Multirow doesn't work

Question

I have been trying to use \multirow to merge the cells for x ,y1 and y2 but I can't make it through.I tried to make table using an online table generator online table generator and tried to modify it for my needs but there is something wrong here. Could you help me fix the error?

\documentclass[14pt, a4paper, twoside]{report} % 'twoside' when printing
%\setcounter{secnumdepth}{3}
\usepackage[utf8]{inputenc}             % UTF-8 input
\usepackage[english]{babel}             % Set language to english           
\usepackage{amsmath}            
\usepackage{amsfonts}               
\usepackage{amsthm}                             
\usepackage{geometry}
\usepackage{array}
\newcolumntype{?}{!{\vrule width 1pt}} %Thick vertical line
\newcolumntype{H}{>{\setbox0=\hbox\bgroup}c<{\egroup}@{}}
\newcolumntype{Z}{>{\setbox0=\hbox\bgroup}c<{\egroup}@{\hspace*{-\tabcolsep}}}
\usepackage{booktabs}
\usepackage{multirow}
\usepackage{subcaption} 
\usepackage{tabularx}
\usepackage{floatrow, makecell}%
\makeatother
% Center the table horizontally
\newcolumntype{P}[1]{>{\centering\arraybackslash}p{#1}}
% Center the table vertically
\newcolumntype{M}[1]{>{\centering\arraybackslash}m{#1}}
% Center the table horizontally and vertically
\newcolumntype{C}[1]{>{\centering\arraybackslash}m{#1}}

\usepackage{float}











\begin{document}


\begin{table}[H]\footnotesize\setlength{\tabcolsep}{5pt}\textbf{}
    \centering
    \caption{Total Effect}
    \bgroup
    \def\arraystretch{1.5}%  1 is the default, change whatever you need
    \begin{tabular}{ ? p{0.4em} | p{2em}? p{3.2cm} | p{4.1cm}| p{4.2cm} | p{3.7cm}| } 
        \toprule
        & Si \newline index&Max         & Mean &Median &Eqm  \\
        \Xhline{4\arrayrulewidth}
        
        \multirow{3}{*}{$x$} &$s_{T}$& 
                             $\left[x_{0}\right],\,\newline
                             \left[\left(\text{ all others}\right)\right]$                     &
                             $\left[b\,\,\delta_{2},\,\delta_{1},\,\omega_{2},\,\omega_{1},\,\psi,\,x_{0}\right],\,\newline                                                              \left[\phi,\,\left(a,\,{y_{1}}_{0},\,{y_{2}}_{0}\right)\right]$   &
                             $\left[b,\,\delta_{2},\,\delta_{1},\,\omega_{2},\,\omega_{1},\,\psi,\,\phi\right],\,\newline \left[{y_{1}}_{0},\,a,\,x_{0},\,{y_{2}}_{0}\right]$    &
                            $\left[b,\,\delta_{2},\,\delta_{1},\,\omega_{1},\,\omega_{2},\,\psi,\,\phi\right],\,\newline             \left[x_{0},\,\left({a,\,y_{1}}_{0},\,{y_{2}}_{0}\right)\right]$   \\
   
        \hline
        
                      &$\mu^{\star}$     & 
                        $\left[x_{0}\right],\,\newline
                        \left[\left(\text{ all others}\right)\right] $              &
                        $\left[b,\,x_{0},\,\delta_{1},\,\omega_{1},\,\delta_{2},\,\omega_{2}\right],\,\newline
                         \left[\psi,\,\phi,\,{y_{2}}_{0},\,{y_{1}}_{0},\,a\right]$   &
                        $\left[b,\,x_{0},\,\omega_{1},\,\delta_{1},\,\delta_{2}\omega_{2}\right],\,\newline
                        \left[\psi,\,\phi,\,a,\,{y_{2}}_{0},\,{y_{1}}_{0}\right]$    &
                        $\left[b,\,x_{0},\,\delta_{1},\,\omega_{1},\,\delta_{2}\omega_{2}\right],\,\newline
                        \left[\psi,\,\phi,\,a,\,{y_{2}}_{0},\,{y_{1}}_{0}\right]$   \\
    
