  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).
