Tikz: draw edge from node to label of another edge

Question

I'm trying to figure out how to draw an edge between a node in tikz and the label of an edge between two other nodes. Here's an example of what I'm trying to do:

Here's my code:

\documentclass[11pt]{article}
\usepackage[margin=1in, top=1.5in]{geometry}
\usepackage{amsmath,amssymb,bbm}
\usepackage{graphicx}
\usepackage{tikz}
\usetikzlibrary{arrows, positioning}

\setlength{\parindent}{0.25in}
\newcommand{\assign}{:=}
\usepackage[hang,small,bf]{caption}


\begin{document}

\begin{figure}[!h]
  \centering
  \begin{tikzpicture}[shorten >=1pt,node distance=3cm,on grid,auto]
    \tikzstyle{state}=[shape=circle,thick,draw,minimum size=1.5cm]

    \node[state] (A1) {$A_1$};
    \node[state,above of=A1] (B1) {$B_1$};
    \node[state,above of=B1] (C1) {$C_1$};

    \node[state,right of=A1] (A2) {$A_2$};
    \node[state,above of=A2] (B2) {$B_2$};
    \node[state,above of=B2] (C2) {$C_2$};



    \path[->,draw,thick]
    (A1) edge node {$l_A$} (B2)
    (B1) edge node {$l_B$} (B2)

    ;

  \end{tikzpicture}
  \caption{Model}
  \label{fig:f1}
\end{figure}


\end{document}

Can someone tell me how I can get this effect?

Thanks!

Answer 1

This TeX.SX answer shows how to apply to your case a path from a node to the midpoint of two ther nodes:

\documentclass[tikz]{standalone}
\usetikzlibrary{calc}

\begin{document}
\begin{tikzpicture}[shorten >=1pt,node distance=3cm,auto]%,on grid
\tikzstyle{state}=[shape=circle,thick,draw,minimum size=1.5cm]

\node[state] (A1) {$A_1$};
\node[state,above of=A1] (B1) {$B_1$};
\node[state,above of=B1] (C1) {$C_1$};

\node[state,right of=A1] (A2) {$A_2$};
\node[state,above of=A2] (B2) {$B_2$};
\node[state,above of=B2] (C2) {$C_2$};

\path [->,draw,thick] (C1) -- ($ (B1) !.5! (B2) $);
\path [->,draw,thick] (C1) -- ($ (A1) !.5! (B2) $);

\path[->,draw,thick]
  (A1) edge node[near start] {$l_A$} (B2)
  (B1) edge node[near end] {$l_B$} (B2);

\end{tikzpicture}
\end{document}

This is only a rough starting point: please post a comment saying if this sketch fits or if you'd like some further development.