        \hline
            
        
                 
                     &$\delta$  &
    $\left[x_{0}\right],\,\newline
    \left[\left(\text{ all others}\right)\right]$&
    $\left[b,\,\delta_{2},\,x_{0},\,\omega_{2},\,\delta_{1},\,\omega_{1}\right],\,\newline\left[\psi,\,a,\,\left({\phi,\,y_{2}}_{0},\,{y_{1}}_{0}\right)\right]$&
    $\left[b,\,\delta_{2},\,\omega_{2},\,\delta_{1},\,\omega_{1},\,\psi\right],\,\newline\left[a,\,{y_{2}}_{0},\,x_{0},\,\phi,\,{y_{1}}_{0}\right]$&
    $\left[b,\,\delta_{2},\,\omega_{2},\,\delta_{1},\,\omega_{1},\,\psi\right],\,\newline\left[a,\,x_{0},\,{y_{2}}_{0},\,\phi,\,{y_{1}}_{0}\right]$   \\
    
    
        \Xhline{4\arrayrulewidth}
        
        
        
 \multirow{3}{*}{$y_{1}$}       &$s_{T}$& 
                             $\left[{y_{1}}_{0}\right],\,\newline\left[\left(\text{ all others}\right)\right]$&
                             $\left[b,\,\delta_{2},\,\delta_{1},\,\psi,\,\omega_{1},\,\omega_{2}\right],\,\newline\left[\phi,\,{y_{1}}_{0},\,x_{0},\,{y_{2}}_{0},\,a\right]$&
                             $\left[b,\,\delta_{2},\,\delta_{1},\,\psi,\,\omega_{1},\,\omega_{2},\,\phi\right],\,\newline\left[x_{0},\,{y_{2}}_{0},\,\left(a,\,{y_{1}}_{0}\right)\right]$&
                             $\left[\omega_{1},\,b,\,\delta_{2},\,\delta_{1},\phi,\,\psi,\,\omega_{2}\right],\,\newline\left[x_{0},\,{y_{2}}_{0},\,a,\,{y_{1}}_{0}\right]$   \\
   
       \hline
       
                            &$\mu^{\star}$& 
                             $\left[{y_{1}}_{0}\right],\,\newline\left[\left(\text{ all others}\right)\right] $              &
                             $\left[b,\,x_{0},\,\phi,\,\omega_{1},\,\delta_{1},\,{y_{1}}_{0}\right],\,\newline
                              \left[\delta_{2},\,\psi,\,\omega_{2},\,{y_{2}}_{0},\,a\right]$   &
 
                             $\left[b,\,x_{0},\,\delta_{2},\,\omega_{1},\,\omega_{2},\,\phi,\,\psi,\,\delta_{1}\right],\,\newline\left[{y_{2}}_{0},\,{y_{1}}_{0},\,a\right]$    &
                             $\left[b,\,\delta_{2},\,\omega_{1},\,x_{0},\,\delta_{1},\,\omega_{2},\,\psi,\,\phi\right],\,\newline\left[a,\,{y_{1}}_{0},\,{y_{2}}_{0}\right]$   \\
 
       \hline
     &$\delta$  & 
                            $\left[{y_{2}}_{0}\right],\,\newline\left[\left(\text{ all others}\right)\right]$&
                            $\left[{y_{1}}_{0},\,b,\,\psi,\,\delta_{2},\,\omega_{2},\,\phi\right],\,\newline\left[x_{0},\,{y_{2}}_{0},\,a,\,\omega_{1},\,\delta_{1}\right]$   &
                            $\left[\omega_{2},\,b,\,\delta_{1},\,\delta_{2},\,\psi,\,\phi,\,\right],\,\newline\left[\left(a,\,\omega_{1},\,x_{0},\,{y_{1}}_{0},\,{y_{2}}_{0}\right)\right]$    &
                            $\left[\left(a,\,\phi,\, \omega_{1},\,x_{0},\,{y_{1}}_{0},\,{y_{2}}_{0},\ \omega_{2}\right)\right],\,\newline\left[b,\,\delta_{2},\,\psi,\,\delta_{1}\right]$   \\
  
