Causal Interaction in Factorial Experiments: Application to Conjoint Analysis

References

• Athey, S., and Imbens, G. (2016), “Recursive Partitioning for Heterogeneous Causal Effects,” Proceedings of the National Academy of Sciences, 113, 7353–7360.
   PubMed Web of Science ®Google Scholar
• Bertrand, M., and Mullainathan, S. (2004), “Are Emily and Greg More Employable Than Lakisha and Jamal?: A Field Experiment on Labor Market Discrimination,” American Economic Review, 94, 991–1013.
   Web of Science ®Google Scholar
• Bondell, H. D., and Reich, B. J. (2009), “Simultaneous Factor Selection and Collapsing Levels in ANOVA,” Biometrics, 65, 169–177.
   PubMed Web of Science ®Google Scholar
• Breiman, L. (1996), “Heuristics of Instability and Stabilization in Model Selection,” The Annals of Statistics, 24, 2350–2383.
   Web of Science ®Google Scholar
• Bühlmann, P., and Dezeure, R. (2016), Discussion of “Regularized Regression for Categorical Data” by Tutz and Gertheiss, Statistical Modelling, 16, 205–211.
   Web of Science ®Google Scholar
• Carlson, E. (2015), “Ethnic Voting and Accountability in Africa: A Choice Experiment in Uganda,” World Politics, 67, 353–385.
   Web of Science ®Google Scholar
• Chernozhukov, V., Chetverikov, D., Demirer, M., Duflo, E., Hansen, C., Newey, W., and Robins, J. (2018), “Double/Debiased Machine Learning for Treatment and Structural Parameters,” The Econometrics Journal, 21, C1–C68.
   Web of Science ®Google Scholar
• Cox, D. R. (1958), Planning of Experiments, New York: Wiley.
   Google Scholar
• ——— (1984), “Interaction,” International Statistical Review, 52, 1–24.
   Web of Science ®Google Scholar
• Dasgupta, T., Pillai, N. S., and Rubin, D. B. (2015), “Causal Inference From 2k Factorial Designs by Using Potential Outcomes,” Journal of the Royal Statistical Society, Series B, 77, 727–753.
   Google Scholar
• de González, A. B., and Cox, D. R. (2007), “Interpretation of Interaction: A Review,” The Annals of Applied Statistics, 1, 371–385.
   Web of Science ®Google Scholar
• Efron, B. (2014), “Estimation and Accuracy After Model Selection,” Journal of the American Statistical Association, 109, 991–1007.
   PubMed Web of Science ®Google Scholar
• Egami, N., Ratkovic, M., and Imai, K. (2017), “FindIt: Finding Heterogeneous Treatment Effects,” available at the Comprehensive R Archive Network (CRAN), available at https://CRAN.R-project.org/package=FindIt.
   Google Scholar
• Green, D. P., and Kern, H. L. (2012), “Modeling Heterogeneous Treatment Effects in Survey Experiments With Bayesian Additive Regression Trees,” Public Opinion Quarterly, 76, 491–511.
   Web of Science ®Google Scholar
• Green, P. E., Krieger, A. M., and Wind, Y. (2001), “Thirty Years of Conjoint Analysis: Reflections and Prospects,” Interfaces, 31, 56–73.
   Web of Science ®Google Scholar
• Green, P. E., and Rao, V. R. (1971), “Conjoint Measurement for Quantifying Judgmental Data,” Journal of Marketing Research, 8, 355–363.
   Web of Science ®Google Scholar
• Grimmer, J., Messing, S., and Westwood, S. J. (2017), “Estimating Heterogeneous Treatment Effects and the Effects of Heterogeneous Treatments With Ensemble Methods,” Political Analysis, 25, 413–434.
   Web of Science ®Google Scholar
• Hainmueller, J., and Hopkins, D. J. (2015), “The Hidden American Immigration Consensus: A Conjoint Analysis of Attitudes Toward Immigrants,” American Journal of Political Science, 59, 529–548.
   Web of Science ®Google Scholar
• Hainmueller, J., Hopkins, D. J., and Yamamoto, T. (2014), “Causal Inference in Conjoint Analysis: Understanding Multidimensional Choices via Stated Preference Experiments,” Political Analysis, 22, 1–30.
   Web of Science ®Google Scholar
• Hastie, T., Tibshirani, R., and Wainwright, M. (2015), Statistical Learning With Sparsity: The Lasso and Generalizations, Boca Raton, FL: CRC Press.
   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
• Huang, J., Breheny, P., and Ma, S. (2012), “A Selective Review of Group Selection in High-Dimensional Models,” Statistical Science, 27, 481–499.
   Web of Science ®Google Scholar
• Huang, J., Ma, S., Xie, H., and Zhang, C.-H. (2009), “A Group Bridge Approach for Variable Selection,” Biometrika, 96, 339–355.
