Partially linear model estimation for missing response data

This paper will discuss the estimation of a partially linear (semiparametric) model with missing responses using the normal approach. An estimator class is defined which includes special cases, namely the partially linear imputation estimator, the marginal mean estimator and the trend score weighted estimator. The estimator class is asymptotically normal. The three special estimators have the same asymptotic variance. Based on the above conditions, the mean F will be estimated, say θ. The three special estimators above will be used to estimate the mean F, namely in the form of point estimates and confidence intervals with some missing responses using the normal approach method.

Double/Debiased Machine Learning for Logistic Partially Linear Model

We propose double/debiased machine learning approaches to infer parametric component of a logistic partially linear model. Our framework is based on a Neyman orthogonal score equation consisting two nuisance models for nonparametric component of the logistic model and conditional mean of the exposure with among the control group. To estimate the nuisance models, we separately consider the use of high dimensional (HD) sparse regression and (nonparametric) machine learning (ML) methods. In the HD case, we derive certain moment equations to calibrate the first order bias of the nuisance models, which preserves model double robustness property. In the ML case, we handle the non-linearity of the logit link through a novel and easy-to-implement “full model refitting” procedure. We evaluate our methods through simulation and apply them in assessing the effect of the emergency contraceptive (EC) pill on early gestation and new births based on a 2008 policy reform in Chile.

Approximate Bayesian inference for joint linear and partially linear modeling of longitudinal zero-inflated count and time to event data

Joint modeling of zero-inflated count and time-to-event data is usually performed by applying the shared random effect model. This kind of joint modeling can be considered as a latent Gaussian model. In this paper, the approach of integrated nested Laplace approximation (INLA) is used to perform approximate Bayesian approach for the joint modeling. We propose a zero-inflated hurdle model under Poisson or negative binomial distributional assumption as sub-model for count data. Also, a Weibull model is used as survival time sub-model. In addition to the usual joint linear model, a joint partially linear model is also considered to take into account the non-linear effect of time on the longitudinal count response. The performance of the method is investigated using some simulation studies and its achievement is compared with the usual approach via the Bayesian paradigm of Monte Carlo Markov Chain (MCMC). Also, we apply the proposed method to analyze two real data sets. The first one is the data about a longitudinal study of pregnancy and the second one is a data set obtained of a HIV study.