  
  
        \Xhline{4\arrayrulewidth}



     \multirow{3}{*}{$y_{2}$}                       &$s_{T}$           & 
                            $\left[\omega_{2},\,b,{y_{2}}_{0},\,x_{0},\,\omega_{1},\,\phi,\,\psi\right],\,\newline
                            \left[\delta_{2},\,{y_{1}}_{0},\,\left(a,\,\delta_{1}\right)\right]$                          & $\left[b,\,\delta_{2},\,\delta_{1},\,\phi,\,\omega_{2},\,\psi,\,\omega_{1}\right],\,\newline
                            \left[x_{0},\,{y_{2}}_{0},\,\left(a,\,{y_{1}}_{0}\right)\right]$                              &
                            $\left[b,\,\delta_{2},\,\delta_{1},\,\omega_{2},\,\phi,\,\psi,\,\omega_{1}\right],\,\newline
                            \left[x_{0},\,{y_{1}}_{0},\,{y_{2}}_{0},\,a\right]$                                           &
                            $\left[\phi,\, \delta_{2},\,\psi,\,b,\,\omega_{1},\,\delta_{1},\,\omega_{2}\right],\,\newline \left[x_{0},\,\left(a,\,{y_{1}}_{0},\,{y_{2}}_{0}\right)\right]$                              \\
 
\hline

                            &$\mu^{\star}$      & 
                            $\left[\omega_{2},\,b,\,\psi,\,\omega_{1},\,\phi,\,x_{0} \right],\,\newline
                            \left[\delta_{2},\,{y_{2}}_{0},\,{y_{1}}_{0},\,\delta_{1},\,a\right]$                               &
  $\left[b,\,\omega_{2},\,\delta_{2},\,\phi,\,x_{0},\,\omega_{1},\,\psi\right],\,\newline
                            \left[\delta_{1},\,{y_{2}}_{0},\,{y_{1}}_{0},\,a\right]$                                            &
                           $\left[b,\,\delta_{2},\,\omega_{2},\,x_{0},\,\phi,\,\psi,\,\omega_{1},\,\delta_{1}\right],\,\newline
                            \left[{y_{2}}_{0},\,a,\,{y_{1}}_{0}\ \right]$                                                        &
                            $\left[\delta_{2},\,\omega_{2},\,\delta_{1},\,b,a,\,x_{0},\,\omega_{1}\right],\,\newline
                            \left[{{y_{1}}_{0},\,\psi,\,\phi,\,y_{2}}_{0}\right]$   \\

\hline

                           &$\delta$&  
                           $\left[{y_{2}}_{0},\,b,\,\omega_{2},\,\omega_{1},\,\phi,\,\psi\right],\,\newline\left[\delta_{2},\,\delta_{1},\,x_{0},\,{y_{1}}_{0},\,a\right]$  &  
                           $\left[{y_{2}}_{0},\,b,\,\delta_{1},\,\omega_{1},\,\psi,\,{y_{1}}_{0},\,a,\,\omega_{1},\,\phi\right],\,\newline\left[\delta_{2},\,x_{0},\,a\right]$   &
                           $\left[b,\,\delta_{1},\,\omega_{1},\,\psi,\,{y_{1}}_{0},\,a,\,{y_{2}}_{0},\,\phi,\, x_{0}\right],\,\newline\left[\delta_{2}\right]$    &
                           $\left[b,\,\delta_{2},\,\omega_{2},\,\omega_{1},\,\psi,\,\phi\right],\,\newline\left[\delta_{1},\,{y_{1}}_{0},\, x_{0},\,{y_{2}}_{0},\,a\right]$   \\

        
        \bottomrule
    \end{tabular} 
    \egroup

The output is as in the picture which is not what I want

Answer 1

Following up on my earlier comments, here's how I'd rewrite the table code. In addition to getting rid of all \left and \right sizing directives and all \, thinspace directives, I'd also get rid of all vertical lines and use fewer, but well-spaced horizontal lines. Finally, I'd use a tabular* environment instead of a tabualar environment, set the \tabcolsep length parameter to 0pt, and let LaTeX figure out the optimal amount of intercolumn whitespace.

