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This article is motivated by the lack of flexibility in Bayesian quantile regression for ordinal models where the error follows an asymmetric Laplace (AL) distribution. The inflexibility arises because the skewness of the distribution is completely specified when a quantile is chosen. To overcome this shortcoming, we derive the cumulative distribution function (and the moment-generating function) of the generalized asymmetric Laplace (GAL) distribution – a generalization of AL distribution that separates the skewness from the quantile parameter – and construct a working likelihood for the ordinal quantile model. The resulting framework is termed flexible Bayesian quantile regression for ordinal (FBQROR) models. However, its estimation is not straightforward. We address estimation issues and propose an efficient Markov chain Monte Carlo (MCMC) procedure based on Gibbs sampling and joint Metropolis–Hastings algorithm. The advantages of the proposed model are demonstrated in multiple simulation studies and implemented to analyze public opinion on homeownership as the best long-term investment in the United States following the Great Recession.

Word‐of‐mouth (WOM) has been found to significantly influence consumers' decision making. Much attention has been paid to the effect of WOM characteristics such as the number of postings, the dispersion of online conversations, the reputation of the reviewers, and the review quality on product sales. Little research, however, has examined the interaction process of online reviews. The purpose of this paper is to investigate the consumers' product attitude formation process in online WOM. Three research questions will be addressed in this paper, i.e. the effect of prior responses on the following repliers' product attitude, the negativity effect and the role of main messages in shaping consumers' product attitude formation process.

The product attitude formation process of online WOM is investigated using the data of product reviews (main messages) and their corresponding responses. The paper collected 26 product reviews from various web sites and kept the first 40‐50 responses for each review, which resulted in 26 main messages and 1,173 observations (i.e. responses) in total. A hierarchical Bayesian ordinal choice model is then specified and estimated with the Markov Chain Monte Carlo method to address the research questions and to capture the main message heterogeneity.

The paper finds that the impact of prior responses (e.g. the proportion of positive and negative responses) on the product attitudes of the following responses differs significantly across products. This heterogeneity can be well explained by the characteristics of the main messages at the second‐level specification. Thereby, factors that influence consumers' product attitudes in the interaction process of online WOM include prior responses and main message characteristics. Another interesting finding is that positive responses have larger impacts on product attitudes than negative ones.

This research contributes to both academic research and the firms' online WOM management. Theoretically, this research is the first attempt to examine the formation process of attitudes toward new products in online communications. This research contributes by modeling how the dynamic process of online WOM influences new product attitudes. Furthermore, inconsistent with the “negativity effect” proposed by researchers (e.g. Skowronski and Carlston), the paper finds that positive responses matter more than negative ones in online communications. In addition, the way the paper configures the data for online communications is innovative and provides a perspective to quantitatively model the communication process. Managerially, this research provides implications for firms to intervene in the online communication process and influence consumer attitude of new products.

Several inferential procedures are advocated in the literature. The most commonly used techniques are the frequentist and the Bayesian inferential procedures. Bayesian methods afford inferences based on small data sets and are especially useful in studies with limited data availability. Bayesian approaches also help incorporate prior knowledge, especially subjective knowledge, into predictions. Considering the increasing difficulty in data acquisition, the application of Bayesian techniques can be hugely beneficial to managers, especially in analysing limited data situations like a study of expert opinion. Another factor constraining the broader application of Bayesian statistics in business was computational power requirements and the availability of appropriate analytical tools. However, with the increase in computational power, connectivity and the development of appropriate software programmes, Bayesian applications have become more attractive. This chapter attempts to unravel the applications of the Bayesian inferential procedure in marketing management.

Factor analysis is the most used tool in organizational research and its widespread use in scale validations contribute to decision-making in management. However, standard factor analysis is not always applied correctly mainly due to the misuse of ordinal data as interval data and the inadequacy of the former for classical factor analysis. The purpose of this paper is to present and apply the Bayesian factor analysis for mixed data (BFAMD) in the context of empirical using the Bayesian paradigm for the construction of scales.

