Kurbanoglu, N. & Takunyaci, M. (2021). A structural equation modeling on relationship between self-efficacy, physics laboratory anxiety and attitudes. Journal of Family, Counseling and Education, 6(1), 47-56.
Little, T., Slegers, D., & Card, N. (2006). A non-arbitrary method of identifying and scaling latent variables in SEM and MACS models. Structural Equation Modeling, 13(1), 59-72.
Model diagram for Reference-Group Method
Tikz code
\documentclass[border = 10pt]{standalone}\input{../SEMstyles.tex}\begin{document}\begin{tikzpicture}%%%% Grade 7%% pos manifest\node [manifest] (pos71) {$pos_1$};\node [manifest] (pos72) [right = 1.5cm of pos71] {$pos_2$};\node [manifest] (pos73) [right = 1.5cm of pos72] {$pos_3$};%% neg manifest\node [manifest] (neg71) [right = 3cm of pos73] {$neg_1$};\node [manifest] (neg72) [right = 1.5cm of neg71] {$neg_2$};\node [manifest] (neg73) [right = 1.5cm of neg72] {$neg_3$};%% POS and NEG latents\node [latent] (POS7) [above = 3cm of pos73] {$POS$};\node [latent] (NEG7) [above = 3cm of neg71] {$NEG$};%% Latent variances and covariance\path [covariance] (POS7.35) edge ["$\upphi_{7,12}$", bend left = 40] (NEG7.145);\path [variance] (POS7.120) edge ["$\upphi_{7,11}\!=\!1$" {above = 1pt}, bend left = 100, looseness = 2.5] (POS7.60);\path [variance] (NEG7.120) edge ["$\upphi_{7,22}\!=\!1$" {above = 1pt}, bend left = 100, looseness = 2.5] (NEG7.60);%% Latent means\node [constant, black!30] (M7) [below = 1.5cm of $(pos73) !0.5! (neg71)$] {1};\path [regression, black!30] (M7) edge ["$\upkappa_{7,1}\!=\!0$", pos = 0.6] (POS7);\path [regression, black!30] (M7) edge ["$\upkappa_{7,2}\!=\!0$", pos = 0.6] (NEG7);%%% POS factor\foreach\i [count = \j] in {170, 150, 130} {%% Loadings\path [regression] (POS7) edge ["$\uplambda_\j$"] (pos7\j.90);%% Residuals\node [residual2] (e7\j) [above left = 4mm of pos7\j, xshift = 1mm] {$\uptheta_{7,\j}$};\path [regression] (e7\j) edge (pos7\j.north west);%% Intercepts\path [regression, black!30] (M7.\i) edge ["$\uptau_\j$"] (pos7\j.south east);}%%% NEG factor\foreach\i [count = \j, evaluate = \j as \k using int(\j + 3)] in {50, 30, 10} {%% Loadings\path [regression] (NEG7) edge ["$\uplambda_\k$"] (neg7\j.90);%% Residuals\node [residual2] (e7\k) [above right = 4mm of neg7\j, xshift = -1mm] {$\uptheta_{7,\k}$};\path [regression] (e7\k) edge (neg7\j.north east);%% Intercepts\path [regression, black!30] (M7.\i) edge ["$\uptau_\k$"] (neg7\j.south west);}%%%% Grade 8%% pos manifests\node [manifest] (pos81) [below = 7.5cm of pos71] {$pos_1$};\node [manifest] (pos82) [right = 1.5cm of pos81] {$pos_2$};\node [manifest] (pos83) [right = 1.5cm of pos82] {$pos_3$};%% neg manifests\node [manifest] (neg81) [right = 3cm of pos83] {$neg_1$};\node [manifest] (neg82) [right = 1.5cm of neg81] {$neg_2$};\node [manifest] (neg83) [right = 1.5cm of neg82] {$neg_3$};%% POS and NEG latents\node [latent] (POS8) [above = 3cm of pos83] {$POS$};\node [latent] (NEG8) [above = 3cm of neg81] {$NEG$};%% Latent variances and covariance\path [covariance] (POS8.35) edge ["$\upphi_{8,12}$", bend left = 40] (NEG8.145);\path [variance] (POS8.120) edge ["$\upphi_{8,11}$" {name = C1, above = 1pt}, bend left = 100, looseness = 2.5] (POS8.60);\path [variance] (NEG8.120) edge ["$\upphi_{8,22}$" {name = C2, above = 1pt}, bend left = 100, looseness = 2.5] (NEG8.60); % C1 and C2 used later to position Grades and dashed line%% latent means\node [constant, black!30] (M8) [below = 1.5cm of $(pos83) !0.5! (neg81)$] {1};\path [regression, black!30] (M8) edge ["$\upkappa_{8,1}$", pos = 0.6] (POS8);\path [regression, black!30] (M8) edge ["$\upkappa_{8,2}$", pos = 0.6] (NEG8);%%% POS factor\foreach\i [count = \j] in {170, 150, 130} {%% Loadings\path [regression] (POS8) edge ["$\uplambda_\j$"] (pos8\j.90);%% Residuals\node [residual2] (e8\j) [above left = 4mm of pos8\j, xshift = 1mm] {$\uptheta_{8,\j}$};\path [regression] (e8\j) edge (pos8\j.north west);%% Intercepts\path [regression, black!30] (M8.