\documentclass[10pt, a4paper, twoside]{report}  % '14pt' is not a valid option
\usepackage[utf8]{inputenc}      
\usepackage[english]{babel}              
\usepackage{amsmath,amssymb,amsthm}                             
\usepackage[margin=2.5cm]{geometry} % select margin widths
\usepackage{array,booktabs}
\usepackage{floatrow} % place caption below table by default
\begin{document}

\begin{table}
\footnotesize
\setlength{\tabcolsep}{0pt}  % make LaTeX out amount of intercol. whitespace
\caption{Total Effect}
\begin{tabular*}{\textwidth}{@{\extracolsep{\fill}} 
    c p{2.2em} p{2.9cm} p{3.7cm} p{3.7cm}  p{3.5cm} } 
\toprule
& Si \mbox{index} & Max  & Mean & Median & Eqm \\

\midrule
        
$x$
  & $s_{T}$
  & $[x_0],[(\text{all others})]$ 
  & $[b,\delta_2,\delta_1,\omega_2,\omega_1,\psi,x_0],
    \newline
    [\phi,(a,y_{1_0},y_{2_0})]$   
  & $[b,\delta_2,\delta_1,\omega_2,\omega_1,\psi,\phi],
    \newline
    [y_{1_0},a,x_0,y_{2_0}]$    
  & $[b,\delta_2,\delta_1,\omega_1,\omega_2,\psi,\phi],
    \newline
    [x_0,({a,y_1}_0,y_{2_0})]$ \\
   
\addlinespace
        
  & $\mu^{\star}$     
  & $[x_0],[(\text{all others})] $
  & $[b,x_0,\delta_1,\omega_1,\delta_2,\omega_2],
    \newline
    [\psi,\phi,y_{2_0},y_{1_0},a]$   
  & $[b,x_0,\omega_1,\delta_1,\delta_2\omega_2],
    \newline
    [\psi,\phi,a,y_{2_0},y_{1_0}]$    
  & $[b,x_0,\delta_1,\omega_1,\delta_2\omega_2],
    \newline
    [\psi,\phi,a,y_{2_0},y_{1_0}]$ \\
    
\addlinespace

  & $\delta$  
  & $[x_0],[(\text{all others})]$
  & $[b,\delta_2,x_0,\omega_2,\delta_1,\omega_1],
    \newline
    [\psi,a,({\phi,y_2}_0,y_{1_0})]$
  & $[b,\delta_2,\omega_2,\delta_1,\omega_1,\psi],
    \newline
    [a,y_{2_0},x_0,\phi,y_{1_0}]$
  & $[b,\delta_2,\omega_2,\delta_1,\omega_1,\psi],
    \newline
    [a,x_0,y_{2_0},\phi,y_{1_0}]$ \\
    
\midrule
    
$y_1$
  & $s_{T}$
  & $[y_{1_0}],[(\text{all others})]$
  & $[b,\delta_2,\delta_1,\psi,\omega_1,\omega_2],
    \newline[\phi,y_{1_0},x_0,y_{2_0},a]$
  & $[b,\delta_2,\delta_1,\psi,\omega_1,\omega_2,\phi],
    \newline
    [x_0,y_{2_0},(a,y_{1_0})]$
  & $[\omega_1,b,\delta_2,\delta_1,\phi,\psi,\omega_2],
    \newline
    [x_0,y_{2_0},a,y_{1_0}]$ \\
   
