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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:
Author : Matthew C. Harding
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (137 download)
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.
Author : Petr Mariel
Publisher : Springer Nature
ISBN 13 : 3030626695
Total Pages : 136 pages
Book Rating : 4.0/5 (36 download)
Download or read book Environmental Valuation with Discrete Choice Experiments written by Petr Mariel and published by Springer Nature. This book was released on 2020-11-30 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: This open access book offers up-to-date advice and practical guidance on how to undertake a discrete choice experiment as a tool for environmental valuation. It discusses crucial issues in designing, implementing and analysing choice experiments. Compiled by leading experts in the field, the book promotes discrete choice analysis in environmental valuation through a more solid scientific basis for research practice. Instead of providing strict guidelines, the book helps readers avoid common mistakes often found in applied work. It is based on the collective reflections of the scientific network of researchers using discrete choice modelling in the field of environmental valuation (www.envecho.com).
Author : Badi H. Baltagi
Publisher : Emerald Group Publishing
ISBN 13 : 1781903085
Total Pages : 576 pages
Book Rating : 4.7/5 (819 download)
Download or read book Essays in Honor of Jerry Hausman written by Badi H. Baltagi and published by Emerald Group Publishing. This book was released on 2012-12-17 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: Aims to annually publish original scholarly econometrics papers on designated topics with the intention of expanding the use of developed and emerging econometric techniques by disseminating ideas on the theory and practice of econometrics throughout the empirical economic, business and social science literature.
Author : G. Arminger
Publisher : Springer Science & Business Media
ISBN 13 : 1489912924
Total Pages : 603 pages
Book Rating : 4.4/5 (899 download)
Download or read book Handbook of Statistical Modeling for the Social and Behavioral Sciences written by G. Arminger and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 603 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contributors thoroughly survey the most important statistical models used in empirical reserch in the social and behavioral sciences. Following a common format, each chapter introduces a model, illustrates the types of problems and data for which the model is best used, provides numerous examples that draw upon familiar models or procedures, and includes material on software that can be used to estimate the models studied. This handbook will aid researchers, methodologists, graduate students, and statisticians to understand and resolve common modeling problems.
Author : Takeshi Amemiya
Publisher : Harvard University Press
ISBN 13 : 9780674005600
Total Pages : 540 pages
Book Rating : 4.0/5 (56 download)
Download or read book Advanced Econometrics written by Takeshi Amemiya and published by Harvard University Press. This book was released on 1985 with total page 540 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main features of this text are a thorough treatment of cross-section models—including qualitative response models, censored and truncated regression models, and Markov and duration models—and a rigorous presentation of large sample theory, classical least-squares and generalized least-squares theory, and nonlinear simultaneous equation models.
Author : James L. Pratt
Publisher :
ISBN 13 :
Total Pages : 380 pages
Book Rating : 4.:/5 (365 download)
Download or read book The Laplace Approximation and Inference in Generalized Linear Models with Two Or More Random Effects written by James L. Pratt and published by . This book was released on 1994 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This thesis proposes an approximate maximum likelihood estimator and likelihood ratio test for parameters in a generalized linear model when two or more random effects are present. Substantial progress in parameter estimation for such models has been made with methods involving generalized least squares based on the approximate marginal mean and covariance matrix. However, tests and confidence intervals based on this approach have been limited to what is provided through asymptotic normality of estimates. The proposed solution is based on maximizing a Laplace approximation to the log-likelihood function. This approximation is remarkably accurate and has previously been demonstrated to work well for obtaining likelihood based estimates and inferences in generalized linear models with a single random effect. This thesis concentrates on extensions to the case of several random effects and the comparison of the likelihood ratio inference from this approximate likelihood analysis to the Wald-like inferences for existing estimators. The shapes of the Laplace approximate and true log-likelihood functions are practically identical, implying that maximum likelihood estimates and likelihood ratio inferences are obtained from the Laplace approximation to the log-likelihood. Use of the Laplace approximation circumvents the need for numerical integration, which can be practically impossible to compute when there are two random effects. However, both the Laplace and exact (via numerical integration) methods require numerical optimization, a sometimes slow process, for obtaining estimates and inferences. The proposed Laplace method for estimation and inference is demonstrated for three real (and some simulated) data sets, along with results from alternative methods which involve use of marginal means and covariances. The Laplace approximate method and another denoted as Restricted Maximum Likelihood (REML) performed rather similarly for estimation and hypothesis testing. The REML approach produced faster analyses and was much easier to implement while the Laplace implementation provided likelihood ratio based inferences rather than those relying on asymptotic normality.
