Get ref to show full, cumulative reference to nested item

Question

I'm using enumitem and trying to label items with only their current level, but reference them with their full "absolute" value. Here's a sample document:

\documentclass[letterpaper]{article}
\usepackage{enumitem}
\newlist{parin}{enumerate}{4}
\setlist[parin,1]{label=\arabic*.,ref=\arabic*,leftmargin=*}
\setlist[parin,2]{label=(\alph*),ref=\theenumi\alph*,leftmargin=*}
\setlist[parin,3]{label=(\arabic*),ref=\theenumii\arabic*,leftmargin=*}
\setlist[parin,4]{label=(\roman*),ref=\theenumiii\roman*,leftmargin=*}
\begin{document}
\begin{parin}
\item Foo
\label{foo}
\begin{parin}
\item Bar
\label{bar}
\begin{parin}
\item Baz
\label{baz}
\begin{parin}
\item Label Me
\label{labelme}
\end{parin}
\end{parin}
\end{parin}
\end{parin}
\ref{foo}
\ref{bar}
\ref{baz}
\ref{labelme}
\end{document}

The expected output is for the references to appear as:

1 1a 1a1 1a1i

But instead, they appear as:

1 0a 1 i

Would love some guidance, thanks!

Answer 1

Your new list is parin, so the associated counters are parini, parinii, pariniii, and not enumi, enumii, enumiii:

\documentclass[letterpaper]{article}
\usepackage{enumitem}
\newlist{parin}{enumerate}{4}
\setlist[parin,1]{label=\arabic*.,ref=\arabic*,leftmargin=*}
\setlist[parin,2]{label=(\alph*),ref=\theparini\alph*,leftmargin=*}
\setlist[parin,3]{label=(\arabic*),ref=\theparinii\arabic*,leftmargin=*}
\setlist[parin,4]{label=(\roman*),ref=\thepariniii\roman*,leftmargin=*}
\begin{document}
\begin{parin}
\item Foo
\label{foo}
\begin{parin}
\item Bar
\label{bar}
\begin{parin}
\item Baz
\label{baz}
\begin{parin}
\item Label Me
\label{labelme}
\end{parin}
\end{parin}
\end{parin}
\end{parin}
\ref{foo}
\ref{bar}
\ref{baz}
\ref{labelme}
\end{document}