\addlinespace

  & $\mu^{\star}$
  & $[y_{1_0}],[(\text{all others})] $
  & $[b,x_0,\phi,\omega_1,\delta_1,y_{1_0}],
    \newline
    [\delta_2,\psi,\omega_2,y_{2_0},a]$
  & $[b,x_0,\delta_2,\omega_1,\omega_2,\phi,\psi,\delta_1],
    \newline
    [y_{2_0},y_{1_0},a]$ 
  & $[b,\delta_2,\omega_1,x_0,\delta_1,\omega_2,\psi,\phi],
    \newline
    [a,y_{1_0},y_{2_0}]$ \\
 
\addlinespace

  & $\delta$  
  & $[y_{2_0}],[(\text{all others})]$
  & $[y_{1_0},b,\psi,\delta_2,\omega_2,\phi],
    \newline
    [x_0,y_{2_0},a,\omega_1,\delta_1]$   
  & $[\omega_2,b,\delta_1,\delta_2,\psi,\phi,],
    \newline
    [(a,\omega_1,x_0,y_{1_0},y_{2_0})]$    
  & $[(a,\phi, \omega_1,x_0,y_{1_0},y_{2_0},\omega_2)],
    \newline
    [b,\delta_2,\psi,\delta_1]$ \\

\midrule

$y_2$
  & $s_{T}$ 
  & $[\omega_2,b,y_{2_0},x_0,\omega_1,\phi,\psi],
    \newline
    [\delta_2,y_{1_0},(a,\delta_1)]$                          
  & $[b,\delta_2,\delta_1,\phi,\omega_2,\psi,\omega_1],
    \newline
    [x_0,y_{2_0},(a,y_{1_0})]$                                
  & $[b,\delta_2,\delta_1,\omega_2,\phi,\psi,\omega_1],
    \newline
    [x_0,y_{1_0},y_{2_0},a]$                                          
  & $[\phi, \delta_2,\psi,b,\omega_1,\delta_1,\omega_2],
    \newline 
    [x_0,(a,y_{1_0},y_{2_0})]$ \\
 
\addlinespace

  & $\mu^{\star}$
  & $[\omega_2,b,\psi,\omega_1,\phi,x_0 ],
    \newline
    [\delta_2,y_{2_0},y_{1_0},\delta_1,a]$
  & $[b,\omega_2,\delta_2,\phi,x_0,\omega_1,\psi],
    \newline
    [\delta_1,y_{2_0},y_{1_0},a]$ 
  & $[b,\delta_2,\omega_2,x_0,\phi,\psi,\omega_1,\delta_1],
    \newline
    [y_{2_0},a,y_{1_0}]$ 
  & $[\delta_2,\omega_2,\delta_1,b,a,x_0,\omega_1],
    \newline
    [{y_{1_0},\psi,\phi,y_2}_0]$ \\

\addlinespace

  & $\delta$
  & $[y_{2_0},b,\omega_2,\omega_1,\phi,\psi],
    \newline
    [\delta_2,\delta_1,x_0,y_{1_0},a]$  
  & $[y_{2_0},b,\delta_1,\omega_1,\psi,y_{1_0},a,\omega_1,\phi],
    \newline
    [\delta_2,x_0,a]$   
  & $[b,\delta_1,\omega_1,\psi,y_{1_0},a,y_{2_0},\phi, x_0],
    \newline
    [\delta_2]$
  & $[b,\delta_2,\omega_2,\omega_1,\psi,\phi],
    \newline
    [\delta_1,y_{1_0}, x_0,y_{2_0},a]$ \\

\bottomrule
\end{tabular*} 
\end{table}
\end{document}

Answer 2

There's little hope to fit such a table in a reasonable text width: even at \footnotesize I get an overfull by 145pt, which is about a third of the standard text width.

You can rotate the table with sidewaystable.

