Dataset Information

Endogeneity in High Dimensions.

ABSTRACT: Most papers on high-dimensional statistics are based on the assumption that none of the regressors are correlated with the regression error, namely, they are exogenous. Yet, endogeneity can arise incidentally from a large pool of regressors in a high-dimensional regression. This causes the inconsistency of the penalized least-squares method and possible false scientific discoveries. A necessary condition for model selection consistency of a general class of penalized regression methods is given, which allows us to prove formally the inconsistency claim. To cope with the incidental endogeneity, we construct a novel penalized focused generalized method of moments (FGMM) criterion function. The FGMM effectively achieves the dimension reduction and applies the instrumental variable methods. We show that it possesses the oracle property even in the presence of endogenous predictors, and that the solution is also near global minimum under the over-identification assumption. Finally, we also show how the semi-parametric efficiency of estimation can be achieved via a two-step approach.

SUBMITTER: Fan J

PROVIDER: S-EPMC4286899 | biostudies-literature | 2014 Jun

REPOSITORIES: biostudies-literature

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Endogeneity in High Dimensions.

Fan Jianqing J Liao Yuan Y

Annals of statistics 20140601 3

Most papers on high-dimensional statistics are based on the assumption that none of the regressors are correlated with the regression error, namely, they are exogenous. Yet, endogeneity can arise incidentally from a large pool of regressors in a high-dimensional regression. This causes the inconsistency of the penalized least-squares method and possible false scientific discoveries. A necessary condition for model selection consistency of a general class of penalized regression methods is given, ...[more]

PMID: 25580040

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Project description:BackgroundMortality modelling in the critical care paradigm traditionally uses logistic regression, despite the availability of estimators commonly used in alternate disciplines. Little attention has been paid to covariate endogeneity and the status of non-randomized treatment assignment. Using a large registry database, various binary outcome modelling strategies and methods to account for covariate endogeneity were explored.MethodsPatient mortality data was sourced from the Australian & New Zealand Intensive Society Adult Patient Database for 2016. Hospital mortality was modelled using logistic, probit and linear probability (LPM) models with intensive care (ICU) providers as fixed (FE) and random (RE) effects. Model comparison entailed indices of discrimination and calibration, information criteria (AIC and BIC) and binned residual analysis. Suspect covariate and ventilation treatment assignment endogeneity was identified by correlation between predictor variable and hospital mortality error terms, using the Stata™ "eprobit" estimator. Marginal effects were used to demonstrate effect estimate differences between probit and "eprobit" models.ResultsThe cohort comprised 92,693 patients from 124 intensive care units (ICU) in calendar year 2016. Patients mean age was 61.8 (SD 17.5) years, 41.6% were female and APACHE III severity of illness score 54.5(25.6); 43.7% were ventilated. Of the models considered in predicting hospital mortality, logistic regression (with or without ICU FE) and RE logistic regression dominated, more so the latter using information criteria indices. The LPM suffered from many predictions outside the unit [0,1] interval and both poor discrimination and calibration. Error terms of hospital length of stay, an independent risk of death score and ventilation status were correlated with the mortality error term. Marked differences in the ventilation mortality marginal effect was demonstrated between the probit and the "eprobit" models which were scenario dependent. Endogeneity was not demonstrated for the APACHE III score.ConclusionsLogistic regression accounting for provider effects was the preferred estimator for hospital mortality modelling. Endogeneity of covariates and treatment variables may be identified using appropriate modelling, but failure to do so yields problematic effect estimates.

Dataset Information

Endogeneity in High Dimensions.

Publications

Endogeneity in High Dimensions.

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