A New Utility-Consistent Econometric Approach to Multivariate Count Data Modeling

In the current paper, we propose a new utility‐consistent modeling framework to explicitly link a count data model with an event‐type multinomial‐choice model. The proposed framework uses a multinomial probit kernel for the event‐type choice model and introduces unobserved heterogeneity in both the count and discrete‐choice components. Additionally, this paper establishes important new results regarding the distribution of the maximum of multivariate normally distributed variables, which form the basis to embed the multinomial probit model within a joint modeling system for multivariate count data. The model is applied to analyzing out‐of‐home non‐work episodes pursued by workers, using data from the National Household Travel Survey. Copyright © 2014 John Wiley & Sons, Ltd.

[1]  Marc G. Genton,et al.  On the exact distribution of the maximum of absolutely continuous dependent random variables , 2008 .

[2]  W. M. Gorman.  SEPARABLE UTILITY AND AGGREGATION , 1959 .

[3]  M. Greig,et al.  Extremes in a random assembly. , 1967, Biometrika.

[4]  Chandra R. Bhat,et al.  An empirical investigation into the time-use and activity patterns of dual-earner couples with and without young children , 2015 .

[5]  K. Krizek,et al.  E‐Shopping and its Relationship with In‐store Shopping: Empirical Evidence from the Netherlands and the USA , 2006 .

[6]  D. Hensher,et al.  Urban Commuters’ Mode-switching Behaviour in Taipai, with an Application of the Bounded Rationality Principle , 2010 .

[7]  Chandra R. Bhat,et al.  The maximum approximate composite marginal likelihood (MACML) estimation of multinomial probit-based unordered response choice models , 2011 .

[8]  Chandra R. Bhat,et al.  Comprehensive Model of Worker Nonwork-Activity Time Use and Timing Behavior , 2009 .

[9]  Chandra R. Bhat,et al.  A multiple discrete–continuous extreme value model: formulation and application to discretionary time-use decisions , 2005 .

[10]  Daniel Gianola,et al.  A comparison between Poisson and zero-inflated Poisson regression models with an application to number of black spots in Corriedale sheep , 2008, Genetics Selection Evolution.

[11]  Kenneth E. Train,et al.  Discrete Choice Methods with Simulation , 2016 .

[12]  Bruce G. Lindsay,et al.  ISSUES AND STRATEGIES IN THE SELECTION OF COMPOSITE LIKELIHOODS , 2011 .

[13]  Chandra R. Bhat,et al.  A count data model with endogenous covariates: Formulation and application to roadway crash frequency at intersections , 2014 .

[14]  John M. Olin.  Markov Chain Monte Carlo Analysis of Correlated Count Data , 2003 .

[15]  Kay W. Axhausen,et al.  An analysis of the impact of information and communication technologies on non-maintenance shopping activities , 2002 .

[16]  V. P. Godambe.  An Optimum Property of Regular Maximum Likelihood Estimation , 1960 .

[17]  Daniel J. Phaneuf,et al.  Kuhn-Tucker Demand System Approaches to Non-Market Valuation , 2005 .

[18]  Gregory K. Leonard,et al.  A utility-consistent, combined discrete choice and count data model Assessing recreational use losses due to natural resource damage , 1995 .

[19]  J. V. Ommeren,et al.  The effect of search imperfections on commuting behaviour: Evidence from employed and self-employed workers☆ , 2008 .

[20]  Chandra R. Bhat,et al.  A simulation evaluation of the maximum approximate composite marginal likelihood (MACML) estimator for mixed multinomial probit models , 2011 .

[21]  Jan Rouwendal,et al.  Assessing the value of museums with a combined discrete choice/count data model , 2005 .

[22]  R. Crane,et al.  Sex Changes Everything , 2009 .

[23]  Michael Keane,et al.  A Note on Identification in the Multinomial Probit Model , 1992 .

[24]  N. Reid,et al.  AN OVERVIEW OF COMPOSITE LIKELIHOOD METHODS , 2011 .

[25]  Johanna Zmud,et al.  Trip-Chaining Trends in the United States: Understanding Travel Behavior for Policy Making , 2005 .