\documentclass[a4paper, twoside]{report} % 'twoside' when printing
\usepackage{booktabs,array,amsmath,rotating}

\begin{document}


\begin{sidewaystable}[htp]
\centering

\caption{Total Effect}\label{te}

\begin{tabular}{@{} *{2}{>{$}c<{$}} *{4}{>{$}l<{$}} @{}}
\toprule
& \begin{tabular}{@{}c@{}}Si \\ index\end{tabular}
& \multicolumn{1}{c}{Max}
& \multicolumn{1}{c}{Mean}
& \multicolumn{1}{c}{Median}
& \multicolumn{1}{c@{}}{Eqm}
\\
\midrule
x
  & s_{T}
  & [x_{0}],
  & [b\, \delta_{2}, \delta_{1}, \omega_{2}, \omega_{1}, \psi, x_{0}],
  & [b, \delta_{2}, \delta_{1}, \omega_{2}, \omega_{1}, \psi, \phi],
  & [b, \delta_{2}, \delta_{1}, \omega_{1}, \omega_{2}, \psi, \phi],
\\
  &
  & [(\text{all others})]
  & [\phi,(a,{y_{1}}_{0}, {y_{2}}_{0})]
  & [{y_{1}}_{0}, a, x_{0}, {y_{2}}_{0}]
  & [x_{0}, ({a, y_{1}}_{0}, {y_{2}}_{0})]
\\
\addlinespace
  & \mu^{\star}
  & [x_{0}],
  & [b, x_{0}, \delta_{1}, \omega_{1}, \delta_{2}, \omega_{2}],
  & [b, x_{0}, \omega_{1}, \delta_{1}, \delta_{2}\omega_{2}],
  & [b, x_{0}, \delta_{1}, \omega_{1}, \delta_{2}\omega_{2}],
\\
  &
  & [(\text{all others})]
  & [\psi, \phi, {y_{2}}_{0}, {y_{1}}_{0}, a]
  & [\psi, \phi, a, {y_{2}}_{0}, {y_{1}}_{0}]
  & [\psi, \phi, a, {y_{2}}_{0}, {y_{1}}_{0}]
\\
\addlinespace
  & \delta
  & [x_{0}],
  &  [b, \delta_{2}, x_{0}, \omega_{2}, \delta_{1}, \omega_{1}],
  &  [b, \delta_{2}, \omega_{2}, \delta_{1}, \omega_{1}, \psi],
  &  [b, \delta_{2}, \omega_{2}, \delta_{1}, \omega_{1}, \psi],
\\
  &
  & [(\text{all others})]
  & [\psi, a, ({\phi, y_{2}}_{0}, {y_{1}}_{0})]
  & [a, {y_{2}}_{0}, x_{0}, \phi, {y_{1}}_{0}]
  & [a, x_{0}, {y_{2}}_{0}, \phi, {y_{1}}_{0}]
\\
\midrule
y_{1}
  & s_{T}
  & [{y_{1}}_{0}],
  & [b, \delta_{2}, \delta_{1}, \psi, \omega_{1}, \omega_{2}],
  & [b, \delta_{2}, \delta_{1}, \psi, \omega_{1}, \omega_{2}, \phi],
  & [\omega_{1}, b, \delta_{2}, \delta_{1},\phi, \psi, \omega_{2}],
\\
  &
  & [(\text{all others})]
  & [\phi, {y_{1}}_{0}, x_{0}, {y_{2}}_{0}, a]
  & [x_{0}, {y_{2}}_{0}, (a, {y_{1}}_{0})]
  & [x_{0}, {y_{2}}_{0}, a, {y_{1}}_{0}]
\\
\addlinespace
  & \mu^{\star}
  & [{y_{1}}_{0}],
  & [b, x_{0}, \phi, \omega_{1}, \delta_{1}, {y_{1}}_{0}],
  & [b, x_{0}, \delta_{2}, \omega_{1}, \omega_{2}, \phi, \psi, \delta_{1}],
  & [b, \delta_{2}, \omega_{1}, x_{0}, \delta_{1}, \omega_{2}, \psi, \phi],
\\
  &
  & [(\text{all others})]
  & [\delta_{2}, \psi, \omega_{2}, {y_{2}}_{0}, a]
