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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).

This chapter compares the performance of the maximum simulated likelihood (MSL) approach with the composite marginal likelihood (CML) approach in multivariate ordered-response situations. The ability of the two approaches to recover model parameters in simulated data sets is examined, as is the efficiency of estimated parameters and computational cost. Overall, the simulation results demonstrate the ability of the CML approach to recover the parameters very well in a 5–6 dimensional ordered-response choice model context. In addition, the CML recovers parameters as well as the MSL estimation approach in the simulation contexts used in this study, while also doing so at a substantially reduced computational cost. Further, any reduction in the efficiency of the CML approach relative to the MSL approach is in the range of nonexistent to small. When taken together with its conceptual and implementation simplicity, the CML approach appears to be a promising approach for the estimation of not only the multivariate ordered-response model considered here, but also for other analytically intractable econometric models.

In this article we propose a multivariate dynamic probit model. Our model can be viewed as a nonlinear VAR model for the latent variables associated with correlated binary time-series data. To estimate it, we implement an exact maximum likelihood approach, hence providing a solution to the problem generally encountered in the formulation of multivariate probit models. Our framework allows us to study the predictive relationships among the binary processes under analysis. Finally, an empirical study of three financial crises is conducted.

This paper formulates and analyzes Bayesian model variants for the analysis of systems of spatial panel data with binary-dependent variables. The paper focuses on cases where latent variables of cross-sectional units in an equation of the system contemporaneously depend on the values of the same and, eventually, other latent variables of other cross-sectional units. Moreover, the paper discusses cases where time-invariant effects are exogenous versus endogenous. Such models may have numerous applications in industrial economics, public economics, or international economics. The paper illustrates that the performance of Bayesian estimation methods for such models is supportive of their use with even relatively small panel data sets.

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.

The search for flexible models has led the simple multinomial logit model to evolve into the powerful but computationally very demanding mixed multinomial logit (MMNL) model. That flexibility search lead to discrete choice hybrid choice models (HCMs) formulations that explicitly incorporate psychological factors affecting decision making in order to enhance the behavioral representation of the choice process. It expands on standard choice models by including attitudes, opinions, and perceptions as psychometric latent variables.

In this paper we describe the classical estimation technique for a simulated maximum likelihood (SML) solution of the HCM. To show its feasibility, we apply it to data of stated personal vehicle choices made by Canadian consumers when faced with technological innovations.

We then go beyond classical methods, and estimate the HCM using a hierarchical Bayesian approach that exploits HCM Gibbs sampling considering both a probit and a MMNL discrete choice kernel. We then carry out a Monte Carlo experiment to test how the HCM Gibbs sampler works in practice. To our knowledge, this is the first practical application of HCM Bayesian estimation.

We show that although HCM joint estimation requires the evaluation of complex multi-dimensional integrals, SML can be successfully implemented. The HCM framework not only proves to be capable of introducing latent variables, but also makes it possible to tackle the problem of measurement errors in variables in a very natural way. We also show that working with Bayesian methods has the potential to break down the complexity of classical estimation.

An important but often overlooked obstacle in multivariate discrete data models is the specification of endogenous covariates. Endogeneity can be modeled as latent or observed, representing competing hypotheses about the outcomes being considered. However, little attention has been applied to deciphering which specification is best supported by the data. This paper highlights the use of existing Bayesian model comparison techniques to investigate the proper specification for endogenous covariates and to understand the nature of endogeneity. Consideration of both observed and latent modeling approaches is emphasized in two empirical applications. The first application examines linkages for banking contagion and the second application evaluates the impact of education on socioeconomic outcomes.

We propose a generic algorithm for numerically accurate likelihood evaluation of a broad class of spatial models characterized by a high-dimensional latent Gaussian process and non-Gaussian response variables. The class of models under consideration includes specifications for discrete choices, event counts and limited-dependent variables (truncation, censoring, and sample selection) among others. Our algorithm relies upon a novel implementation of efficient importance sampling (EIS) specifically designed to exploit typical sparsity of high-dimensional spatial precision (or covariance) matrices. It is numerically very accurate and computationally feasible even for very high-dimensional latent processes. Thus, maximum likelihood (ML) estimation of high-dimensional non-Gaussian spatial models, hitherto considered to be computationally prohibitive, becomes feasible. We illustrate our approach with ML estimation of a spatial probit for US presidential voting decisions and spatial count data models (Poisson and Negbin) for firm location choices.

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.

To address the safety concerns generated by truck crashes occurred in big cities, this paper analyzes the zip code tabulation area (ZCTA)-based truck crash frequency across four temporal intervals – morning (6:00–10:00), mid-day (10:00–15:00), afternoon (15:00–19:00), and night (19:00–6:00) in New York City in 2010. A multivariate conditional autoregressive count model is used to recognize both spatial and temporal dependences. The results prove the presence of spatial and temporal dependencies for truck crashes that occurred in neighboring areas. Built environment attributes such as various types of business establishment density and traffic volume for different types of vehicles, which are important factors to consider for crashes occurred in an urban setting, are also examined in the study.