Semiparametric Bayesian Estimation for Marginal Parametric Potential Outcome Modeling: Application to Causal Inference

REFERENCES

• Albert , J. H. and Chib , S. 1993 . Bayesian Analysis of Binary and Polychotomous Response Data . Journal of the American Statistical Association , 88 : 669 – 679 .
   Web of Science ®Google Scholar
• Amemiya , T. 1985 . Advanced Econometrics , Cambridge, , MA : Harvard University Press .
   Google Scholar
• Aral , S. , Muchnik , L. and Sundararajan , A. 2009 . Distinguishing Influence-Based Contagion From Homophily-Driven Diffusion in Dynamic Networks . Proceedings of The National Academy of Sciences of the USA , 106 : 21544 – 21549 .
   PubMed Web of Science ®Google Scholar
• Bartel , A. P. and Sicherman , N. 1999 . Technological Change and Wages: An Interindustry Analysis . Journal of Political Economics , 107 : 285 – 325 .
   Web of Science ®Google Scholar
• Bernardo , J. M. and Smith , A. F. M. 2000 . Bayesian Theory , New York : Wiley .
   Google Scholar
• Bucklin , R. E. and Sismeiro , C. 2003 . A Model of Web Site Browsing Behavior Estimated on Clickstream Data . Journal of Marketing Research , 40 : 249 – 267 .
   Web of Science ®Google Scholar
• Canale , A. and Dunson , D. B. 2011 . Bayesian Kernel Mixtures for Counts . Journal of the American Statistical Association , 106 : 1528 – 1539 .
   PubMed Web of Science ®Google Scholar
• Chen , Y. , Wang , Q. and Xie , J. 2011 . Online Social Interactions: A Natural Experiment on Word of Mouth Versus Observational Learning . Journal of Marketing Research , 48 : 238 – 254 .
   Web of Science ®Google Scholar
• Chib , S. 2007 . Analysis of Treatment Response Data without the Joint Distribution of Potential Outcomes . Journal of Econometrics , 140 : 401 – 412 .
   Web of Science ®Google Scholar
• Chung , Y. and Dunson , D. B. 2009 . Nonparametric Bayes Conditional Distribution Modeling With Variable Selection . Journal of the American Statistical Association , 104 : 1646 – 1660 .
   PubMed Web of Science ®Google Scholar
• Cobb-Clark , D. A. and Tan , M. 2011 . Noncognitive Skills, Occupational Attainment, and Relative Wages . Labour Economics , 18 : 1 – 13 .
   Web of Science ®Google Scholar
• Conley , T. G. , Hansen , C. B. , McCulloch , R. E. and Rossi , P. E. 2008 . A Semi-Parametric Bayesian Approach to the Instrumental Variable Problem . Journal of Econometrics , 144 : 276 – 305 .
   Web of Science ®Google Scholar
• Copas , J. B. and Li , H. G. 1997 . Inference for Non-Random Samples . Journal of the Royal Statistical Society, Series B , 59 : 55 – 95 .
   Google Scholar
• Danaher , P. J. , Mullarkey , G. W. and Essegaier , S. 2006 . Factors Affecting Web Site Visit Duration: A Cross-Domain Analysis . Journal of Marketing Research , 43 : 182 – 194 .
   Web of Science ®Google Scholar
• Dunson , D. B. and Park , J.-H. 2008 . Kernel Stick-Breaking Processes . Biometrika , 95 : 307 – 323 .
   PubMed Web of Science ®Google Scholar
• Dunson , D. B. , Pillai , N. and Park , J.-H. 2007 . Bayesian Density Regression . Journal of the Royal Statistical Society, Series B , 69 : 163 – 183 .
   Google Scholar
• Gabriel , P. E. 2005 . The Effects of Differences in Year-Round, Full-Time Labor Market Experience on Gender Wage Levels in the United States . International Review of Applied Economics , 19 : 369 – 377 .
   Google Scholar
• Gibbons , R. and Katz , L. 1992 . Does Unmeasured Ability Explain Inter-Indutry Wage Differentials? . Review of Economic Studies , 59 : 515 – 535 .