\i) edge ["$\uptau_\j$"] (pos8\j.south east);}%%% NEG factor\foreach\i [count = \j, evaluate = \j as \k using int(\j + 3)] in {50, 30, 10} {%% Loadings\path [regression] (NEG8) edge ["$\uplambda_\k$"] (neg8\j.90);%% Residuals\node [residual2] (e8\k) [above right = 4mm of neg8\j, xshift = -1mm] {$\uptheta_{8,\k}$};\path [regression] (e8\k) edge (neg8\j.north east);%% Intercepts\path [regression, black!30] (M8.\i) edge ["$\uptau_\k$"] (neg8\j.south west);}%% Grades\coordinate (mid) at ($(M7) !0.5! ($(C1) !0.5! (C2)$)$);\coordinate (C3) at (pos81 |- mid); \coordinate (C4) at (neg83 |- mid); \node [above = 0.5cm of C3] {Grade 7};\node [below = 0.5cm of C3] {Grade 8};\draw[densely dashed] ($(C3) !-1.5cm! (C4)$) -- ($(C4) !-1.5cm! (C3)$);\end{tikzpicture}\end{document}
Thompson, M., Liu, Y. & Green, S. (2023). Flexible structural equation modeling approaches for analyzing means. In R. Hoyle (Ed.), Handbook of structural equation modeling (2nd ed., pp. 385-408). New York, NY: Guilford Press.
\documentclass[border = 10pt]{standalone}\input{../SEMstyles.tex}\begin{document}\begin{tikzpicture}\def\gap {2cm} % separation between dependents\def\strat {{"No strategy", "Discussion", "Exercise"}} % strategy groups\def\gend {{"Male", "Female"}} % gender groups%% Dependents\node [manifest] (y1) {Y};\foreach\i [remember = \i as \lasti (initially 1)] in {2,...,6} {\node [manifest] (y\i) [right = \gap of y\lasti] {Y};}\foreach\i [remember = \i as \lasti] in {1,...,6} {%% Residuals\node [residual2] (e\i) [below right = 4mm of y\i] {e};\path [regression] (e\i) edge (y\i.south east) ;%% Means\node [constant] (const\i) [above = 1.5cm of y\i] {1};\path [regression] (const\i) edge ["a$_\i$"] (y\i);%% Groups\tikzmath{\firstrow = \strat[mod((\i-1), 3)]; \secondrow = \gend[int((\i-1)/3)];}\node [group] (gp\i) [above = 0.5cm of const\i] {Group \i:\\\firstrow\\\secondrow};%% Separators\ifnum\i > 1 \coordinate (m1) at ($(y\i.south) !0.5! (y\lasti.south)$);\coordinate (m2) at ($(gp\i.north) !0.5! (gp\lasti.north)$); \draw [densely dashed] ($(m1) !0.6cm!270: (y\i)$) -- ($(m2) !0.2cm!90: (gp\i)$);\fi}\end{tikzpicture}\end{document}
one-way MANOVA model diagram
Tikz code
\documentclass[border = 10pt]{standalone}\input{../SEMstyles.tex}%\usetikzlibrary{bending}\begin{document}\begin{tikzpicture}%% Three groups of four variables.%% Labels in each group are Y1 to Y4.%% Names are y1 to y12.\def\groups {No strategy, Discussion, Exercise}\def\gaps {0.4cm} % small gap between two variables within groups\def\gapb {1cm} % large gap between two variables between groups\def\angles {240, 260, 280, 300} % angeles out of constant%% Covariances in and out angles and bend\def\eout {{350, 335, 310}} % out angle\def\ein {{190, 205, 230}} % in angle\def\bend {{40, 55, 60}} % bend%% Indicators and their residuals\node [manifest] (y1) {Y$_1$};\node [residual2] (e1) [below = 4mm of y1] {e$_{Y_1}$};\path [regression] (e1) edge (y1);\foreach\i [remember = \i as \lasti (initially 1)] in {2,...,12}{\tikzmath{\labnum = int(mod(\i - 1, 4) + 1);}\ifnum\labnum = 1 %% Use label number to determine size of gap\def\gap {\gapb} \else\def\gap {\gaps} \fi\node [manifest] (y\i) [right = \gap of y\lasti] {Y$_\labnum$};\node [residual2] (e\i) [below = 4mm of y\i] {e$_{Y_\labnum}$};\path [regression] (e\i) edge (y\i); }\foreach\j [count = \i, remember = \i as \lasti] in \groups {\tikzmath{\lasty = int(4*\i); % label number for last Y in each group\firsty = int(\lasty - 3);} % label number for first Y in each group%% Means (above the middle of each group)\tikzmath{\xa = int(\firsty + 1); \xb = int(\firsty + 2;}\node [constant] (const\i) [above = 3cm of $(y\xa) !0.5! (y\xb)$] {1};\foreach\c [count = \b] in \angles {\tikzmath{\d = int((\i - 1)*4 + \b);} \path [regression] (const\i.