Bayesian Estimation of the Random Coefficients Logit from Aggregate Count Data PDF Download
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Author: German Zenetti
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
The random coefficients logit model is a workhorse in marketing and empirical industrial organizations research. When only aggregate data are available, it is customary to calibrate the model based on market shares as data input, even if the data are available in the form of aggregate counts. However, market shares are functionally related to model primitives in the random coefficients model whereas finite aggregate counts are only probabilistic functions of these model primitives. A recent paper by Park & Gupta (2009) stresses this distinction but is hamstrung by numerical problems when demonstrating its potential practical importance. We develop Bayesian inference for the likelihood function proposed by Park & Gupta, sidestepping the numerical problem encountered by these authors. We show how taking account of the amount of information about shares by modeling counts directly results in improved inference.
Author: German Zenetti
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
The random coefficients logit model is a workhorse in marketing and empirical industrial organizations research. When only aggregate data are available, it is customary to calibrate the model based on market shares as data input, even if the data are available in the form of aggregate counts. However, market shares are functionally related to model primitives in the random coefficients model whereas finite aggregate counts are only probabilistic functions of these model primitives. A recent paper by Park & Gupta (2009) stresses this distinction but is hamstrung by numerical problems when demonstrating its potential practical importance. We develop Bayesian inference for the likelihood function proposed by Park & Gupta, sidestepping the numerical problem encountered by these authors. We show how taking account of the amount of information about shares by modeling counts directly results in improved inference.
Author: Andres Musalem
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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This article discusses the use of Bayesian methods for estimating logit demand models using aggregate data, i.e. information solely on how many consumers chose each product. We analyze two different demand systems: independent samples and consumer panel. Under the first system, there is a different and independent random sample of N consumers in each period and each consumer makes only a single purchase decision. Under the second system, the same N consumers make a purchase decision in each of T periods. The proposed methods are illustrated using simulated and real data, and managerial insights available via data augmentation are discussed in detail.
Author: Renna Jiang
Publisher:
ISBN:
Category :
Languages : en
Pages : 0
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Book Description
We present a Bayesian approach for analyzing aggregate level sales data in a market with differentiated products. We consider the aggregate share model proposed by Berry, Levinsohn and Pakes (1995) which introduces a common demand shock into an aggregated random coefficient logit model. A full likelihood approach is possible with a specification of the distribution of the common demand shock. We introduce a re-parameterization of the covariance matrix to improve the performance of the random walk Metropolis for covariance parameters. We illustrate the usefulness of our approach with both actual and simulated data. Sampling experiments show that our approach performs well relative to the GMM estimator even in the presence of a mis-specified shock distribution. We view our approach as useful for those who willing to trade off one additional distributional assumption for increased efficiency in estimation.
Author: W. Holmes Finch
Publisher: CRC Press
ISBN: 1040004520
Category : Reference
Languages : en
Pages : 339
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Book Description
Like its bestselling predecessor, Multilevel Modeling Using R, Third Edition provides the reader with a helpful guide to conducting multilevel data modeling using the R software environment. After reviewing standard linear models, the authors present the basics of multilevel models and explain how to fit these models using R. They then show how to employ multilevel modeling with longitudinal data and demonstrate the valuable graphical options in R. The book also describes models for categorical dependent variables in both single-level and multilevel data. The third edition of the book includes several new topics that were not present in the second edition. Specifically, a new chapter has been included, focussing on fitting multilevel latent variable modeling in the R environment. With R, it is possible to fit a variety of latent variable models in the multilevel context, including factor analysis, structural models, item response theory, and latent class models. The third edition also includes new sections in Chapter 11 describing two useful alternatives to standard multilevel models, fixed effects models and generalized estimating equations. These approaches are particularly useful with small samples and when the researcher is interested in modeling the correlation structure within higher-level units (e.g., schools). The third edition also includes a new section on mediation modeling in the multilevel context, in Chapter 11. This thoroughly updated revision gives the reader state-of-the-art tools to launch their own investigations in multilevel modeling and gain insight into their research.
Author: Kenneth Train
Publisher: Cambridge University Press
ISBN: 0521766559
Category : Business & Economics
Languages : en
Pages : 399
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Book Description
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: Andrés Ignacio Musalem
Publisher:
ISBN:
Category :
Languages : en
Pages : 154
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Book Description
Author: Måns Thulin
Publisher: CRC Press
ISBN: 9781032512440
Category : Mathematics
Languages : en
Pages : 0
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Book Description
The past decades have transformed the world of statistical data analysis, with new methods, new types of data, and new computational tools. Modern Statistics with R introduces you to key parts of this modern statistical toolkit. It teaches you: Data wrangling - importing, formatting, reshaping, merging, and filtering data in R. Exploratory data analysis - using visualisations and multivariate techniques to explore datasets. Statistical inference - modern methods for testing hypotheses and computing confidence intervals. Predictive modelling - regression models and machine learning methods for prediction, classification, and forecasting. Simulation - using simulation techniques for sample size computations and evaluations of statistical methods. Ethics in statistics - ethical issues and good statistical practice. R programming - writing code that is fast, readable, and (hopefully!) free from bugs. No prior programming experience is necessary. Clear explanations and examples are provided to accommodate readers at all levels of familiarity with statistical principles and coding practices. A basic understanding of probability theory can enhance comprehension of certain concepts discussed within this book. In addition to plenty of examples, the book includes more than 200 exercises, with fully worked solutions available at: www.modernstatisticswithr.com.
Author: Mary Ann Gregurich
Publisher:
ISBN:
Category : Regression analysis
Languages : en
Pages : 230
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Book Description
A Bayesian approach to estimation of the regression coefficients of a multinominal logit model with ordinal scale response categories is presented. A Monte Carlo method is used to construct the posterior distribution of the link function. The link function is treated as an arbitrary scalar function. Then the Gauss-Markov theorem is used to determine a function of the link which produces a random vector of coefficients. The posterior distribution of the random vector of coefficients is used to estimate the regression coefficients. The method described is referred to as a Bayesian generalized least square (BGLS) analysis. Two cases involving multinominal logit models are described. Case I involves a cumulative logit model and Case II involves a proportional-odds model. All inferences about the coefficients for both cases are described in terms of the posterior distribution of the regression coefficients. The results from the BGLS method are compared to maximum likelihood estimates of the regression coefficients. The BGLS method avoids the nonlinear problems encountered when estimating the regression coefficients of a generalized linear model. The method is not complex or computationally intensive. The BGLS method offers several advantages over Bayesian approaches.
Author: Alan Agresti
Publisher: John Wiley & Sons
ISBN: 1118209990
Category : Mathematics
Languages : en
Pages : 376
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Book Description
Statistical science’s first coordinated manual of methods for analyzing ordered categorical data, now fully revised and updated, continues to present applications and case studies in fields as diverse as sociology, public health, ecology, marketing, and pharmacy. Analysis of Ordinal Categorical Data, Second Edition provides an introduction to basic descriptive and inferential methods for categorical data, giving thorough coverage of new developments and recent methods. Special emphasis is placed on interpretation and application of methods including an integrated comparison of the available strategies for analyzing ordinal data. Practitioners of statistics in government, industry (particularly pharmaceutical), and academia will want this new edition.
Author:
Publisher:
ISBN:
Category : Dissertations, Academic
Languages : en
Pages : 854
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Book Description
