Measurement Errors in Semiparametric Generalized Regression Models

TL;DR

This paper introduces a novel semiparametric method to correct measurement errors in generalized regression models, applicable across various distributions and link functions, improving estimation accuracy.

Contribution

It presents the first flexible approach for measurement error correction in a broad class of generalized linear models, not limited to splines.

Findings

Method performs well in simulations across diverse scenarios

Can handle various basis functions and distributions

Reduces bias caused by measurement errors

Abstract

Regression models that ignore measurement error in predictors may produce highly biased estimates leading to erroneous inferences. It is well known that it is extremely difficult to take measurement error into account in Gaussian nonparametric regression. This problem becomes tremendously more difficult when considering other families such as logistic regression, Poisson and negative-binomial. For the first time, we present a method aiming to correct for measurement error when estimating regression functions flexibly covering virtually all distributions and link functions regularly considered in generalized linear models. This approach depends on approximating the first and the second moment of the response after integrating out the true unobserved predictors in a semiparametric generalized linear model. Unlike previous methods, this method is not restricted to truncated splines and can utilize various basis functions. Through extensive simulation studies, we study the performance of our method under many scenarios.