A New Generalized Heterogeneous Data Model (GHDM) to Jointly Model Mixed Types of Dependent Variables

This paper formulates a generalized heterogeneous data model (GHDM) that jointly handles mixed types of dependent variables—including multiple nominal outcomes, multiple ordinal variables, and multiple count variables, as well as multiple continuous variables. Sufficiency conditions for identification of the GHDM parameters are presented. The maximum approximate composite marginal likelihood (MACML) method is proposed to estimate this jointly mixed model system.

[1]  P. Mokhtarian,et al.  Attitudes toward travel and land use and choice of residential neighborhood type: Evidence from the San Francisco bay area , 2007 .

[2]  Kathleen M. Gates,et al.  Extended unified SEM approach for modeling event-related fMRI data , 2011, NeuroImage.

[3]  Chandra R. Bhat,et al.  An analysis of bicycle route choice preferences in Texas, US , 2009 .

[4]  K. Jöreskog.  Factor analysis by least squares and maximum likelihood methods , 1977 .

[5]  Yingling Fan,et al.  Exploring the Influences of Density on Travel Behavior Using Propensity Score Matching , 2012 .

[6]  Chandra R. Bhat,et al.  A Comprehensive Analysis of Built Environment Characteristics on Household Residential Choice and Auto Ownership Levels , 2007 .

[7]  Alexander R. De Leon,et al.  Analysis of Mixed Data : Methods & Applications , 2013 .

[8]  Chandra R. Bhat,et al.  Integrated Model of Residential Location, Work Location, Vehicle Ownership, and Commute Tour Characteristics , 2013 .

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

[10]  Sungyop Kim,et al.  Intra-regional residential movement of the elderly: testing a suburban-to-urban migration hypothesis , 2011 .

[11]  Chandra R. Bhat,et al.  The Composite Marginal Likelihood (CML) Inference Approach with Applications to Discrete and Mixed Dependent Variable Models , 2014 .

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

[13]  R V Gueorguieva,et al.  Joint analysis of repeatedly observed continuous and ordinal measures of disease severity , 2006, Statistics in medicine.

[14]  James J. Heckman,et al.  Four Parameters of Interest in the Evaluation of Social Programs , 2001 .

[15]  Chandra R. Bhat,et al.  Joint Model of Choice of Residential Neighborhood and Bicycle Ownership , 2008 .

[16]  P. Schmidt,et al.  Limited-Dependent and Qualitative Variables in Econometrics. , 1984 .

[17]  Till Dannewald,et al.  Incorporating Latent Variables into Discrete Choice Models — A Simultaneous Estimation Approach Using SEM Software , 2008 .

[18]  David C. Stapleton,et al.  Analyzing Political Participation Data with a Mimic Model , 1978 .

[19]  Sylvia J. T. Jansen,et al.  What is the worth of values in guiding residential preferences and choices? , 2012, Journal of Housing and the Built Environment.

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

[21]  Linda L. Day,et al.  Choosing a House: The Relationship between Dwelling Type, Perception of Privacy and Residential Satisfaction , 2000 .

[22]  Chandra R. Bhat,et al.  A New Estimation Approach to Integrate Latent Psychological Constructs in Choice Modeling , 2014 .

[23]  Joan L. Walker,et al.  Hybrid Choice Models: Progress and Challenges , 2002 .

[24]  Geert Molenberghs,et al.  Joint models for continuous and discrete longitudinal data , 2008 .

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

[26]  Y. Shiftan,et al.  Transit market research using structural equation modeling and attitudinal market segmentation , 2008 .

[27]  Alex J. Sutton,et al.  Methods for Meta-Analysis in Medical Research , 2000 .

[28]  D. Brownstone,et al.  The impact of residential density on vehicle usage and fuel consumption , 2010 .

[29]  Moshe Ben-Akiva,et al.  Hybrid Choice Models with Logit Kernel: Applicability to Large Scale Models1 , 2005 .

[30]  Ricardo A. Daziano,et al.  Incorporating pro-environmental preferences towards green automobile technologies through a Bayesian hybrid choice model , 2013 .

[31]  A. Vedlitz,et al.  Examining the determinants of public environmental concern: Evidence from national public surveys , 2014 .

[32]  Jaroslaw Harezlak,et al.  Factorization and latent variable models for joint analysis of binary and continuous outcomes , 2013 .

[33]  D. Brownstone,et al.  The Impact of Residential Density on Vehicle Usage and Energy Consumption , 2005 .

[34]  Chandra R. Bhat,et al.  A Joint Count-Continuous Model of Travel Behavior with Selection Based on a Multinomial Probit Residential Density Choice Model , 2014 .

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

[36]  Richard M. Ryan,et al.  Self-Determination Theory and Diminished Functioning , 2011, Personality & social psychology bulletin.

[37]  R. P. McDonald,et al.  Structural Equations with Latent Variables , 1989 .

[38]  Kenneth A. Bollen,et al.  Structural Equations with Latent Variables , 1989 .

[39]  Alexander R. de Leon,et al.  General mixed‐data model: Extension of general location and grouped continuous models , 2007 .

[40]  R. Gifford,et al.  Personal and social factors that influence pro-environmental concern and behaviour: a review. , 2014, International journal of psychology : Journal international de psychologie.

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

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

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

[44]  Joshua Auld,et al.  A behavioral housing search model: Two-stage hazard-based and multinomial logit approach to choice-set formation and location selection , 2012 .

[45]  P. Bentler,et al.  Bias in Factor Score Regression and a Simple Solution , 2011 .

[46]  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 .

[47]  Robert M. O'Brien,et al.  Identification of Confirmatory Factor Analysis Models of Arbitrary Complexity , 1996 .

[48]  W. Clark,et al.  Does commuting distance matter? Commuting tolerance and residential change , 2002 .

[49]  Y. Zhu,et al.  ANOVA extensions for mixed discrete and continuous data , 2008, Comput. Stat. Data Anal..

[50]  A. D. de Leon,et al.  Classification with discrete and continuous variables via general mixed-data models , 2011 .

[51]  C. Mulley,et al.  Understanding neighbourhood design impact on travel behaviour: An application of structural equations model to a British metropolitan data , 2012 .

[52]  Rajesh Paleti,et al.  A Spatial Multivariate Count Model for Firm Location Decisions , 2014 .

[53]  Chandra R. Bhat,et al.  Accommodating Immigration Status and Self-Selection Effects in a Joint Model of Household Auto Ownership and Residential Location Choice , 2013 .

[54]  A. Champion.  A Changing Demographic Regime and Evolving Poly centric Urban Regions: Consequences for the Size, Composition and Distribution of City Populations , 2001 .

[55]  Robert M. O'Brien,et al.  Identification of Simple Measurement Models with Multiple Latent Variables and Correlated Errors , 1994 .

[56]  M. Feddag.  Composite Likelihood Estimation for Multivariate Probit Latent Traits Models , 2013 .

[57]  James J. Heckman,et al.  The relationship between treatment parameters within a latent variable framework , 2000 .

[58]  Chandra R. Bhat,et al.  Modeling the choice continuum: an integrated model of residential location, auto ownership, bicycle ownership, and commute tour mode choice decisions , 2011 .

[59]  Xinyu Cao,et al.  Examining the impacts of residential self-selection on travel behavior: A focus on methodologies , 2008 .