Propensity score-based diagnostics for categorical response regression models.
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.
Department of Biostatistics, University of Michigan, Ann Arbor, MI, 48109, USA.
Philip S
PS
Boonstra
Department of Biostatistics, University of Michigan, Ann Arbor, MI, 48109, USA.
Irina
I
Bondarenko
Department of Epidemiology, University of Michigan, Ann Arbor, MI, 48109, USA.
Sung Kyun
SK
Park
VA Normative Aging Study, Veterans Affairs Boston Healthcare System, Boston, MA, USA and Department of Epidemiology, Boston University School of Medicine and School of Public Health, Boston, MA, USA.
Pantel S
PS
Vokonas
Department of Biostatistics, University of Michigan, Ann Arbor, MI, 48109, USA.
Bhramar
B
Mukherjee
D000368:Aged; D000369:Aged, 80 and over; D000375:Aging / Q000502:physiology; D001786:Blood Glucose / Q000032:analysis; D001900:Boston; D002097:C-Reactive Protein / Q000032:analysis; D015984:Causality; D003198:Computer Simulation; D005260:Female; D006801:Humans; D007854:Lead / Q000032:analysis; D007958:Leukocyte Count; D016015:Logistic Models; D008297:Male; D008875:Middle Aged; D010300:Parkinson Disease / Q000209:etiology; D057216:Propensity Score; D011446:Prospective Studies; D012189:Retrospective Studies; D013977:Tibia / Q000737:chemistry
D001786:Blood Glucose; D007854:Lead; D002097:C-Reactive Protein
balancing score; multinomial logistic; proportional odds; residual diagnostic; score test