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Using Penalized Likelihood To Select Parameters In A Random Coefficients Multinomial Logit Model
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Book Synopsis Using Penalized Likelihood to Select Parameters in a Random Coefficients Multinomial Logit Model by : Joel Horowitz
Download or read book Using Penalized Likelihood to Select Parameters in a Random Coefficients Multinomial Logit Model written by Joel Horowitz and published by . This book was released on 2019 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The multinomial logit model with random coefficients is widely used in applied research. This paper is concerned with estimating a random coefficients logit model in which the distribution of each coefficient is characterized by finitely many parameters. Some of these parameters may be zero. The paper gives conditions under which with probability approaching 1 as the sample size approaches infinity, penalized maximum likelihood (PML) estimation with the adaptive LASSO (AL) penalty function distinguishes correctly between zero and non-zero parameters in a random coefficients logit model. If one or more parameters are zero, then PML with the AL penalty function often reduces the asymptotic mean-square estimation error of any continuously differentiable function of the model’s parameters, such as a market share or an elasticity. The paper describes a method for computing the PML estimates of a random coefficients logit model. It also presents the results of Monte Carlo experiments that illustrate the numerical performance of the PML estimates. Finally, it presents the results of PML estimation of a random coefficients logit model of choice among brands of butter and margarine in the British groceries market.
Book Synopsis Implementation and Application of the Multidimensional Random Coefficients Multinomial Logit Model by : Wenzhong Wang
Download or read book Implementation and Application of the Multidimensional Random Coefficients Multinomial Logit Model written by Wenzhong Wang and published by . This book was released on 1994 with total page 616 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Simulated Maximum Likelihood Estimator for the Random Coefficient Logit Model Using Aggregate Data by : Sungho Park
Download or read book A Simulated Maximum Likelihood Estimator for the Random Coefficient Logit Model Using Aggregate Data written by Sungho Park and published by . This book was released on 2008 with total page 38 pages. Available in PDF, EPUB and Kindle. Book excerpt: We propose a Simulated Maximum Likelihood estimation method for the random coefficient logit model using aggregate data, accounting for heterogeneity and endogeneity. Our method allows for two sources of randomness in observed market shares - unobserved product characteristics and sampling error. Because of the latter, our method is suitable when sample sizes underlying the shares are finite. By contrast, the commonly used approach of Berry, Levinsohn and Pakes (1995) assumes that observed shares have no sampling error. Our method can be viewed as a generalization of Villas-Boas and Winer (1999) and is closely related to the quot;control functionquot; approach of Petrin and Train (2004). We show that the proposed method provides unbiased and efficient estimates of demand parameters. We also obtain endogeneity test statistics as a by-product, including the direction of endogeneity bias. The model can be extended to incorporate Markov regime-switching dynamics in parameters and is open to other extensions based on Maximum Likelihood. The benefits of the proposed approach are achieved by assuming normality of the unobserved demand attributes, an assumption that imposes constraints on the types of pricing behaviors that are accommodated. However, we find in simulations that demand estimates are fairly robust to violations of these assumptions.
Book Synopsis Using the Penalized Likelihood Method for Model Selection with Nuisance Parameters Present Only Under the Alternative by : Arie Preminger
Download or read book Using the Penalized Likelihood Method for Model Selection with Nuisance Parameters Present Only Under the Alternative written by Arie Preminger and published by . This book was released on 2005 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the problem of model selection with nuisance parameters present only under the alternative. The common approach for testing in this case is to determine the true model through the use of some functionals over the nuisance parameters space. Since in such cases the distribution of these statistics is not known, critical values had to be approximated usually through computationally intensive simulations. Furthermore, the computed critical values are data and model dependent and hence cannot be tabulated. We address this problem by using the penalized likelihood method to choose the correct model. We start by viewing the likelihood ratio as a function of the unidentified parameters. By using the empirical process theory and the uniform law of the iterated logarithm (LIL) together with sufficient conditions on the penalty term, we derive the consistency properties of this method. Our approach generates a simple and consistent procedure for model selection. This methodology is presented in the context of switching regression models. We also provide some Monte Carlo simulations to analyze the finite sample performance of our procedure.
Book Synopsis Using Halton Sequences in Random Parameters Logit Models by : Tong Zeng
Download or read book Using Halton Sequences in Random Parameters Logit Models written by Tong Zeng and published by . This book was released on 2016 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: Quasi-random numbers that are evenly spread over the integration domain have become used as alternatives to pseudo-random numbers in maximum simulated likelihood problems to reduce computational time. In this paper, we carry out Monte Carlo experiments to explore the properties of quasi-random numbers, which are generated by the Halton sequence, in estimating the random parameters logit model. We vary the number of Halton draws, the sample size and the number of random coefficients. We show that increases in the number of Halton draws influence the efficiency of the random parameters logit model estimators only slightly. The maximum simulated likelihood estimator is consistent. We find that it is not necessary to increase the number of Halton draws when the sample size increases for this result to be evident.
