UMG 符號參考與圖形風格指南

bash Scripts/Shared/build_tikz_figure.sh \
     Scripts/Ch06/fig06_06_crosslevel_umg_V01.tex Figures/Ch06/fig06_06_crosslevel_umg

\begin{figure}[tbp]
\caption{Unified Model Graph of the Cross-Classified Random-Effects Model}
\label{fig:ch26-crossed}
{\centering\includegraphics[width=\linewidth]{fig26_02_crossed_umg.pdf}\par}
\fignote{Overlapping plates: ... (mechanics only)}
\end{figure}

% ============================================================
% Title:  UMG TikZ lexicon: visual primitives of the Unified
%         Model Graph (UMG) system
% File:   umg-style.tex
% Author: H.-T. Yu
% Date:   2026-06-12
% ============================================================
% Input this file in the preamble of any document (manuscript or
% standalone figure) that draws UMG diagrams. Requires TikZ.
%
% Channel-to-attribute mapping (see Table 2 of the manuscript):
%   Fill (luminance) -> observability  (shaded = observed; white = latent)
%   Shape            -> support        (circle = continuous; square = categorical)
%   Border           -> role           (single = random variable; double = deterministic)
%   Diamond          -> fixed unknown parameter (frequentist target of estimation)
%   Triangle         -> known constant (e.g., the unit constant for means)
%   Rounded box      -> plate (exchangeable replication; nesting = hierarchy)
% ------------------------------------------------------------
\usetikzlibrary{arrows.meta,positioning,fit,backgrounds,shapes.geometric,calc}

\tikzset{
  % ----- Vertex primitives -----------------------------------------
  % continuous latent random variable: white circle
  vCL/.style={draw, circle, minimum size=9.5mm, inner sep=1pt, line width=0.7pt, fill=white},
  % continuous observed random variable: shaded circle
  vCO/.style={draw, circle, minimum size=9.5mm, inner sep=1pt, line width=0.7pt, fill=black!13},
  % categorical latent random variable (e.g., latent class): white square
  vDL/.style={draw, rectangle, minimum size=8.5mm, inner sep=2pt, line width=0.7pt, fill=white},
  % categorical observed random variable (e.g., item response): shaded square
  vDO/.style={draw, rectangle, minimum size=8.5mm, inner sep=2pt, line width=0.7pt, fill=black!13},
  % fixed unknown parameter: open diamond
  vP/.style={draw, diamond, aspect=1.15, minimum size=7.5mm, inner sep=0.5pt, line width=0.7pt, fill=white},
  % deterministic node: double border (shape follows support)
  vDetC/.style={draw, circle, double, double distance=1.1pt, minimum size=9.5mm, inner sep=1pt, line width=0.5pt, fill=white},
  vDetD/.style={draw, rectangle, double, double distance=1.1pt, minimum size=8.5mm, inner sep=2pt, line width=0.5pt, fill=white},
  % known constant: triangle (RAM heritage); label inside
  vK/.style={draw, isosceles triangle, isosceles triangle apex angle=60,
             shape border rotate=90, minimum size=7mm, inner sep=0.5pt,
             line width=0.7pt, fill=white},
  % small disturbance/residual node (continuous latent, reduced size)
  vEps/.style={draw, circle, minimum size=6.5mm, inner sep=0.5pt, line width=0.6pt, fill=white},
  % ----- Edge primitives -------------------------------------------
  % stochastic/functional dependence (regression, loading)
  eReg/.style={->, >={Stealth[length=2.8mm]}, line width=0.7pt},
  % covariance / unanalyzed association (symmetric)
  eCov/.style={<->, >={Stealth[length=2.5mm]}, line width=0.7pt},
  % deterministic assignment
  eDet/.style={->, >={Stealth[length=2.8mm]}, line width=0.7pt, dashed},
  % mixing edge: latent class -> parameter set (open arrowhead)
  eMix/.style={->, >={Triangle[open, length=3mm]}, line width=0.7pt},
  % variance stub: double-headed self-loop on a node
  eVar/.style={<->, >={Stealth[length=2mm]}, line width=0.6pt, looseness=5},
  % edge parameter label
  elab/.style={font=\small, fill=white, inner sep=1pt, sloped=false},
  elabplain/.style={font=\small, inner sep=1.5pt},
  % ----- Plates ------------------------------------------------------
  plate/.style={draw, rounded corners=4pt, inner sep=9pt, line width=0.6pt},
  platelab/.style={anchor=south east, inner sep=4pt, font=\small\itshape},
  platelabnw/.style={anchor=north west, inner sep=4pt, font=\small\itshape},
  % ----- Auxiliary ---------------------------------------------------
  dist/.style={font=\footnotesize, text=black!70, inner sep=1pt},
  causalbadge/.style={draw, rounded corners=2pt, font=\footnotesize\sffamily,
                      inner sep=2.5pt, fill=black!5},
}