Ignoring the categorical nature of some variables often used in management studies, as the popular Likert scale, may result in a model with false accuracy and possibly biased estimates. To address this issue, Quinn (2004) proposed a Bayesian factor analysis model for mixed data, which is capable of modeling ordinal (qualitative measure) and continuous data (quantitative measure) jointly and allows the inclusion of qualitative information through prior distributions for the parameters’ model. This model, adopted here, presents considering advantages and allows the estimation of the posterior distribution for the latent variables estimated, making the process of inference easier.

The results show that BFAMD is an effective approach for scale validation in management studies making both exploratory and confirmatory analyses possible for the estimated factors and also allowing the analysts to insert a priori information regardless of the sample size, either by using the credible intervals for Factor Loadings or by conducting specific hypotheses tests. The flexibility of the Bayesian approach presented is counterbalanced by the fact that the main estimates used in factor analysis as uniqueness and communalities commonly lose their usual interpretation due to the choice of using prior distributions.

Considering that the development of scales through factor analysis aims to contribute to appropriate decision-making in management and the increasing misuse of ordinal scales as interval in organizational studies, this proposal seems to be effective for mixed data analyses. The findings found here are not intended to be conclusive or limiting but offer a useful starting point from which further theoretical and empirical research of Bayesian factor analysis can be built.

This chapter develops a framework for quantile regression in binary longitudinal data settings. A novel Markov chain Monte Carlo (MCMC) method is designed to fit the model and its computational efficiency is demonstrated in a simulation study. The proposed approach is flexible in that it can account for common and individual-specific parameters, as well as multivariate heterogeneity associated with several covariates. The methodology is applied to study female labor force participation and home ownership in the United States. The results offer new insights at the various quantiles, which are of interest to policymakers and researchers alike.

In this paper, we consider the analysis of models for univariate and multivariate ordinal outcomes in the context of the latent variable inferential framework of Albert and Chib (1993). We review several alternative modeling and identification schemes and evaluate how each aids or hampers estimation by Markov chain Monte Carlo simulation methods. For each identification scheme we also discuss the question of model comparison by marginal likelihoods and Bayes factors. In addition, we develop a simulation-based framework for analyzing covariate effects that can provide interpretability of the results despite the nonlinearities in the model and the different identification restrictions that can be implemented. The methods are employed to analyze problems in labor economics (educational attainment), political economy (voter opinions), and health economics (consumers’ reliance on alternative sources of medical information).

A major stumbling block in multivariate discrete data analysis is the problem of evaluating the outcome probabilities that enter the likelihood function. Calculation of these probabilities involves high-dimensional integration, making simulation methods indispensable in both Bayesian and frequentist estimation and model choice. We review several existing probability estimators and then show that a broader perspective on the simulation problem can be afforded by interpreting the outcome probabilities through Bayes’ theorem, leading to the recognition that estimation can alternatively be handled by methods for marginal likelihood computation based on the output of Markov chain Monte Carlo (MCMC) algorithms. These techniques offer stand-alone approaches to simulated likelihood estimation but can also be integrated with traditional estimators. Building on both branches in the literature, we develop new methods for estimating response probabilities and propose an adaptive sampler for producing high-quality draws from multivariate truncated normal distributions. A simulation study illustrates the practical benefits and costs associated with each approach. The methods are employed to estimate the likelihood function of a correlated random effects panel data model of women's labor force participation.

Bayesian Econometrics is a volume in the series Advances in Econometrics that illustrates the scope and diversity of modern Bayesian econometric applications, reviews some recent advances in Bayesian econometrics, and highlights many of the characteristics of Bayesian inference and computations. This first paper in the volume is the Editors’ introduction in which we summarize the contributions of each of the papers.

Constructing and evaluating behavioral science models is a complex process. Decisions must be made about which variables to include, which variables are related to each other, the functional forms of the relationships, and so on. The last 10 years have seen a substantial extension of the range of statistical tools available for use in the construction process. The progress in tool development has been accompanied by the publication of handbooks that introduce the methods in general terms (Arminger et al., 1995; Tinsley & Brown, 2000a). Each chapter in these handbooks cites a wide range of books and articles on specific analysis topics.