   PubMed Web of Science ®Google Scholar
• Imai, K., and Ratkovic, M. (2013), “Estimating Treatment Effect Heterogeneity in Randomized Program Evaluation,” Annals of Applied Statistics, 7, 443–470.
   Web of Science ®Google Scholar
• Jaccard, J., and Turrisi, R. (2003), Interaction Effects in Multiple Regression, Thousand Oaks, CA: Sage Publications.
   Google Scholar
• Lim, M., and Hastie, T. (2015), “Learning Interactions via Hierarchical Group-Lasso Regularization,” Journal of Computational and Graphical Statistics, 24, 627–654.
   PubMed Web of Science ®Google Scholar
• Lu, J. (2016a), “Covariate Adjustment in Randomization-Based Causal Inference for 2k Factorial Designs,” Statistics & Probability Letters, 119, 11–20.
   Web of Science ®Google Scholar
• ——— (2016b), “On Randomization-Based and Regression-Based Inferences for 2k Factorial Designs,” Statistics & Probability Letters, 112, 72–78.
   Web of Science ®Google Scholar
• Luce, R. D., and Tukey, J. W. (1964), “Simultaneous Conjoint Measurement: A New Type of Fundamental Measurement,” Journal of Mathematical Psychology, 1, 1–27.
   Web of Science ®Google Scholar
• Marshall, D., Bridges, J. F., Hauber, B., Cameron, R., Donnalley, L., Fyie, K., and Johnson, F. R. (2010), “Conjoint Analysis Applications in Health: How are Studies Being Designed and Reported?” The Patient: Patient-Centered Outcomes Research, 3, 249–256.
   Web of Science ®Google Scholar
• Marshall, P., and Bradlow, E. T. (2002), “A Unified Approach to Conjoint Analysis Models,” Journal of the American Statistical Association, 97, 674–682.
   Web of Science ®Google Scholar
• McFadden, D. (1974), “Conditional Logit Analysis of Qualitative Choice Behavior,” in Frontiers in Econometrics, ed. P. Zarembka, New York: Academic Press, pp. 105–142.
   Google Scholar
• Meier, L., Van De Geer, S., and Bühlmann, P. (2008), “The Group Lasso for Logistic Regression,” Journal of the Royal Statistical Society, Series B, 70, 53–71.
   Google Scholar
• Meinshausen, N., and Bühlmann, P. (2010), “Stability Selection,” Journal of the Royal Statistical Society, Series B, 72, 417–473.
   Google Scholar
• Murphy, S. A. (2003), “Optimal Dynamic Treatment Regimes (with discussions),” Journal of the Royal Statistical Society, Series B, 65, 331–366.
   Google Scholar
• Post, J. B., and Bondell, H. D. (2013), “Factor Selection and Structural Identification in the Interaction ANOVA Model,” Biometrics, 69, 70–79.
   PubMed Web of Science ®Google Scholar
• Robins, J. M. (2004), “Optimal Structural Nested Models for Optimal Sequential Decisions,” in Proceedings of the Second Seattle Symposium in Biostatistics: Analysis of Correlated Data, New York: Springer, pp. 189–326.
   Google Scholar
• Rubin, D. B. (1990), Comments on “On the Application of Probability Theory to Agricultural Experiments. Essay on Principles. Section 9” by J. Splawa-Neyman translated from the Polish and edited by D. M. Dabrowska and T. P. Speed, Statistical Science, 5, 472–480.
   Google Scholar
• Scheffe, H. (1959), The Analysis of Variance, New York: Wiley.
   Google Scholar
• VanderWeele, T. (2015), Explanation in Causal Inference: Methods for Mediation and Interaction, Oxford: Oxford University Press.
   Google Scholar
• VanderWeele, T. J., and Knol, M. J. (2014), “A Tutorial on Interaction,” Epidemiologic Methods, 3, 33–72.
   Google Scholar
• Wager, S., and Athey, S. (2017), “Estimation and Inference of Heterogeneous Treatment Effects Using Random Forests,” Journal of the American Statistical Association.
   Web of Science ®Google Scholar
• Wasserman, L., and Roeder, K. (2009), “High Dimensional Variable Selection,” Annals of Statistics, 37, 2178–2201.
   PubMed Web of Science ®Google Scholar
• Wu, C. J., and Hamada, M. S. (2011), Experiments: Planning, Analysis, and Optimization (Vol. 552), New York: Wiley.
   Google Scholar
• Yuan, M., and Lin, Y. (2006), “Model Selection and Estimation in Regression With Grouped Variables,” Journal of the Royal Statistical Society, Series B, 68, 49–67.
   Google Scholar
• Zhao, P., Rocha, G., and Yu, B. (2009), “The Composite Absolute Penalties Family for Grouped and Hierarchical Variable Selection,” The Annals of Statistics, 37, 3468–3497.
   Web of Science ®Google Scholar