Modeling Qualitative Outcomes by Supplementing Participant Data with General Population Data: A Calibrated Qualitative Response Estimation Approach

Erard, Brian (2017): Modeling Qualitative Outcomes by Supplementing Participant Data with General Population Data: A Calibrated Qualitative Response Estimation Approach.

Abstract

Often providers of a program or service have detailed information about their clients, but only limited information about potential clients. Likewise, ecologists frequently have extensive knowledge regarding habitats where a given animal or plant species is known to be present, but they lack comparable information on habitats where they are certain not to be present. In epidemiology, comprehensive information is routinely collected about patients who have been diagnosed with a given disease; however, commensurate information may not be available for individuals who are known to be free of the disease. While it may be highly beneficial to learn about the determinants of participation (in a program or service) or presence (in a habitat or of a disease), the lack of a comparable sample of observations on subjects that are not participants (or that are non-present) precludes the application of standard qualitative response models, such as logit or probit. In this paper, we examine how one can overcome this challenge by combining a participant-only sample with a supplementary sample of covariate values from the general population. We derive some new estimators of conditional response probabilities based on this sampling scheme by exploiting the parameter restrictions implied by the relationship between the marginal and conditional response probabilities in the supplementary sample. When the prevalence rate in the population is known, we demonstrate that the choice of estimator is especially important when this rate is relatively high. Our simulation results indicate that some of our new estimators for this case rival the small sample performance of the best existing estimators. Our estimators for the case where the prevalence rate is unknown also perform comparably to the best existing estimator for this situation in our simulations. In contrast to most existing estimators, our new estimators are straightforward to apply to exogenously stratified samples (such as when the supplementary sample is drawn from a Census survey), even when the underlying stratification criteria are not available. Our new estimators also readily generalize to accommodate situations with polychotomous outcomes.

• Item Type: MPRA Paper
• Language: English
• Keywords: Qualitative response, Probit, Logit, Case Control Sampling, Use Control Sampling, Presence Pseudo-Absence Sampling, Contaminated Controls, Supplementary Sampling, Prevalence, Take-Up, Habitat Selection
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C18 - Methodological Issues: General; C - Mathematical and Quantitative Methods > C4 - Econometric and Statistical Methods: Special Topics; C - Mathematical and Quantitative Methods > C5 - Econometric Modeling > C51 - Model Construction and Estimation

References

Brent, R.P. 1973. Algorithms for Minimization Without Derivatives, Englewood Cliffs, NJ: Prentice-Hall.

Breslow, N.E. 1996. Statistics in Epidemiology: The Case-Control Study, Journal of the American Statistical Association, 91(433), 14-28.

Burden, B.C., D.T. Canon, K.R. Mayer, and D.P. Moynihan. 2014. Election Laws, Mobilization, and Turnout: The Unanticipated Consequences of Election Reform, American Journal of Political Science, 58(1), 95-109.

Cosslett, S.R. 1981. Efficient Estimation of Discrete Choice Models. In Structural Analysis of Discrete Data with Econometric Applications, ed. C. Manski and D. McFadden, Cambridge: MIT Press, 51-111.

Erard, B., J. Guyton, P. Langetieg, M. Payne, and A. Plumley. 2016. What Drives Income Tax Filing Compliance? IRS Research Bulletin, Publication 1500, Washington, DC: Internal Revenue Service, 32-37.

Cosslett, S.R. 1981. Efficient Estimation of Discrete Choice Models, in Structural Analysis of Discrete Data with Econometric Applications, ed. C. Manski and D. McFadden, Cambridge: MIT Press, 51-111.

Imbens, G.W. 1996. An Efficient Method of Moments Estimator for Discrete Choice Models with Choice –Based Sampling. Econometrica, 60(5), 1187-1214.

Keating, K.A. and S. Cherry 2004. Use and Interpretation of Logistic Regression in Habitat Selection Studies. Journal of Wildlife Management, 68(4), 774-789.

Lancaster, T. and G. Imbens. 1996. Case Controlled Studies with Contaminated Controls. Journal of Econometrics, 71, 145-160.

Lele, S.R. 2009. A New Method for Estimation of Resource Selection Probability Function. Journal of Wildlife Management, 73(1), 122-127.

Lele, S.R. and J.L. Keim 2006. Weighted Distributions and Estimation of Resource Selection Probability Functions. Ecology, 87(12), 3021-3028.

Manski, C.F. and D. McFadden 1981. Alternative Estimators and Sample Designs for Discrete Choice Analysis, in Structural Analysis of Discrete Data with Econometric Applications, ed. C. Manski and D. McFadden, Cambridge: MIT Press, 2-49.

Phillips, S.J. and J. Elith 2013. On Estimating Probability of Presence from Use-Availability or Presence-Background Data. Ecology, 94(6), 1409-1419.

Rosenman, R., S. Goates, and L. Hill 2012. Participation in Universal Prevention Programs. Applied Economics, 44(2), 219-28.

Royle, J.A., R.B. Chandler, C. Yackulic, and J.D. Nichols. 2012. Likelihood Analysis of Species Occurrence Probability from Presence-Only Data for Modelling Species Distributions. Methods in Ecology and Evolution, 3, 545-554.

Solymos, P. and S.R. Lele. 2016. Revisiting Resource Section Probability Functions and Single-Visit Methods: Clarifications and Extensions. Methods in Ecology and Evolution, 7(2), 196-205.

Steinberg, D. and N.S. Cardell 1992. Estimating Logistic Regression Models When the Dependent Variable Has No Variance. Communication in Statistics –Theory and Methods, 21(2), 423-450.

Ward, G., T. Hastie, S. Barry, J. Elith, and J.R. Leathwick 2009. Presence-Only Data and the EM Algorithm. Biometrics, 65, 554-563.