Author : Kenneth Train
Publisher : Cambridge University Press
ISBN 13 : 0521766559
Total Pages : 399 pages
Book Rating : 4.5/5 (217 download)
Download or read book Discrete Choice Methods with Simulation written by Kenneth Train and published by Cambridge University Press. This book was released on 2009-07-06 with total page 399 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book describes the new generation of discrete choice methods, focusing on the many advances that are made possible by simulation. Researchers use these statistical methods to examine the choices that consumers, households, firms, and other agents make. Each of the major models is covered: logit, generalized extreme value, or GEV (including nested and cross-nested logits), probit, and mixed logit, plus a variety of specifications that build on these basics. Simulation-assisted estimation procedures are investigated and compared, including maximum stimulated likelihood, method of simulated moments, and method of simulated scores. Procedures for drawing from densities are described, including variance reduction techniques such as anithetics and Halton draws. Recent advances in Bayesian procedures are explored, including the use of the Metropolis-Hastings algorithm and its variant Gibbs sampling. The second edition adds chapters on endogeneity and expectation-maximization (EM) algorithms. No other book incorporates all these fields, which have arisen in the past 25 years. The procedures are applicable in many fields, including energy, transportation, environmental studies, health, labor, and marketing.
Author :
Publisher :
ISBN 13 :
Total Pages : 832 pages
Book Rating : 4.3/5 ( download)
Download or read book Finance India written by and published by . This book was released on 2008 with total page 832 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 788 pages
Book Rating : 4.3/5 (91 download)
Download or read book Current Index to Statistics, Applications, Methods and Theory written by and published by . This book was released on 1994 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Current Index to Statistics (CIS) is a bibliographic index of publications in statistics, probability, and related fields.
Download or read book Computational Approaches for Maximum Likelihood Estimation for Nonlinearmixed Models written by and published by . This book was released on 2000 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: The nonlinear mixed model is an important tool for analyzingpharmacokinetic and other repeated-measures data. In particular, these models are used when the measured response for anindividual, has a nonlinear relationship with unknown, random, individual-specificparameters, . Ideally, the method of maximum likelihood is used to find estimates forthe parameters ofthe model after integrating out the random effects in the conditionallikelihood. However, closed form solutions tothe integral are generally not available. As a result, methods have beenpreviously developed to find approximatemaximum likelihood estimates for the parameters in the nonlinear mixedmodel. These approximate methods include FirstOrder linearization, Laplace's approximation, importance sampling, andGaussian quadrature. The methods are availabletoday in several software packages for models of limited sophistication;constant conditional error variance is requiredfor proper utilization of most software. In addition, distributionalassumptions are needed. This work investigates howrobust two of these methods, First Order linearization and Laplace'sapproximation, are to these assumptions. The findingis that Laplace's approximation performs well, resulting in betterestimation than first order linearization when bothmodels converge to a solution. A method must provide good estimates of the likelihood at points inthe parameter space near the solution. This workcompares this ability among the numerical integration techniques, Gaussian quadrature, importance sampling, and Laplace'sapproximation. A new "scaled" and "centered" version of Gaussianquadrature is found to be the most accurate technique. In addition, the technique requires evaluation of the integrand at onlya few abscissas. Laplace's method also performs well; it is more accurate than importance sampling with even 100importance samples over two dimensions. Even so, Laplace's method still does not perform as well as Gaussian quadrature. Overall, Laplace's a.
