\documentclass[10pt]{article}

\usepackage{fullpage}
\usepackage{setspace}
\usepackage{parskip}
\usepackage{titlesec}
\usepackage[section]{placeins}
\usepackage{xcolor}
\usepackage{breakcites}
\usepackage{lineno}
\usepackage{hyphenat}





\PassOptionsToPackage{hyphens}{url}
\usepackage[colorlinks = true,
            linkcolor = blue,
            urlcolor  = blue,
            citecolor = blue,
            anchorcolor = blue]{hyperref}
\usepackage{etoolbox}
\makeatletter
\patchcmd\@combinedblfloats{\box\@outputbox}{\unvbox\@outputbox}{}{%
  \errmessage{\noexpand\@combinedblfloats could not be patched}%
}%
\makeatother


\usepackage{natbib}




\renewenvironment{abstract}
  {{\bfseries\noindent{\abstractname}\par\nobreak}\footnotesize}
  {\bigskip}

\titlespacing{\section}{0pt}{*3}{*1}
\titlespacing{\subsection}{0pt}{*2}{*0.5}
\titlespacing{\subsubsection}{0pt}{*1.5}{0pt}


\usepackage{authblk}


\usepackage{graphicx}
\usepackage[space]{grffile}
\usepackage{latexsym}
\usepackage{textcomp}
\usepackage{longtable}
\usepackage{tabulary}
\usepackage{booktabs,array,multirow}
\usepackage{amsfonts,amsmath,amssymb}
\providecommand\citet{\cite}
\providecommand\citep{\cite}
\providecommand\citealt{\cite}
% You can conditionalize code for latexml or normal latex using this.
\newif\iflatexml\latexmlfalse
\providecommand{\tightlist}{\setlength{\itemsep}{0pt}\setlength{\parskip}{0pt}}%

\AtBeginDocument{\DeclareGraphicsExtensions{.pdf,.PDF,.eps,.EPS,.png,.PNG,.tif,.TIF,.jpg,.JPG,.jpeg,.JPEG}}

\usepackage[utf8]{inputenc}
\usepackage[greek,english]{babel}



\usepackage{float}








\begin{document}

\title{Dependent variable selection in phylogenetic generalized least squares
regression analysis under Pagel's lambda model}



\author[1]{Zheng-Lin Chen}%
\author[1]{Hong-Ji  Guo}%
\author[1]{Deng-Ke Niu}%
\affil[1]{Beijing Normal University}%


\vspace{-1em}



  
  \date{May 15, 2024}


\begingroup
\let\center\flushleft
\let\endcenter\endflushleft
\maketitle
\endgroup





\selectlanguage{english}
\begin{abstract}
Phylogenetic generalized least squares (PGLS) regression is widely used
to detect evolutionary correlations. In contrast to the equal treatment
of analyzed traits in conventional correlation methods such as Pearson
and Spearman's rank tests, we must designate one trait as the
independent variable and the other as the dependent variable. However,
in our PGLS regression analyses (using Pagel's \selectlanguage{greek}\emph{λ} \selectlanguage{english}model) of both
empirical and simulated datasets, switching independent and dependent
variables yielded many conflicting results. A serious problem with PGLS
regression that has not been noticed before is that selecting an
inappropriate trait as the dependent variable will often result in an
error. To assess correlations in simulated data, we established a gold
standard by analyzing changes in traits along phylogenetic branches.
Next, we tested seven potential criteria for dependent variable
selection: log-likelihood, Akaike information criterion,
\emph{R}\textsuperscript{2}, \emph{p}-value, Pagel's \selectlanguage{greek}\emph{λ}, \selectlanguage{english}Blomberg
et al.'s \emph{K}, and the estimated \selectlanguage{greek}\emph{λ} \selectlanguage{english}in Pagel's \selectlanguage{greek}\emph{λ} \selectlanguage{english}model.
We determined that the last three criteria performed equally well in
selecting the dependent variable and were superior to the other four.
For practicality, we suggest using the trait with a higher \selectlanguage{greek}\emph{λ} \selectlanguage{english}or
\emph{K} value as the dependent variable in future PGLS regressions. In
analyzing the evolutionary relationship between two traits, we should
designate the trait with a stronger phylogenetic signal as the dependent
variable even if it could logically assume the cause in the
relationship.%
\end{abstract}%



\sloppy


\textbf{Hosted file}

\verb`0616 response variable.docx`  available at \url{https://authorea.com/users/629715/articles/649826-dependent-variable-selection-in-phylogenetic-generalized-least-squares-regression-analysis-under-pagel-s-lambda-model}

\selectlanguage{english}
\FloatBarrier
\end{document}