Book Synopsis Maximum Penalized Likelihood Estimation by : Paul P. Eggermont
Download or read book Maximum Penalized Likelihood Estimation written by Paul P. Eggermont and published by Springer Science & Business Media. This book was released on 2009-06-02 with total page 580 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unique blend of asymptotic theory and small sample practice through simulation experiments and data analysis. Novel reproducing kernel Hilbert space methods for the analysis of smoothing splines and local polynomials. Leading to uniform error bounds and honest confidence bands for the mean function using smoothing splines Exhaustive exposition of algorithms, including the Kalman filter, for the computation of smoothing splines of arbitrary order.
Book Synopsis Using a Laplace Approximation to Estimate the Random Coefficients Logit Model By Nonlinear Least Squares by : Matthew C. Harding
Download or read book Using a Laplace Approximation to Estimate the Random Coefficients Logit Model By Nonlinear Least Squares written by Matthew C. Harding and published by . This book was released on 2008 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Current methods of estimating the random coefficients logit model employ simulations of the distribution of the taste parameters through pseudo-random sequences. These methods suffer from difficulties in estimating correlations between parameters and computational limitations such as the curse of dimensionality. This article provides a solution to these problems by approximating the integral expression of the expected choice probability using a multivariate extension of the Laplace approximation. Simulation results reveal that our method performs very well, in terms of both accuracy and computational time.
Book Synopsis Maximum Penalized Likelihood Estimation by : P.P.B. Eggermont
Download or read book Maximum Penalized Likelihood Estimation written by P.P.B. Eggermont and published by Springer Nature. This book was released on 2020-12-15 with total page 514 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with parametric and nonparametric density estimation from the maximum (penalized) likelihood point of view, including estimation under constraints. The focal points are existence and uniqueness of the estimators, almost sure convergence rates for the L1 error, and data-driven smoothing parameter selection methods, including their practical performance. The reader will gain insight into technical tools from probability theory and applied mathematics.
Book Synopsis Shrinkage Parameter Selection in Generalized Linear and Mixed Models by : Erin K. Melcon
Download or read book Shrinkage Parameter Selection in Generalized Linear and Mixed Models written by Erin K. Melcon and published by . This book was released on 2014 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Penalized likelihood methods such as lasso, adaptive lasso, and SCAD have been highly utilized in linear models. Selection of the penalty parameter is an important step in modeling with penalized techniques. Traditionally, information criteria or cross validation are used to select the penalty parameter. Although methods of selecting this have been evaluated in linear models, general linear models and linear mixed models have not been so thoroughly explored.This dissertation will introduce a data-driven bootstrap (Empirical Optimal Selection, or EOS) approach for selecting the penalty parameter with a focus on model selection. We implement EOS on selecting the penalty parameter in the case of lasso and adaptive lasso. In generalized linear models we will introduce the method, show simulations comparing EOS to information criteria and cross validation, and give theoretical justification for this approach. We also consider a practical upper bound for the penalty parameter, with theoretical justification. In linear mixed models, we use EOS with two different objective functions; the traditional log-likelihood approach (which requires an EM algorithm), and a predictive approach. In both of these cases, we compare selecting the penalty parameter with EOS to selection with information criteria. Theoretical justification for both objective functions and a practical upper bound for the penalty parameter in the log-likelihood case are given. We also applied our technique to two datasets; the South African heart data (logistic regression) and the Yale infant data (a linear mixed model). For the South African data, we compare the final models using EOS and information criteria via the mean squared prediction error (MSPE). For the Yale infant data, we compare our results to those obtained by Ibrahim et al. (2011).
Book Synopsis Maximum Likelihood Estimation of a Binary Choice Model with Random Coefficients of Unknown Distribution by : Hidehiko Ichimura
Download or read book Maximum Likelihood Estimation of a Binary Choice Model with Random Coefficients of Unknown Distribution written by Hidehiko Ichimura and published by . This book was released on 1993 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Variable Selection Via Penalized Likelihood by :
Download or read book Variable Selection Via Penalized Likelihood written by and published by . This book was released on 2014 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Variable selection via penalized likelihood plays an important role in high dimensional statistical modeling and it has attracted great attention in recent literature. This thesis is devoted to the study of variable selection problem. It consists of three major parts, all of which fall within the framework of penalized least squares regression setting. In the first part of this thesis, we propose a family of nonconvex penalties named the K-Smallest Items (KSI) penalty for variable selection, which is able to improve the performance of variable selection and reduce estimation bias on the estimates of the important coefficients. We fully investigate the theoretical properties of the KSI method and show that it possesses the weak oracle property and the oracle property in the high-dimensional setting where the number of coefficients is allowed to be much larger than the sample size. To demonstrate its numerical performance, we applied the KSI method to several simulation examples as well as the well known Boston housing dataset. We also extend the idea of the KSI method to handle the group variable selection problem. In the second part of this thesis, we propose another nonconvex penalty named Self-adaptive penalty (SAP) for variable selection. It is distinguished from other existing methods in the sense that the penalization on each individual coefficient takes into account directly the influence of other estimated coefficients. We also thoroughly study the theoretical properties of the SAP method and show that it possesses the weak oracle property under desirable conditions. The proposed method is applied to the glioblastoma cancer data obtained from The Cancer Genome Atlas. In many scientific and engineering applications, covariates are naturally grouped. When the group structures are available among covariates, people are usually interested in identifying both important groups and important variables within the selected groups. In statistics, this is a group variable selection problem. In the third part of this thesis, we propose a novel Log-Exp-Sum(LES) penalty for group variable selection. The LES penalty is strictly convex. It can identify important groups as well as select important variables within the group. We develop an efficient group-level coordinate descent algorithm to fit the model. We also derive non-asymptotic error bounds and asymptotic group selection consistency for our method in the high-dimensional setting. Numerical results demonstrate the good performance of our method in both variable selection and prediction. We applied the proposed method to an American Cancer Society breast cancer survivor dataset. The findings are clinically meaningful and may help design intervention programs to improve the quality of life for breast cancer survivors.
