TikZ: Bottom right align text in rectangle

Question

I am making some graphical models with tikz, and I have added a rectangle (plate./style) around three nodes. As you can see in the picture the text "N" is vertically/horizontally center aligned. I want to align the text "N" to the bottom right of the "plate" i.e. I want "N" at the bottom right corner of the rounded rectangle. Since I will be doing this repeatedly, I want this setting to be made inside tikzset.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{fit}

\tikzset{
  latentnode/.style={draw, minimum width=5mm, shape=circle, ultra thick, black},
  dagconn/.style={arrows=->, black, thick},
  plate/.style={draw, shape=rectangle, rounded corners=0.5ex, thick,
    minimum width=3.1cm, text width=3.1cm, align=right, inner sep=10pt, innerysep=10pt}
}

\begin{document}

\begin{figure}[t!]
 \begin{tikzpicture}[scale=1]
   \node[latentnode] (1) [label=below left:$z_1$] at (1,3) {};
   \node[latentnode] (2) [label=below left:$z_2$] at (2.5,3) {};
   \node[latentnode] (3) [label=below left:$z_3$] at (4,3) {};
   \node[latentnode] (x1) [label=left:$x_1$] at (1,1.5) {};
   \node[latentnode] (x2) [label=left:$x_2$] at (2.5,1.5) {};
   \node[latentnode] (x3) [label=left:$x_3$] at (4,1.5) {};
   \node[plate, inner sep=20pt, fit=(1) (2) (3)] (plate1) {N};

   \draw[dagconn] (1) to (2);
   \draw[dagconn] (2) to (3);
   \draw[dagconn] (1) to (x1);
   \draw[dagconn] (2) to (x2);
   \draw[dagconn] (3) to (x3);
 \end{tikzpicture}
\end{figure}

\end{document}

Answer 1

Use an argument for the plate style and use it to place the label using the south.east anchor:

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{fit}

\tikzset{
  latentnode/.style={draw, minimum width=5mm, shape=circle, ultra thick, black},
  dagconn/.style={arrows=->, black, thick},
  plate/.style={draw, shape=rectangle, rounded corners=0.5ex, thick,
    minimum width=3.1cm, text width=3.1cm, align=right, inner sep=10pt, inner ysep=10pt,label={[xshift=-14pt,yshift=14pt]south east:#1}}
}

\begin{document}

\begin{figure}[t!]
 \begin{tikzpicture}[scale=1]
   \node[latentnode] (1) [label=below left:$z_1$] at (1,3) {};
   \node[latentnode] (2) [label=below left:$z_2$] at (2.5,3) {};
   \node[latentnode] (3) [label=below left:$z_3$] at (4,3) {};
   \node[latentnode] (x1) [label=left:$x_1$] at (1,1.5) {};
   \node[latentnode] (x2) [label=left:$x_2$] at (2.5,1.5) {};
   \node[latentnode] (x3) [label=left:$x_3$] at (4,1.5) {};
   \node[plate=N, inner sep=20pt, fit=(1) (2) (3)] (plate1) {};

   \draw[dagconn] (1) to (2);
   \draw[dagconn] (2) to (3);
   \draw[dagconn] (1) to (x1);
   \draw[dagconn] (2) to (x2);
   \draw[dagconn] (3) to (x3);
 \end{tikzpicture}
\end{figure}

\end{document}

Answer 2

This solution is similar to Gonzalo's answer but instead of label uses append after command option to place the node. It also uses positioning library although it's not strictly necessary.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{fit, positioning}

\tikzset{
  latentnode/.style={draw, minimum width=5mm, shape=circle, ultra thick, black},
  dagconn/.style={arrows=->, black, thick},
  plate/.style={draw, shape=rectangle, rounded corners=0.5ex, thick,
    minimum width=3.1cm, text width=3.1cm, align=right, inner sep=10pt, inner ysep=10pt, 
    append after command={node[above left= 3pt of \tikzlastnode.south east] {#1}}}
}

\begin{document}

\begin{figure}[t!]
 \begin{tikzpicture}[scale=1]
   \node[latentnode] (1) [label=below left:$z_1$] at (1,3) {};
   \node[latentnode] (2) [label=below left:$z_2$] at (2.5,3) {};
   \node[latentnode] (3) [label=below left:$z_3$] at (4,3) {};
   \node[latentnode] (x1) [label=left:$x_1$] at (1,1.5) {};
   \node[latentnode] (x2) [label=left:$x_2$] at (2.5,1.5) {};
   \node[latentnode] (x3) [label=left:$x_3$] at (4,1.5) {};
   \node[plate=N, inner sep=20pt, fit=(1) (2) (3)] (plate1) {};

   \draw[dagconn] (1) to (2);
   \draw[dagconn] (2) to (3);
   \draw[dagconn] (1) to (x1);
   \draw[dagconn] (2) to (x2);
   \draw[dagconn] (3) to (x3);
 \end{tikzpicture}
\end{figure}

\end{document}

Answer 3

Does this qualify as "inside tikz"? I introduce a macro \shft{} that takes its argument and moves it down 43pt (actually 43pt plus its own height) and over 112pt.

\documentclass{article}
\usepackage{tikz}
\usetikzlibrary{fit}
\usepackage{stackengine}
\def\shft#1{\stackunder[43pt]{}{\kern112pt #1}}
\tikzset{
  latentnode/.style={draw, minimum width=5mm, shape=circle, ultra thick, black},
  dagconn/.style={arrows=->, black, thick},
  plate/.style={draw, shape=rectangle, rounded corners=0.5ex, thick,
    minimum width=3.1cm, text width=3.1cm, align=right, inner sep=10pt, %innerysep=10pt
}
}
\begin{document}
\begin{figure}[t!]
 \begin{tikzpicture}[scale=1]
   \node[latentnode] (1) [label=below left:$z_1$] at (1,3) {};
   \node[latentnode] (2) [label=below left:$z_2$] at (2.5,3) {};
   \node[latentnode] (3) [label=below left:$z_3$] at (4,3) {};
   \node[latentnode] (x1) [label=left:$x_1$] at (1,1.5) {};
   \node[latentnode] (x2) [label=left:$x_2$] at (2.5,1.5) {};
   \node[latentnode] (x3) [label=left:$x_3$] at (4,1.5) {};
   \node[plate, inner sep=20pt, fit=(1) (2) (3)] (plate1) {\shft{N}};

   \draw[dagconn] (1) to (2);
   \draw[dagconn] (2) to (3);
   \draw[dagconn] (1) to (x1);
   \draw[dagconn] (2) to (x2);
   \draw[dagconn] (3) to (x3);
 \end{tikzpicture}
\end{figure}
\end{document}