Author : Hyungsik Roger Moon
Publisher :
ISBN 13 :
Total Pages : 57 pages
Book Rating : 4.:/5 (13 download)
Download or read book Estimation of Random Coefficients Logit Demand Models with Interactive Fixed Effects written by Hyungsik Roger Moon and published by . This book was released on 2017 with total page 57 pages. Available in PDF, EPUB and Kindle. Book excerpt: We extend the Berry, Levinsohn and Pakes (BLP, 1995) random coefficients discrete choice demand model, which underlies much recent empirical work in IO. We add interactive fixed effects in the form of a factor structure on the unobserved product characteristics. The interactive fixed effects can be arbitrarily correlated with the observed product characteristics (including price), which accommodates endogeneity and, at the same time, captures strong persistence in market shares across products and markets. We propose a two-step least squares-minimum distance (LS-MD) procedure to calculate the estimator. Our estimator is easy to compute, and Monte Carlo simulations show that it performs well. We consider an empirical illustration to US automobile demand.
Author : Joel Horowitz
Publisher :
ISBN 13 :
Total Pages : pages
Book Rating : 4.:/5 (116 download)
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.
Author : Lei Nie
Publisher :
ISBN 13 :
Total Pages : 206 pages
Book Rating : 4.:/5 (57 download)
Download or read book Laplace Approximation in Nonlinear Mixed-effect Models written by Lei Nie and published by . This book was released on 2002 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Duane A. Meeter
Publisher :
ISBN 13 :
Total Pages : 366 pages
Book Rating : 4.:/5 (89 download)
Download or read book Problems in the Analysis of Non-linear Models by Least Squares written by Duane A. Meeter and published by . This book was released on 1966 with total page 366 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Zhentong Lu
Publisher :
ISBN 13 :
Total Pages : 71 pages
Book Rating : 4.:/5 (13 download)
Download or read book Semi-Nonparametric Estimation of Random Coefficient Logit Model for Aggregate Demand written by Zhentong Lu and published by . This book was released on 2020 with total page 71 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this paper, we propose a two-step semi-nonparametric estimator for the widely used random coefficient logit demand model. In the first step, exploiting the structure of logit choice probabilities, we transform the full demand system into a partial linear model and estimate the fixed (non-random) coefficients using standard linear sieve generalized method of moment (GMM). In the second step, we construct a sieve minimum distance (MD) estimator to uncover the distribution of random coefficients nonparametrically. We establish the asymptotic properties of the estimator and show the semi-nonparametric identification of the model in a large market environment. Monte Carlo simulations and empirical illustrations support the theoretical results and demonstrate the usefulness of our estimator in practice.
Author : Xian Liu
Publisher : Elsevier
ISBN 13 : 0128014822
Total Pages : 531 pages
Book Rating : 4.1/5 (28 download)
Download or read book Methods and Applications of Longitudinal Data Analysis written by Xian Liu and published by Elsevier. This book was released on 2015-09-01 with total page 531 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods and Applications of Longitudinal Data Analysis describes methods for the analysis of longitudinal data in the medical, biological and behavioral sciences. It introduces basic concepts and functions including a variety of regression models, and their practical applications across many areas of research. Statistical procedures featured within the text include: descriptive methods for delineating trends over time linear mixed regression models with both fixed and random effects covariance pattern models on correlated errors generalized estimating equations nonlinear regression models for categorical repeated measurements techniques for analyzing longitudinal data with non-ignorable missing observations Emphasis is given to applications of these methods, using substantial empirical illustrations, designed to help users of statistics better analyze and understand longitudinal data. Methods and Applications of Longitudinal Data Analysis equips both graduate students and professionals to confidently apply longitudinal data analysis to their particular discipline. It also provides a valuable reference source for applied statisticians, demographers and other quantitative methodologists. From novice to professional: this book starts with the introduction of basic models and ends with the description of some of the most advanced models in longitudinal data analysis Enables students to select the correct statistical methods to apply to their longitudinal data and avoid the pitfalls associated with incorrect selection Identifies the limitations of classical repeated measures models and describes newly developed techniques, along with real-world examples.
