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A Simulated Maximum Likelihood Estimator For The Random Coefficient Logit Model Using Aggregate Data
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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 Comparison of SML and GMM Estimators for the Random Coefficient Logit Model Using Aggregate Data by : Sungho Park
Download or read book Comparison of SML and GMM Estimators for the Random Coefficient Logit Model Using Aggregate Data written by Sungho Park and published by . This book was released on 2015 with total page 36 pages. Available in PDF, EPUB and Kindle. Book excerpt: A Simulated Maximum Likelihood (SML) estimator for the random coefficient logit model using aggregate data is found to be more efficient than the widely used Generalized Method of Moments estimator (GMM) of Berry-Levinsohn-Pakes (1995). In particular, the SML estimator is better than the GMM estimator in recovery of heterogeneity parameters, which are often of central interest in marketing research. With the GMM estimator, the analyst must determine what moment conditions to use for parameter identification, especially the heterogeneity parameters. With the SML estimator, the moment conditions are automatically determined as the gradients of the log-likelihood function, and these are the most efficient ones if the model is correctly specified. Another limitation of the GMM estimator is that the product market shares must be strictly positive while the SML estimator can handle zero market share observations. Properties of the SML and GMM estimators are demonstrated in simulated data and in data from the US photographic film market.
Book Synopsis Semi-Nonparametric Estimation of Random Coefficient Logit Model for Aggregate Demand by : Zhentong Lu
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.
Book Synopsis Maximum Likelihood Estimation by : Scott R. Eliason
Download or read book Maximum Likelihood Estimation written by Scott R. Eliason and published by SAGE. This book was released on 1993 with total page 100 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a short introduction to Maximum Likelihood (ML) Estimation. It provides a general modeling framework that utilizes the tools of ML methods to outline a flexible modeling strategy that accommodates cases from the simplest linear models (such as the normal error regression model) to the most complex nonlinear models linking endogenous and exogenous variables with non-normal distributions. Using examples to illustrate the techniques of finding ML estimators and estimates, the author discusses what properties are desirable in an estimator, basic techniques for finding maximum likelihood solutions, the general form of the covariance matrix for ML estimates, the sampling distribution of ML estimators; the use of ML in the normal as well as other distributions, and some useful illustrations of likelihoods.
Book Synopsis Discrete Choice Methods with Simulation by : Kenneth Train
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.
Book Synopsis Maximum Likelihood Estimation in the Random Coefficient Regression Model Via the EM Algorithm by : Jiang-Ming Wu
Download or read book Maximum Likelihood Estimation in the Random Coefficient Regression Model Via the EM Algorithm written by Jiang-Ming Wu and published by . This book was released on 1995 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Estimating the Mixed Logit Model by Maximum Simulated Likelihood and Hierarchical Bayes by : Deniz Akinc
Download or read book Estimating the Mixed Logit Model by Maximum Simulated Likelihood and Hierarchical Bayes written by Deniz Akinc and published by . This book was released on 2017 with total page 34 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this study, we compare the parameter estimates of the mixed logit model obtained with maximum likelihood and with hierarchical Bayesian estimation. The choice of the priors in Bayesian estimation and of the type and the number of quasi-random draws for maximum likelihood estimation have a big impact on the estimates. Our main focus is on the effect of the prior for the covariance matrix in hierarchical Bayes estimation. We investigate several priors such as Inverse Wisharts, the Separation Strategy, Scaled Inverse Wisharts and the Huang Half-t priors and we compute the root mean square errors of the resulting estimates for the mean, covariance matrix and individual parameters in a large simulation study. We show that the default settings in many software packages can lead to very unreliable results and that it is important to check the robustness of the results.
Book Synopsis Maximum Likelihood Estimation for Sample Surveys by : Raymond L. Chambers
Download or read book Maximum Likelihood Estimation for Sample Surveys written by Raymond L. Chambers and published by CRC Press. This book was released on 2012-05-02 with total page 374 pages. Available in PDF, EPUB and Kindle. Book excerpt: Sample surveys provide data used by researchers in a large range of disciplines to analyze important relationships using well-established and widely used likelihood methods. The methods used to select samples often result in the sample differing in important ways from the target population and standard application of likelihood methods can lead to
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 Likelihood Estimation and Inference by : Russell B. Millar
Download or read book Maximum Likelihood Estimation and Inference written by Russell B. Millar and published by John Wiley & Sons. This book was released on 2011-07-26 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book takes a fresh look at the popular and well-established method of maximum likelihood for statistical estimation and inference. It begins with an intuitive introduction to the concepts and background of likelihood, and moves through to the latest developments in maximum likelihood methodology, including general latent variable models and new material for the practical implementation of integrated likelihood using the free ADMB software. Fundamental issues of statistical inference are also examined, with a presentation of some of the philosophical debates underlying the choice of statistical paradigm. Key features: Provides an accessible introduction to pragmatic maximum likelihood modelling. Covers more advanced topics, including general forms of latent variable models (including non-linear and non-normal mixed-effects and state-space models) and the use of maximum likelihood variants, such as estimating equations, conditional likelihood, restricted likelihood and integrated likelihood. Adopts a practical approach, with a focus on providing the relevant tools required by researchers and practitioners who collect and analyze real data. Presents numerous examples and case studies across a wide range of applications including medicine, biology and ecology. Features applications from a range of disciplines, with implementation in R, SAS and/or ADMB. Provides all program code and software extensions on a supporting website. Confines supporting theory to the final chapters to maintain a readable and pragmatic focus of the preceding chapters. This book is not just an accessible and practical text about maximum likelihood, it is a comprehensive guide to modern maximum likelihood estimation and inference. It will be of interest to readers of all levels, from novice to expert. It will be of great benefit to researchers, and to students of statistics from senior undergraduate to graduate level. For use as a course text, exercises are provided at the end of each chapter.
