An adaptive linear regression approach for modeling heavy-tailed longitudinal data

Abstract

Longitudinal data, in which repeated responses of each individual are collected at different times or under different conditions, are not uncommon in many fields. It is common to assume that the responses of each individual are normally distributed. This assumption may be violated in practice for many reasons. These include outliers, contaminated data, and heavy-tailed distributions. Hence, there is a need for techniques that capable of dealing with such non-normal responses. The adaptive linear regression estimator (ALR) proposed mainly to handle non-normal cross-sectional data. It is a linear combination of ordinary least squares method (OLS) and least absolute deviations method (LAD). In this article the adaptive linear regression estimator (ALR) is modified and developed to deal with heavy-tailed longitudinal data. The asymptotic properties of modified adaptive linear regression estimator (MALR) are also derived. The MALR estimator is efficient for both light-tailed and heavy-tailed distributions. Simulation studies are conducted to evaluate the modified approach. Also, the new approach is applied to real data that represent measurements of the amount of pain experienced during labor.