihood Estimator ◽  
Adjustment Procedure ◽  
Nested Logit Models ◽  
Weighted Estimation

Choice-based samples oversample infrequently chosen alternatives to obtain an effective representation of the behavior of people who select these alternatives. However, the use of choice-based samples requires recognition of the sampling process in formulating the estimation procedure. In general, this procedure can be accomplished by applying weights to the observed choices in the estimation process. Unfortunately, the use of such weighted estimation procedures for choice models does not yield efficient estimators. However, for the special case of the multinomial logit model with a full set of alternative-specific constants, the standard maximum likelihood estimator–-which is efficient–-can be used with adjustment of the alternative-specific constants. The same maximum likelihood estimator can also be used with adjustment to estimate nested logit models with choice-based samples. The proof of this property is qualitatively described, and examples demonstrate how to apply the adjustment procedure.

The Comparison Between the Bayes Estimator and the Maximum Likelihood Estimator of the Reliability Function for Negative Exponential Distribution

2018 ◽  
pp. 439
Author(s):  
Hazim Mansour Gorgees ◽  
Bushra Abdualrasool Ali ◽  
Raghad Ibrahim Kathum
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Exponential Distribution ◽  
Reliability Function ◽  
Bayes Estimator ◽  
Likelihood Estimator ◽  
Monte Carlo Simulation Technique ◽  
Negative Exponential Distribution ◽  
Negative Exponential ◽  
Better Than

     In this paper, the maximum likelihood estimator and the Bayes estimator of the reliability function for negative exponential distribution has been derived, then a Monte –Carlo simulation technique was employed to compare the performance of such estimators. The integral mean square error (IMSE) was used as a criterion for this comparison. The simulation results displayed that the Bayes estimator performed better than the maximum likelihood estimator for different samples sizes.

scholarly journals Transforming variables to central normality

2021 ◽  
Author(s):  
Jakob Raymaekers ◽  
Peter J. Rousseeuw
Keyword(s):  
Maximum Likelihood ◽  
Maximum Likelihood Estimator ◽  
Simulation Study ◽  
Real Data ◽  
Data Sets ◽  
Transformation Parameter ◽  
Likelihood Estimator ◽  
Extensive Simulation ◽  
Highly Sensitive

AbstractMany real data sets contain numerical features (variables) whose distribution is far from normal (Gaussian). Instead, their distribution is often skewed. In order to handle such data it is customary to preprocess the variables to make them more normal. The Box–Cox and Yeo–Johnson transformations are well-known tools for this. However, the standard maximum likelihood estimator of their transformation parameter is highly sensitive to outliers, and will often try to move outliers inward at the expense of the normality of the central part of the data. We propose a modification of these transformations as well as an estimator of the transformation parameter that is robust to outliers, so the transformed data can be approximately normal in the center and a few outliers may deviate from it. It compares favorably to existing techniques in an extensive simulation study and on real data.

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