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 Handbook of Marketing Decision Models by : Berend Wierenga
Download or read book Handbook of Marketing Decision Models written by Berend Wierenga and published by Springer. This book was released on 2017-07-12 with total page 598 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Second Edition of this book presents the state of the art in this important field. Marketing decision models constitute a core component of the marketing discipline and the area is changing rapidly, not only due to fundamental advances in methodology and model building, but also because of the recent developments in information technology, the Internet and social media. This Handbook contains eighteen chapters that cover the most recent developments of marketing decision models in different domains of marketing. Compared to the previous edition, thirteen chapters are entirely new, while the remaining chapters represent complete updates and extensions of the previous edition. This new edition of the Handbook has chapters on models for substantive marketing problems, such as customer relationship management, customer loyalty management, website design, Internet advertising, social media, and social networks. In addition, it contains chapters on recent methodological developments that are gaining popularity in the area of marketing decision models, such as structural modeling, learning dynamics, choice modeling, eye-tracking and measurement. The introductory chapter discusses the main developments of the last decade and discusses perspectives for future developments.
Book Synopsis Modelling Transport by : Juan de Dios Ortúzar
Download or read book Modelling Transport written by Juan de Dios Ortúzar and published by John Wiley & Sons. This book was released on 2024-02-15 with total page 724 pages. Available in PDF, EPUB and Kindle. Book excerpt: MODELLING TRANSPORT Comprehensive Textbook Resource for Understanding Transport Modelling Modelling Transport provides unrivalled depth and breadth of coverage on the topic of transport modelling. Each topic is approached as a modelling exercise with discussion of the roles of theory, data, model specification, estimation, validation, and application. The authors present the state of the art and its practical application in a pedagogic manner, easily understandable to both students and practitioners. An accompanying website hosts a solutions manual. Sample topics and learning resources included in the work are as follows: State-of-the-art developments in the field of transport modelling, including new research and examples Factors to consider for better modelling and forecasting Information and analysis on dynamic assignment and micro-simulation and model design and specification Agent and Activity Based Modelling Modelling new modes and services Graduate students in transportation engineering and planning, transport economics, urban studies, and geography programs along with researchers and practitioners in the transportation and urban planning industry can use Modelling Transport as a comprehensive reference work for a wide array of topics pertaining to this field.
Book Synopsis Essays on Time-varying Consumer Preferences by : Sŏng-ho Pak
Download or read book Essays on Time-varying Consumer Preferences written by Sŏng-ho Pak and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Consumer preferences are changing over time. In this dissertation, we provide three studies regarding changes in consumer preferences and methods of modeling time-varying preferences. In Chapter 1, 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. We show that the proposed method provides unbiased and efficient estimates of demand parameters. We also obtain endogeneity test statistics as a byproduct, 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. We propose a structural model of market evolution and apply the proposed model to the South Korean cigarette market data in Chapter 2. In the South Korean cigarette market, consumers have shown dramatic changes in their cigarette preferences. While most consumers smoked high-tar cigarettes ten years ago, now most consumers prefer low-tar cigarettes. Another interesting trend in this market is Given the strong dynamics in the growing popularity of super-slim cigarettes. preferences, we raise two critical questions - 1) what are the sources of preference change, and 2) how does the firm (KT&G Corporation, a de-facto monopolist in the market) react to these preference changes. We answer these questions using a unique In the proposed demand structural model of consumer demand and firm behavior. model, evolution of consumers' preferences is driven by an exogenous effect and a new product introduction effect. On the one hand, the increasing preference for low- tar cigarettes can be explained by consumers' growing heath consciousness, an exogenous effect. Due to stringent government restrictions on promotion and advertising of tobacco products, new product introduction is an important marketing instrument for KT&G. We hypothesize that a new product carries critical This is the information that subsequently influences consumer preferences. introduction effect. We propose an aggregate random coefficient logit model wherein the parameters evolve as a function of the introduction and exogenous effects. This model allows us to separate the two effects and examine their relative significance. Another key research question we study is how the firm reacts to the To answer this question, we build two supply side models. preference changes. First, we specify the firm's pricing model which elucidates the influence of the timevarying preferences on the firm's