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Propensity score‐based diagnostics for categorical response regression models
Author(s) -
Boonstra Philip S.,
Bondarenko Irina,
Park Sung Kyun,
Vokonas Pantel S.,
Mukherjee Bhramar
Publication year - 2013
Publication title -
statistics in medicine
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.996
H-Index - 183
eISSN - 1097-0258
pISSN - 0277-6715
DOI - 10.1002/sim.5940
Subject(s) - categorical variable , statistics , logistic regression , causal inference , goodness of fit , econometrics , inference , computer science , propensity score matching , mathematics , artificial intelligence
For binary or categorical response models, most goodness‐of‐fit statistics are based on the notion of partitioning the subjects into groups or regions and comparing the observed and predicted responses in these regions by a suitable chi‐squared distribution. Existing strategies create this partition based on the predicted response probabilities, or propensity scores, from the fitted model. In this paper, we follow a retrospective approach, borrowing the notion of balancing scores used in causal inference to inspect the conditional distribution of the predictors, given the propensity scores, in each category of the response to assess model adequacy. We can use this diagnostic under both prospective and retrospective sampling designs, and it may ascertain general forms of misspecification. We first present simple graphical and numerical summaries that can be used in a binary logistic model. We then generalize the tools to propose model diagnostics for the proportional odds model. We illustrate the methods with simulation studies and two data examples: (i) a case‐control study of the association between cumulative lead exposure and Parkinson's disease in the Boston, Massachusetts, area and (ii) and a cohort study of biomarkers possibly associated with diabetes, from the VA Normative Aging Study. Copyright © 2013 John Wiley & Sons, Ltd.