Book Synopsis Regularization Parameter Selection for Penalized Empirical Likelihood Estimator by : Tomohiro Ando
Download or read book Regularization Parameter Selection for Penalized Empirical Likelihood Estimator written by Tomohiro Ando and published by . This book was released on 2018 with total page 28 pages. Available in PDF, EPUB and Kindle. Book excerpt: Penalized estimation is a useful technique for variable selection when the number of candidate variables is large. A crucial issue in penalized estimation is the selection of the regularization parameter because the performance of the estimator largely depends on an appropriate choice. However, no theoretically sound selection method currently exists for the penalized estimation of moment restriction models. To address this important issue, we develop a novel information criterion, which we call the empirical likelihood information criterion, to select the regularization parameter of the penalized empirical likelihood estimator. The information criterion is derived as an estimator of the expected value of the Kullback-Leibler information criterion from an estimated model to the true data generating process. We present a Monte Carlo simulation that demonstrates the efficacy of the proposed method.
Book Synopsis The Performance of an Approximation to a Random Parameter Multinomial Logit Model by : J. M. C. Santos-Silva
Download or read book The Performance of an Approximation to a Random Parameter Multinomial Logit Model written by J. M. C. Santos-Silva and published by . This book was released on 1992 with total page 37 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Penalized Likelihood Methods for Sparse Datasets, with Applications to Genetic Epidemiology by : Ying Yu
Download or read book Penalized Likelihood Methods for Sparse Datasets, with Applications to Genetic Epidemiology written by Ying Yu and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Increasingly, logistic regression methods for genetic association studies of binary phenotypes must be able to accommodate data sparsity, which arises from unbalanced case-control ratios and/or rare exposures. Sparseness leads to maximum likelihood estimates (MLEs) of log odds-ratio parameters that are biased away from their null value of zero and tests with inflated type I errors. Different penalized-likelihood methods have been developed to mitigate sparse-data bias. We study penalized logistic and conditional regression using a class of log-F priors indexed by a shrinkage parameter m to shrink the biased MLE towards zero. The thesis is organized in three parts. First, we propose a two-step methodology for implementing log-F penalization for inference of regression parameters from logistic regression, with application to genome-wide association studies. In the first step we estimate the shrinkage parameter, and in the second step we use the penalized regression estimator to estimate single-variant associations across the genome. Next, we explore log-F penalization for inference of regression parameters from conditional logistic regression, with application to data from matched case-control and case-parent trio studies. In the first two projects we use simulation to study the statistical properties of our methods and make comparisons to methods that use Firth penalization. Finally, we apply log-F-penalized logistic regression to data from the UK Biobank, to investigate the method's feasibility for genome-wide, biobank-scale data. The complexity and size of biobank data present unique challenges, and we make modifications to our methodology to increase its flexibility and adaptability to such datasets.
Book Synopsis Maximum Penalized Likelihood Estimation by : P.P.B. Eggermont
Download or read book Maximum Penalized Likelihood Estimation written by P.P.B. Eggermont and published by Springer. This book was released on 2001-06-21 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with parametric and nonparametric density estimation from the maximum (penalized) likelihood point of view, including estimation under constraints. The focal points are existence and uniqueness of the estimators, almost sure convergence rates for the L1 error, and data-driven smoothing parameter selection methods, including their practical performance. The reader will gain insight into technical tools from probability theory and applied mathematics.
Book Synopsis Maximum Likelihood for the Multinomial Probit Model by : Nicholas M. Kiefer
Download or read book Maximum Likelihood for the Multinomial Probit Model written by Nicholas M. Kiefer and published by . This book was released on 1995 with total page 48 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Using a Laplace Approximation to Estimate the Random Coefficients Logit Model by Non-linear Least Squares by :
Download or read book Using a Laplace Approximation to Estimate the Random Coefficients Logit Model by Non-linear Least Squares written by and published by . This book was released on 2005 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