   Web of Science ®Google Scholar
• Gill , J. and Casella , G. 2009 . Nonparametric Priors for Ordinal Bayesian Social Science Models: Specification and Estimation . Journal of the American Statistical Association , 104 : 453 – 464 .
   Web of Science ®Google Scholar
• Heckman , J. J. , Stixrud , J. and Urzua , S. 2006 . The Effects of Cognitive and Noncognitive Abilities on Labor Market Outcomes and Social Behavior . Journal of Labor Economics , 24 : 411 – 482 .
   Web of Science ®Google Scholar
• Hellerstein , J. K. , Neumark , D. and Troske , K. R. 1999 . Wages, Productivity, and Worker Characteristics: Evidence From Plant-Level Production Functions and Wage Equations . Journal of Labor Economics , 17 : 409 – 446 .
   Web of Science ®Google Scholar
• Hill , J. L. 2012 . Bayesian Nonparametric Modeling for Causal Inference . Journal of Computational and Graphical Statistics , 20 : 217 – 240 .
   Web of Science ®Google Scholar
• Hirano , K. 2002 . Semiparametric Bayesian Inference in Autoregressive Panel Data Models . Econometrica , 70 : 781 – 799 .
   Web of Science ®Google Scholar
• Hoshino , T. , Kurata , H. and Shigemasu , K. 2006 . A Propensity Score Adjustment for Multiple Group Structural Equation Modeling . Psychometrika , 71 : 691 – 712 .
   Web of Science ®Google Scholar
• Ibrahim , J. G. , Chen , M.-H. and Lipsitz , S. R. 2001 . Missing Responses in Generalized Linear Mixed Models When the Missing Data Mechanism is Nonignorable . Biometrika , 88 : 897 – 904 .
   Google Scholar
• Ibrahim , J. G. , Chen , M.-H. , Lipsitz , S. R. and Herring , A. H. 2005 . Missing-Data Methods for Generalized Linear Models: A Comparative Review . Journal of the American Statistical Association , 100 : 332 – 346 .
   Web of Science ®Google Scholar
• Ilmakunnas , P. , Maliranta , M. and Vainiomaki , J. 2004 . The Role of Employer and Employee Characteristics for Plant Productivity . Journal of Productivity Analysis , 21 : 249 – 276 .
   Web of Science ®Google Scholar
• Ishwaran , H. and James , L. F. 2001 . Gibbs Sampling Methods for Stick-Breaking Priors . Journal of the American Statistical Association , 96 : 161 – 173 .
   Web of Science ®Google Scholar
• Johnson , T. J. and Kaye , B. K. 2004 . Wag the Blog: How Reliance on Traditional Media and the Internet Influence Credibility Perceptions of Weblogs Among Blog Users . Journalism & Mass Communication Quarterly , 81 : 622 – 642 .
   Web of Science ®Google Scholar
• Judge , T. A. , Higgins , C. A. , Thoresen , C. J. and Barrick , M. R. 1999 . The Big Five personality traits and career Success Across the Life Span . Personnel Psychology , 52 : 621 – 652 .
   Web of Science ®Google Scholar
• Koop , G. , Poirier , D. J. and Tobias , J. L. 2007 . Bayesian Econometric Methods , New York : Cambridge University Press .
   Google Scholar
• Lee , J. and Berger , J. O. 2001 . Semiparametric Bayesian Analysis of Selection Models . Journal of the American Statistical Association , 96 : 1397 – 1409 .
   Web of Science ®Google Scholar
• Lee , L.-F. 1983 . Generalized Econometric Models With Selectivity . Econometrica , 51 : 507 – 512 .
   Web of Science ®Google Scholar
• Lemieux , T. , MacLeod , B. and Parent , D. 2009 . Performance Pay and Wage Inequality . The Quarterly Journal of Economics , 124 : 1 – 49 .
   Web of Science ®Google Scholar
• Little , R. J. A. 1985 . A Note About Models for Selectivity Bias . Econometrica , 53 : 1469 – 1474 .
   Web of Science ®Google Scholar
• Müller , M. , Erkanli , A. and West , M. 1996 . Bayesian Curve Fitting Using Multivariate Normal Mixtures . Biometrika , 83 : 67 – 79 .
