How to change the tablenotes using threeparttable

Question

See below for the code I use and the table it generates. How can I change the text below the table (i.e. the notes), so it is not strictly below the table, but stretched out more? It can be two lines max, while now it takes 4 lines because of the centering below the table...

    \begin{table}
       \centering
        \begin{threeparttable}
        \caption{standardised factor loadings for the 5-item models for Motivation}
        \label{cross5items}
            \begin{tabular}{c c c c c}
            \toprule 
            & time 0  & time 1 & time 3 & time 4 \\
            \midrule
            $\lambda_1$     & 0.678 & 0.692 & 0.688 & 0.685  \\
            $\lambda_3$     & 0.499 & 0.516 & 0.610 & 0.573     \\
            $\lambda_4$     & 0.730 & 0.775 & 0.697 & 0.744     \\
            $\lambda_5$     & 0.442 & 0.510 & 0.506 & 0.655       \\
            $\lambda_6$     & 0.876 & 0.781 & 0.856 & 0.828\\
            \bottomrule  
            \end{tabular} 
                \begin{tablenotes}
                \small
            \item   $\lambda_k$ is the standardised factor loading of item $k$, with the standard error in brackets. All factor loadings were highly significant: $p_{MLR}$ and $p_{MLE}$ <.001.

                \end{tablenotes}

        \end{threeparttable}
    \end{table}

Answer 1

If you don't need (or want!) the legend below the tabular environment to be confined to the width of the tabular, you may do so either by placing the legend outside of the threeparttable environment, or by getting rid of the threeparttable machinery entirely.

\documentclass{article}
\usepackage{amsmath,booktabs,ragged2e}
\usepackage[flushleft]{threeparttable}
\begin{document}

%% first, the original table
\begin{table}
\centering
\begin{threeparttable}[ht]
\caption{with \texttt{threeparttable}}
\label{tab:a}
\begin{tabular}{@{} ccccc @{}}
    \toprule 
    & time 0  & time 1 & time 3 & time 4 \\
    \midrule
    $\lambda_1$ & 0.678 & 0.692 & 0.688 & 0.685  \\
    $\lambda_3$ & 0.499 & 0.516 & 0.610 & 0.573  \\
    $\lambda_4$ & 0.730 & 0.775 & 0.697 & 0.744  \\
    $\lambda_5$ & 0.442 & 0.510 & 0.506 & 0.655  \\
    $\lambda_6$ & 0.876 & 0.781 & 0.856 & 0.828  \\
    \bottomrule  
\end{tabular} 
\begin{tablenotes}
\small
\item[]$\lambda_k$ is the standardised factor loading of item $k$, 
with the standard error in brackets. All factor loadings were highly 
significant: $p_{\textrm{MLR}}$ and $p_{\textrm{MLE}} <.001$.
\end{tablenotes}
\end{threeparttable}
\end{table}

%% next, a solution without a 'tablenotes' environment.
\begin{table}
\centering
\begin{threeparttable}[ht]
\caption{without \texttt{tablenotes}}
\label{tab:b}
\begin{tabular}{@{} ccccc @{}}
    \toprule 
    & time 0  & time 1 & time 3 & time 4 \\
    \midrule
    $\lambda_1$ & 0.678 & 0.692 & 0.688 & 0.685  \\
    $\lambda_3$ & 0.499 & 0.516 & 0.610 & 0.573  \\
    $\lambda_4$ & 0.730 & 0.775 & 0.697 & 0.744  \\
    $\lambda_5$ & 0.442 & 0.510 & 0.506 & 0.655  \\
    $\lambda_6$ & 0.876 & 0.781 & 0.856 & 0.828  \\
    \bottomrule  
\end{tabular} 
\end{threeparttable}% important to leave a blank line next:

\smallskip
\justifying
\small
\noindent
$\lambda_k$ is the standardised factor loading of item $k$, with the 
standard error in brackets. All factor loadings were highly significant: 
$p_{\textrm{MLR}}$ and $p_{\textrm{MLE}} <.001$.
\end{table}

%% finally, a solution that doesn't employ any part of the `threeparttable` machinery
\begin{table}[h]
\centering
% \smallskip % optional
\caption{without \texttt{threeparttable}}
\label{tab:c}
\begin{tabular}{@{} ccccc @{}}
    \toprule 
    & time 0  & time 1 & time 3 & time 4 \\
    \midrule
    $\lambda_1$ & 0.678 & 0.692 & 0.688 & 0.685  \\
    $\lambda_3$ & 0.499 & 0.516 & 0.610 & 0.573  \\
    $\lambda_4$ & 0.730 & 0.775 & 0.697 & 0.744  \\
    $\lambda_5$ & 0.442 & 0.510 & 0.506 & 0.655  \\
    $\lambda_6$ & 0.876 & 0.781 & 0.856 & 0.828  \\
    \bottomrule  
\end{tabular} 

\smallskip
\justifying
\small
\noindent
$\lambda_k$ is the standardised factor loading of item $k$, with the 
standard error in brackets. All factor loadings were highly significant: 
$p_{\textrm{MLR}}$ and $p_{\textrm{MLE}}<.001$.

\end{table}
\end{document}