% Residual stub: arrow into #1 from direction #2 (angle), with label #3.
% Compact abbreviation for an explicit disturbance node; see Section 4.5.
\newcommand{\umgstub}[3]{%
  \draw[eReg] ($(#1)+(#2:0.95)$) -- (#1);
  \node[elabplain] at ($(#1)+(#2:1.25)$) {#3};%
}

\documentclass[border=3pt]{standalone}
\usepackage[T1]{fontenc}
\usepackage{newpxtext,newpxmath}
\usepackage[scale=0.95]{sourcesanspro}
\usepackage{tikz}
\input{umg-style.tex}
\tikzset{mk/.style={circle, fill=black, text=white, font=\sffamily\bfseries\scriptsize, inner sep=0.6pt, minimum size=3.6mm}}
\begin{document}
\begin{tikzpicture}
% parameters outside all plates
\node[vP] (g00) at (0.0,6.0) {$\gamma_{00}$};
\node[vP] (g01) at (1.1,6.0) {$\gamma_{01}$};
\node[vP] (g02) at (2.2,6.0) {$\gamma_{02}$};
\node[vP] (g10) at (4.6,6.0) {$\gamma_{10}$};
\node[vP] (g11) at (5.7,6.0) {$\gamma_{11}$};
% cluster level
\node[vCL] (b0) at (1.1,2.6) {$\beta_{0j}$};
\node[vCL] (b1) at (5.1,2.6) {$\beta_{1j}$};
\node[vCO] (z)  at (3.1,4.0) {$z_j$};
\node[vDetC] (xb) at (-0.9,2.6) {$\bar x_j$};
% unit level
\node[vCO] (x) at (1.6,0.2) {$x_{ij}$};
\node[vCO] (y) at (4.3,0.2) {$y_{ij}$};
% edges
\draw[eReg] (g00) -- (b0); \draw[eReg] (g01) -- (b0); \draw[eReg] (g02) -- (b0);
\draw[eReg] (g10) -- (b1); \draw[eReg] (g11) -- (b1);
\draw[eReg] (z) -- (b0); \draw[eReg] (z) -- (b1);
\draw[eDet] (x) to[bend left=25] (xb);
\draw[eReg] (xb) -- (b0);
\draw[eReg] (b0) -- (y); \draw[eReg] (b1) -- (y); \draw[eReg] (x) -- (y);
\draw[eCov] (b0) to[bend right=12] node[elab, below]{\scriptsize $\tau_{01}$} (b1);
\draw[eVar] (b0.205) to[out=205, in=255, looseness=6] node[elabplain, below left]{\scriptsize $\tau_0^2$} (b0.255);
\draw[eVar] (b1.30) to[out=30, in=-30, looseness=6] node[elabplain, right]{\scriptsize $\tau_1^2$} (b1.330);
\umgstub{y}{0}{$\sigma^2$}
\begin{scope}[on background layer]
  \coordinate (yr) at ($(y)+(1.55,0)$);
  \node[plate, fit=(x)(y)(yr), inner xsep=16pt, inner ysep=12pt] (pi) {};
  \node[plate, fit=(pi)(b0)(b1)(z)(xb), inner xsep=22pt, inner ysep=16pt] (pj) {};
\end{scope}
\node[platelab, font=\scriptsize\itshape] at (pi.south east) {$i=1,\dots,n_j$};
\node[platelab, font=\scriptsize\itshape] (jlab) at (pj.south east) {$j=1,\dots,J$};
% numbered markers (Table D.2)
\node[mk] at (-0.75,6.25) {1};
\node[mk] at (0.35,3.25) {2};
\node[mk] at (3.75,2.05) {3};
\node[mk] at (3.75,4.55) {4};
\node[mk] at (4.4,3.65) {5};
\node[mk] at (-1.7,3.25) {6};
\node[mk] at (1.0,-0.45) {7};
\node[mk] at (6.0,0.62) {8};
\node[mk, left=2pt of jlab] {9};
\end{tikzpicture}
\end{document}