pricing decisions. Second, we model the firm's decisions regarding new product design and introduction. This model clarifies the firm's decision process regarding the new product under the time-varying consumer preferences. This study provides valuable insights into the sources of preference Also, it changes, and how firms' decisions shape the fundamentals of the market. sheds light on the role and the value of new products design and introduction. proposed model can help a firm develop a new product strategy that will move consumer preferences in a preferred direction. In many categories consumers display cyclical buying: they repeatedly The purchase in the category for several periods, followed by several periods of not buying. One possible explanation for such cyclicality is the joint effect of habit and boredom on repeated purchasing. In Chapter 3, we propose a Markov regime-switching random coefficient logit model to represent these behaviors as stochastic switching between high and low category purchase tendencies. The main feature of the proposed model is that it divides the stream of purchase decisions of a consumer into distinct regimes with different parameter values that characterize high versus low purchase tendencies. In an empirical application of the model to purchases of yogurt-buying households we find that as many as 40.8% display cyclicality between high and low yogurt purchasing tendencies. We show (via simulation) that alternating between high and low purchase tendencies corresponds with changing levels of consumer inventory in a substitute category. If one ignores this phenomenon, a correlation between yogurt inventory and the unexplained part (or error term) in utility arises leading to biased estimates. Predictions from the proposed model track observed yogurt purchases of households over time closely, and the model also fits better than three benchmark models. Also, we show that cyclicality in buying has a key implication for a firm's price promotion strategies: a price reduction that is offered to a household during its high purchasing tendency period will result in greater increases in sales than one that is offered during its low purchasing period. This opens up a new dimension for enhancing the effectiveness of promotions - customized timing of price reductions.
Book Synopsis Maximum Likelihood Estimation of Misspecified Models by : T. Fomby
Download or read book Maximum Likelihood Estimation of Misspecified Models written by T. Fomby and published by Elsevier. This book was released on 2003-12-12 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Comparative study of pure and pretest estimators for a possibly misspecified two-way error component model / Badi H. Baltagi, Georges Bresson, Alain Pirotte -- Estimation, inference, and specification testing for possibly misspecified quantile regression / Tae-Hwan Kim, Halbert White -- Quasimaximum likelihood estimation with bounded symmetric errors / Douglas Miller, James Eales, Paul Preckel -- Consistent quasi-maximum likelihood estimation with limited information / Douglas Miller, Sang-Hak Lee -- An examination of the sign and volatility switching arch models under alternative distributional assumptions / Mohamed F. Omran, Florin Avram -- estimating a linear exponential density when the weighting matrix and mean parameter vector are functionally related / Chor-yiu Sin -- Testing in GMM models without truncation / Timothy J. Vogelsang -- Bayesian analysis of misspecified models with fixed effects / Tiemen Woutersen -- Tests of common deterministic trend slopes applied to quarterly global temperature data / Thomas B. Fomby, Timothy J. Vogelsang -- The sandwich estimate of variance / James W. Hardin -- Test statistics and critical values in selectivity models / R. Carter Hill, Lee C. Adkins, Keith A. Bender -- Introduction / Thomas B Fomby, R. Carter Hill.
Book Synopsis Modeling Markets by : Peter S.H. Leeflang
Download or read book Modeling Markets written by Peter S.H. Leeflang and published by Springer. This book was released on 2014-11-12 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is about how models can be developed to represent demand and supply on markets, where the emphasis is on demand models. Its primary focus is on models that can be used by managers to support marketing decisions. Modeling Markets presents a comprehensive overview of the tools and methodologies that managers can use in decision making. It has long been known that even simple models outperform judgments in predicting outcomes in a wide variety of contexts. More complex models potentially provide insights about structural relations not available from casual observations. In this book, the authors present a wealth of insights developed at the forefront of the field, covering all key aspects of specification, estimation, validation and use of models. The most current insights and innovations in quantitative marketing are presented, including in-depth discussion of Bayesian estimation methods. Throughout the book, the authors provide examples and illustrations. This book will be of interest to researchers, analysts, managers and students who want to understand, develop or use models of marketing phenomena.
Download or read book Choice Modelling written by Stephane Hess and published by Emerald Group Publishing. This book was released on 2010-01-15 with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contains a selection of the best theoretical and applied papers from the inaugural International Choice Modelling Conference. The conference was organised by the Institute for Transport Studies at the University of Leeds and held in Harrogate, North Yorkshire on 30 March to 1 April 2009.
