Double/Debiased Machine Learning for Logistic Partially Linear Model

09/30/2020
by   Molei Liu, et al.
0

We propose double/debiased machine learning approaches to infer (at the parametric rate) the parametric component of a logistic partially linear model with the binary response following a conditional logistic model of a low dimensional linear parametric function of some key (exposure) covariates and a nonparametric function adjusting for the confounding effect of other covariates. We consider a Neyman orthogonal (doubly robust) score equation consisting of two nuisance functions: nonparametric component in the logistic model and conditional mean of the exposure on the other covariates and with the response fixed. To estimate the nuisance models, we separately consider the use of high dimensional (HD) sparse parametric models and more general (typically nonparametric) machine learning (ML) methods. In the HD case, we derive certain moment equations to calibrate the first-order bias of the nuisance models and grant our method a model double robustness property in the sense that our estimator achieves the desirable rate when at least one of the nuisance models is correctly specified and both of them are ultra-sparse. In the ML case, the non-linearity of the logit link makes it substantially harder than the partially linear setting to use an arbitrary conditional mean learning algorithm to estimate the nuisance component of the logistic model. We handle this obstacle through a novel full model refitting procedure that is easy-to-implement and facilitates the use of nonparametric ML algorithms in our framework. Our ML estimator is rate doubly robust in the same sense as Chernozhukov et al. (2018a). We evaluate our methods through simulation studies and apply them in assessing the effect of emergency contraceptive (EC) pill on early gestation foetal with a policy reform in Chile in 2008 (Bentancor and Clarke, 2017).

READ FULL TEXT

page 1

page 2

page 3

page 4

research
08/28/2020

A Note on Debiased/Double Machine Learning Logistic Partially Linear Model

It is of particular interests in many application fields to draw doubly ...
research
01/26/2019

On doubly robust estimation for logistic partially linear models

Consider a logistic partially linear model, in which the logit of the me...
research
10/06/2020

Doubly Robust Covariate Shift Regression with Semi-nonparametric Nuisance Models

Importance weighting is naturally used to adjust for covariate shift. Ho...
research
08/31/2021

Double Machine Learning for Partially Linear Mixed-Effects Models with Repeated Measurements

Traditionally, spline or kernel approaches in combination with parametri...
research
12/17/2021

Doubly Robust Estimation of the Hazard Difference for Competing Risks Data

We consider the conditional treatment effect for competing risks data in...
research
06/02/2022

Coordinated Double Machine Learning

Double machine learning is a statistical method for leveraging complex b...
research
01/29/2021

Regularizing Double Machine Learning in Partially Linear Endogenous Models

We estimate the linear coefficient in a partially linear model with conf...

Please sign up or login with your details

Forgot password? Click here to reset