   Web of Science ®Google Scholar
• Papaspiliopoulos , O. and Roberts , G. O. 2008 . Retrospective MCMC for Dirichlet Process Hierarchical Models . Biometrika , 95 : 169 – 186 .
   Web of Science ®Google Scholar
• Pati , D. , Dunson , D. and Tokdar , S. 2013 . Posterior Consistency in Conditional Distribution Estimation . Journal of Multivariate Analysis , 116 : 456 – 472 .
   PubMed Web of Science ®Google Scholar
• Qin , J. , Leung , D. and Shao , J. 2002 . Estimation With Survey Data Under Nonignorable Nonresponse or Informative Sampling . Journal of the American Statistical Association , 97 : 193 – 200 .
   Web of Science ®Google Scholar
• Qin , J. and Zhang , B. 2007 . Empirical-Likelihood-Based Inference in Missing Response Problems and Its Application in Observational Studies . Journal of the Royal Statistical Society, Series B , 69 : 101 – 122 .
   Google Scholar
• Rodriguez , A. and Dunson , D. 2011 . Nonparametric Bayesian Models Through Probit Stick-Breaking Process . Bayesian Analysis , 6 : 145 – 178 .
   Web of Science ®Google Scholar
• Rosenbaum , P. R. 2002 . Observational Studies (2nd. ed.) , New York, , NY : Springer .
   Google Scholar
• Rosenbaum , P. R. and Rubin , D. B. 1983 . The Central Role of the Propensity Score in Observational Studies for Causal Effects . Biometrika , 70 : 41 – 55 .
   Web of Science ®Google Scholar
• Rotniztky , A. and Robins , J. M. 1995 . Semiparametric Regression Estimation in the Presence of Dependent Censoring . Biometrika , 70 : 805 – 820 .
   Google Scholar
• Rubin , D. B. 1974 . Estimating Causal Effects of Treatments in Randomized and Nonrandomized Studies . Journal of Educational Psychology , 66 : 688 – 701 .
   Web of Science ®Google Scholar
• ——— . 1976 . Inference and Missing Data . Biometrika , 63 : 581 – 590 .
   Web of Science ®Google Scholar
• ——— . 2005 . Causal Inference Using Potential Outcomes: Design, Modeling, Decision . Journal of the American Statistical Association , 100 : 322 – 331 .
   Web of Science ®Google Scholar
• Schwartz , S. L. , Li , F. and Mealli , F. 2011 . A Bayesian Semiparametric Approach to Intermediate Variables in Causal Inference . Journal of the American Statistical Association , 106 : 1331 – 1344 .
   Web of Science ®Google Scholar
• Sethuraman , J. 1994 . A Constructive Definition of Dirichlet Priors . Statistica Sinica , 4 : 639 – 650 .
   Web of Science ®Google Scholar
• Stubbendick , A. L. and Ibrahim , J. G. 2003 . Maximum Likelihood Methods for Nonignorable Missing Responses and Covariates in Random Effects Models . Biometrics , 59 : 1140 – 1150 .
   PubMed Web of Science ®Google Scholar
• Tang , G. , Little , R. J. A. and Raghunathan , T. 2003 . Analysis of Multivariate Missing Data With Nonignorable Nonresponse . Biometrika , 90 : 747 – 746 .
   Web of Science ®Google Scholar
• Trusov , M. , Bucklin , R. E. and Pauwels , K. 2009 . Effects of Word-of-Mouth Versus Traditional Marketing: Findings From an Internet Social Networking Site . Journal of Marketing , 73 : 90 – 102 .
   Web of Science ®Google Scholar
• Walker , S. G. 2007 . Sampling the Dirichlet Mixture Model With Slices . Communications in Statistics: Simulation and Computation , 36 : 45 – 54 .
   Web of Science ®Google Scholar
• Walker , S. G. , Damien , P. , Laud , P. W. and Smith , A. F. M. 1999 . Bayesian Nonparametric Inference for Random Distributions and Related Functions . Journal of the Royal Statistical Society, Series B , 61 : 485 – 527 .
   Google Scholar