  & [{y_{2}}_{0}, {y_{1}}_{0}, a]
  & [a, {y_{1}}_{0}, {y_{2}}_{0}]
\\
\addlinespace
  & \delta
  & [{y_{2}}_{0}],
  & [{y_{1}}_{0}, b, \psi, \delta_{2}, \omega_{2}, \phi],
  & [\omega_{2}, b, \delta_{1}, \delta_{2}, \psi, \phi, ],
  & [(a, \phi,  \omega_{1}, x_{0}, {y_{1}}_{0}, {y_{2}}_{0},\ \omega_{2})],
\\
  &
  & [(\text{all others})]
  & [x_{0}, {y_{2}}_{0}, a, \omega_{1}, \delta_{1}]
  & [(a, \omega_{1}, x_{0}, {y_{1}}_{0}, {y_{2}}_{0})]
  & [b, \delta_{2}, \psi, \delta_{1}]
\\
\midrule
y_{2}
  & s_{T}
  & [\omega_{2}, b,{y_{2}}_{0}, x_{0}, \omega_{1}, \phi, \psi],
  & [b, \delta_{2}, \delta_{1}, \phi, \omega_{2}, \psi, \omega_{1}],
  & [b, \delta_{2}, \delta_{1}, \omega_{2}, \phi, \psi, \omega_{1}],
  & [\phi,  \delta_{2}, \psi, b, \omega_{1}, \delta_{1}, \omega_{2}],
\\
  &
  & [\delta_{2}, {y_{1}}_{0}, (a, \delta_{1})]
  & [x_{0}, {y_{2}}_{0}, (a, {y_{1}}_{0})]
  & [x_{0}, {y_{1}}_{0}, {y_{2}}_{0}, a]
  & [x_{0}, (a, {y_{1}}_{0}, {y_{2}}_{0})]
\\
\addlinespace
  & \mu^{\star}
  & [\omega_{2}, b, \psi, \omega_{1}, \phi, x_{0} ],
  & [b, \omega_{2}, \delta_{2}, \phi, x_{0}, \omega_{1}, \psi],
  & [b, \delta_{2}, \omega_{2}, x_{0}, \phi, \psi, \omega_{1}, \delta_{1}],
  & [\delta_{2}, \omega_{2}, \delta_{1}, b,a, x_{0}, \omega_{1}],
\\
  &
  & [\delta_{2}, {y_{2}}_{0}, {y_{1}}_{0}, \delta_{1}, a]
  & [\delta_{1}, {y_{2}}_{0}, {y_{1}}_{0}, a]
  & [{y_{2}}_{0}, a, {y_{1}}_{0}]
  & [{{y_{1}}_{0}, \psi, \phi, y_{2}}_{0}]
\\
\addlinespace
  & \delta
  & [{y_{2}}_{0}, b, \omega_{2}, \omega_{1}, \phi, \psi],
  & [{y_{2}}_{0}, b, \delta_{1}, \omega_{1}, \psi, {y_{1}}_{0}, a, \omega_{1}, \phi],
  & [b, \delta_{1}, \omega_{1}, \psi, {y_{1}}_{0}, a, {y_{2}}_{0}, \phi,  x_{0}],
  & [b, \delta_{2}, \omega_{2}, \omega_{1}, \psi, \phi],
\\
  &
  & [\delta_{2}, \delta_{1}, x_{0}, {y_{1}}_{0}, a]
  & [\delta_{2}, x_{0}, a]
  & [\delta_{2}]
  & [\delta_{1}, {y_{1}}_{0},  x_{0}, {y_{2}}_{0}, a]
\\
\bottomrule
\end{tabular} 

\end{sidewaystable}

\end{document}

I have avoided all \newline instructions and also the heavy rules. There is no need for \multirow, which might even make the table ambiguous.

Answer 3

It's unclear exactly what changes you want, but I think you need to look into \cline (hint: write \cline{2-6} instead of \hline on lines where you don't want a line through the left column), and replace \toprule and \bottomrule with \hline because they're screwing up the table's spacing at bottom and top