Covariate Measurement Error in a Non-Linear Model for Longitudinal Data

Rosa C. S. Oliveira¹

1. Matemática, Faculdade de Ciências, Porto, Portugal.

Correspondence should be addressed to: rosita21@gmail.com.

Section:Research Paper, Product Type: Journal-Paper
Vol.7 , Issue.2 , pp.17-33, Apr-2020

Online published on Apr 30, 2020

Copyright © Rosa C. S. Oliveira . This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 

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Abstract :
In this paper, we study nonlinear generalized regression models for the analysis of longitudinal data. We indicate a two-stage approach that, in the first stage models a linear model to the longitudinal data to estimate the random effect that characterizes the trajectory for each individual and in the second stage uses the estimated intercept and slope as predictors for the covariates used in a probit model. We show that the straight use of the estimates in the probit model produces biased estimates of their outcome. We show how to adapt a Regression Calibration and a Pseudo-Likelihood approach to this context and compare these approaches with a naive analysis where the estimation error is ignored. Regression Calibration and Pseudo-Likelihood methods seem to be the best choice as they perform well, even for small sample size, if data is not very noisy. It is fair to say, mainly, that the Regression Calibration and Pseudo-Likelihood method perform equally well, nonetheless, Regression Calibration seems to perform a bit better. Nevertheless, naive approach has smaller Mean Squared Error, has a great absolute bias. Regression Calibration seems to be the best. Our study indicates that correcting for measurement errors instead of falsely assume that errors are not present will produce less bias than ignoring exposure measurement error in the analysis.

Key-Words / Index Term :
measurement error, errors-in-variables, general nonlinear model, longitudinal data

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