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\begin{document}

\title{A Mixed Effects Changepoint Quantile Regression Model for Longitudinal
Data}



\author[1]{Ahmed Gad}%
\author[2]{Wafaa I. M. Ibrahim}%
\author[2]{Abdelnaser S. Abdrabou}%
\affil[1]{Cairo University}%
\affil[2]{Affiliation not available}%


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  \date{May 27, 2024}


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\begin{abstract}
The longitudinal individual response profiles could exhibit a mixture of
two or more phases of increase or decrease in trend throughout the
follow up period, with one or more unknown transition points usually
referred to as breakpoints or change points. The existence of such
unknown point disturbs the sample characteristics, so the detection and
estimation of these points is crucial. Most of the proposed statistical
methods in literature, for detecting and estimating change points,
assume distributional assumption that may not hold. A good alternative
in this case is to use a robust approach which is the quantile
regression model. There are trials in the literature to deal with
quantile regression models with a change point. These trials ignore the
within subject dependence of longitudinal data. In this paper we propose
a mixed effect quantile regression model with a change point to account
for dependence structure in the longitudinal data. Fixed effect
parameters, in addition to the location of the change point, are
estimated using profile estimation method. The stochastic approximation
EM algorithm is proposed to estimate the fixed effect parameters
exploiting the link between asymptotic Laplace distribution and the
quantile regression. In addition, the location of the change point is
estimated using the usual optimization methods. A simulation study shows
that the proposed estimation and inferential procedures perform
reasonably well in finite samples. The practical use of the proposed
model is illustrated using a COVID-19 data. The data focus on the effect
of global economic and health factors on the monthly death rate due to
COVID-19 during from the 1st of April 2020 till the 31st of April 2021.%
\end{abstract}%



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