[26]  H. Joe,et al.  Composite likelihood estimation in multivariate data analysis , 2005 .

[27]  C. Bhat.  The multiple discrete-continuous extreme value (MDCEV) model : Role of utility function parameters, identification considerations, and model extensions , 2008 .

[28]  A. Azzalini,et al.  Some properties of skew-symmetric distributions , 2010, 1012.4710.

[29]  Dimitris Karlis,et al.  Bayesian multivariate Poisson models for insurance ratemaking , 2011 .

[30]  N. Reid,et al.  On the robustness of maximum composite likelihood estimate , 2011 .

[31]  Pravin K. Trivedi,et al.  Bayesian analysis of the ordered probit model with endogenous selection , 2008 .

[32]  R. C. Bose,et al.  MOMENTS OF ORDER STATISTICS FROM A NORMAL POPULATION , 1959 .

[33]  Robert B. Noland,et al.  Does the commute mode affect the frequency of walking behavior? The public transit link , 2012 .

[34]  James K. Harter,et al.  Day-of-week mood patterns in the United States: On the existence of ‘Blue Monday’, ‘Thank God it's Friday’ and weekend effects , 2012 .

[35]  Simon Hakim,et al.  A Multivariate Poisson Model of Consumer Choice in a Multi-Airport Region , 2009 .

[36]  W. Greene,et al.  Modeling Ordered Choices: A Primer , 2010 .

[37]  D. McFadden,et al.  MIXED MNL MODELS FOR DISCRETE RESPONSE , 2000 .

[38]  V. Watson,et al.  Is it all about money? An examination of the motives behind moonlighting , 2011 .

[39]  Hoong Chor Chin,et al.  Applying Bayesian hierarchical models to examine motorcycle crashes at signalized intersections. , 2010, Accident; analysis and prevention.

[40]  T. Wales,et al.  Estimation of consumer demand systems with binding non-negativity constraints☆ , 1983 .

[41]  P. W. Wilson,et al.  Analyzing Frequencies of Several Types of Events: A Mixed Multinomial-Poisson Approach , 1990 .

[42]  Daniel J. Phaneuf,et al.  Estimating preferences for outdoor recreation: a comparison of continuous and count data demand system frameworks. , 2003 .

[43]  Chandra R. Bhat,et al.  Joint Model of Participation in Nonwork Activities and Time-of-Day Choice Set Formation for Workers , 2011 .

[44]  G. Molenberghs,et al.  Models for Discrete Longitudinal Data , 2005 .

[45]  N. Balakrishnan,et al.  Order statistics from trivariate normal and tν-distributions in terms of generalized skew-normal and skew-tν distributions , 2009 .

[46]  R. McKelvey,et al.  A statistical model for the analysis of ordinal level dependent variables , 1975 .

[47]  Luigi Pace,et al.  ADJUSTING COMPOSITE LIKELIHOOD RATIO STATISTICS , 2009 .

[48]  Y. L. Tong.  The multivariate normal distribution , 1989 .

[49]  Richard J. Cook,et al.  A robust pairwise likelihood method for incomplete longitudinal binary data arising in clusters , 2011 .

[50]  Luc Devroye.  A Note on Finding Convex Hulls Via Maximal Vectors , 1980, Inf. Process. Lett..

[51]  Chandra R. Bhat,et al.  A latent variable representation of count data models to accommodate spatial and temporal dependence: application to predicting crash frequency at intersections , 2011 .

[52]  Harry Joe,et al.  On weighting of bivariate margins in pairwise likelihood , 2009, J. Multivar. Anal..

[53]  Fred L. Mannering,et al.  Occurence, frequency, and duration of commuters' work-to-home departure delay , 1990 .

[54]  Chandra R. Bhat,et al.  The Impact of Demographics, Built Environment Attributes, Vehicle Characteristics, and Gasoline Prices on Household Vehicle Holdings and Use , 2009 .

[55]  C. Bhat,et al.  Joint Household-Level Analysis of Individuals’ Work Arrangement Choices , 2012 .

[56]  Chandra R. Bhat,et al.  Development of Indicators of Opportunity-Based Accessibility , 2011 .