\c) edge ["a$_{\i{Y_\b}}$", pos = 0.65] (y\d.90); }%% Groups (above the constant)\node [group] (gp\i) [above = 0.5cm of const\i] {Group \i:\\\j};%% Separators\ifnum\i > 1 \tikzmath{\prevy = (int(\firsty - 1);}\coordinate (m1) at ($(y\firsty.south) !0.5! (y\prevy.south)$);\coordinate (m2) at ($(gp\i.north) !0.5! (gp\lasti.north)$); \draw [densely dashed] ($(m1) !1.5cm!90: (y\prevy.south)$) -- ($(m2) !0.2cm!90: (gp\i.north)$);\fi}%% Covariances\foreach\g in {1,5,9} { % three groups of four variables - label for first in each group\foreach\i in {1,2,3} { \foreach\j [parse = true] in {\i+1,...,4}{ \tikzmath{\idash = int(\g + \i - 1); \jdash = int(\g + \j - 1);} % out and in labels for e\tikzmath{\index = \j - \i - 1;} % array element\tikzmath{\first = \eout[\index]; \second = \ein[\index]; \third = \bend[\index];}\path [covariance, black!40, bend right = \third, looseness = 0.75] (e\idash.\first) edge (e\jdash.\second); }}}\end{tikzpicture}\end{document}
one-way LATENT model diagram
Tikz code
\documentclass[tikz, border = 10pt]{standalone}\input{../SEMstyles.tex}\begin{document}\begin{tikzpicture}%% Three groups of four variables.%% Labels in each group are Y1 to Y4.%% Names are y1 to y12.\def\groups {No strategy, Discussion, Exercise}\def\gaps {0.4cm} % small gap between indicators\def\gapb {1cm} % large gap between indicators\def\angles {270/240, 282/253, 294/263, 306/270} % angles for intercepts and loadings% out of constant and latent%% Indicators and their residuals\node [manifest] (y1) {Y$_1$};\node [residual2] (e1) [below = 4mm of y1] {e$_{Y_1}$};\path [regression] (e1) edge (y1);\foreach\i [remember = \i as \lasti (initially 1)] in {2,...,12}{\tikzmath{\labnum = int(mod(\i - 1, 4) + 1);}\ifnum\labnum = 1 %% Use label number to determine size of gap\def\gap {\gapb} \else\def\gap {\gaps} \fi\node [manifest] (y\i) [right = \gap of y\lasti] {Y$_\labnum$};\node [residual2] (e\i) [below = 4mm of y\i] {e$_{Y_\labnum}$};\path [regression] (e\i) edge (y\i); }\foreach\j [count = \i, remember = \i as \lasti] in \groups {\tikzmath{\lasty = int(4*\i); % label number for last Y in each group\firsty = int(\lasty - 3);} % label number for first Y in each group%% Latents and their variances (above last y in each group)\node [latent] (latent\i) [above = 3cm of y\lasty] {LS};\path [variance, bend left = 110, looseness = 3] (latent\i.125) edge ["d"] (latent\i.60);%% Means (above first y in each group)\coordinate (cc) at (y\firsty |- latent\i); % coordinates for the constant\node [constant] (const\i) at (cc) {1}; \path[regression] (const\i) edge ["\ifnum\i = 1 {0} \else {a$_\i$} \fi"] (latent\i);\foreach\c/\d [count = \k] in \angles {%% Intercepts\tikzmath{\e = int((\i - 1)*4 + \k);} \path [regression] (const\i.\c) edge ["$\uptau_\k$", pos = 0.5 - 1/(6*(5-\k))] (y\e.90);%% Loadings\path[regression] (latent\i.\d) edge ["\ifnum\k = 1 {1} \else {$\uplambda_\k$} \fi", pos = 0.5 - 1/(6*\k)] (y\e.90); }%% Groups (above middle of each group of variables)\tikzmath{\xa = int(\firsty + 1); \xb = int(\firsty + 2;}\node [group] (gp\i) [above = 5cm of $(y\xa) !0.5! (y\xb)$] {Group \i:\\\j};%% Separators\ifnum\i > 1\tikzmath{\prevy = (int(\firsty - 1);}\coordinate (m1) at ($(y\firsty.south) !0.5! (y\prevy.south)$);\coordinate (m2) at ($(gp\i.north) !0.5! (gp\lasti.north)$); \draw [densely dashed] ($(m1) !0.7cm!90: (y\prevy.south)$) -- ($(m2) !0.2cm!90: (gp\i.north)$);\fi} \end{tikzpicture}\end{document}