[57]  Glenn Lyons,et al.  A Human Perspective on the Daily Commute: Costs, Benefits and Trade‐offs , 2008 .

[58]  C. Varin,et al.  A comparison of the maximum simulated likelihood and composite marginal likelihood estimation approaches in the context of the multivariate ordered-response model , 2010 .

[59]  Noreen C. McDonald,et al.  Household interactions and children’s school travel: the effect of parental work patterns on walking and biking to school , 2008 .

[60]  D. Louis,et al.  A pseudolikelihood approach for simultaneous analysis of array comparative genomic hybridizations. , 2005, Biostatistics.

[61]  N. Balakrishnan,et al.  Distributions of order statistics and linear combinations of order statistics from an elliptical distribution as mixtures of unified skew-elliptical distributions , 2010, J. Multivar. Anal..

[62]  C. E. Clark.  The Greatest of a Finite Set of Random Variables , 1961 .

[63]  S. Farag.  E-Shopping and its interactions with in-store shopping , 2006 .

[64]  Chandra R. Bhat,et al.  On Accommodating Spatial Dependence in Bicycle and Pedestrian Injury Counts by Severity Level , 2013 .

[65]  D. Damm.  INTERDEPENDENCIES IN ACTIVITY BEHAVIOR , 1980 .

[66]  K. Mardia,et al.  Maximum likelihood estimation using composite likelihoods for closed exponential families , 2009 .

[67]  Monica Musio,et al.  Bayesian semi-parametric ZIP models with space-time interactions: an application to cancer registry data. , 2010, Mathematical medicine and biology : a journal of the IMA.

[68]  Feng Zhang,et al.  Modeling fresh organic produce consumption with scanner data: a generalized double hurdle model approach , 2008 .

[69]  H. A. David,et al.  Order Statistics (2nd ed). , 1981 .

[70]  Chandra R. Bhat,et al.  The Impact of Stop-Making and Travel Time Reliability on Commute Mode Choice , 2006 .

[71]  Stephan Brunow,et al.  The impact of activity chaining on the duration of daily activities , 2013 .

[72]  Richard L. Smith,et al.  Asymptotic properties of computationally efficient alternative estimators for a class of multivariate normal models , 2007 .

[73]  M. Harding,et al.  A Poisson mixture model of discrete choice , 2011 .

[74]  J. Muellbauer,et al.  Economics and consumer behavior , 1980 .

[75]  Hidde P van der Ploeg,et al.  Public health perspectives on household travel surveys active travel between 1997 and 2007. , 2010, American journal of preventive medicine.

[76]  Peter E. Rossi,et al.  Modeling Consumer Demand for Variety , 2002 .

[77]  Erika Sandow.  On the road: social aspects of commuting long distances to work , 2011 .

[78]  George Marsaglia,et al.  Expressing the normal distribution with covariance matrix A + B in terms of one with covariance matrix A , 1963 .

[79]  K. Egan,et al.  Increasing Beach Recreation Benefits by Using Wetlands to Reduce Contamination , 2011, Marine Resource Economics.

[80]  Carlo Gaetan,et al.  Composite likelihood methods for space-time data , 2006 .

[81]  Daniel J. Phaneuf,et al.  Estimating demand systems when outcomes are correlated counts , 2008 .

[82]  D. Cox,et al.  A note on pseudolikelihood constructed from marginal densities , 2004 .

[83]  Arjun K. Gupta,et al.  A multivariate skew normal distribution , 2004 .

[84]  Jennifer Bethell,et al.  Repeat self-harm: application of hurdle models , 2010, British Journal of Psychiatry.

[85]  K. Train.  Discrete Choice Methods with Simulation , 2003 .

[86]  Nils Lid Hjort,et al.  ML, PL, QL in Markov Chain Models , 2008 .

[87]  Hans van Ophem,et al.  A GENERAL METHOD TO ESTIMATE CORRELATED DISCRETE RANDOM VARIABLES , 1999, Econometric Theory.

[88]  F. Witlox,et al.  Commuting trips within tours: how is commuting related to land use? , 2011 .