fix equations

wjschne · Oct 2, 2024 · 5606d4d · 5606d4d
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diff --git a/docs/articles/causalpaths.html b/docs/articles/causalpaths.html
diff --git a/docs/articles/sigma_e_2.pdf b/docs/articles/sigma_e_2.pdf
diff --git a/docs/articles/text_emph_s_text_2_mkern_1_5mu_text_emph_e.pdf b/docs/articles/text_emph_s_text_2_mkern_1_5mu_text_emph_e.pdf
diff --git a/docs/articles/text_emph_s_text_2_mkern_1_5mu_text_emph_x.pdf b/docs/articles/text_emph_s_text_2_mkern_1_5mu_text_emph_x.pdf
diff --git a/docs/pkgdown.yml b/docs/pkgdown.yml
@@ -14,7 +14,7 @@ articles:
   polygons: polygons.html
   rectangles: rectangles.html
   segments: segments.html
-last_built: 2024-10-02T14:24Z
+last_built: 2024-10-02T14:55Z
 urls:
   reference: https://wjschne.github.io/ggdiagram/reference
   article: https://wjschne.github.io/ggdiagram/articles
diff --git a/docs/search.json b/docs/search.json
diff --git a/docs/sitemap.xml b/docs/sitemap.xml
@@ -3,7 +3,6 @@
 <url><loc>https://wjschne.github.io/ggdiagram/articles/angles.html</loc></url>
 <url><loc>https://wjschne.github.io/ggdiagram/articles/arcs.html</loc></url>
 <url><loc>https://wjschne.github.io/ggdiagram/articles/bezier.html</loc></url>
-<url><loc>https://wjschne.github.io/ggdiagram/articles/causalpaths (DESKTOP-9DAV2E9's conflicted copy 2024-10-02).html</loc></url>
 <url><loc>https://wjschne.github.io/ggdiagram/articles/causalpaths.html</loc></url>
 <url><loc>https://wjschne.github.io/ggdiagram/articles/circles.html</loc></url>
 <url><loc>https://wjschne.github.io/ggdiagram/articles/ellipses.html</loc></url>

diff --git a/vignettes/causalpaths.qmd b/vignettes/causalpaths.qmd
@@ -287,19 +287,6 @@ ggdiagram(base_family = my_font, base_size = 16) +
              label = lb_path("*r*~12~", position = .5))
 ```
 
-The model-implied correlations among the four variables is the sum of the direct, indirect (i.e. mediated), spurious (i.e., due to common casuses), and unanalyzed effects (i.e., involving unmodeled correlations):
-
-$$
-\begin{align}
-\color{gray}{r_{12}}\\
-r_{13} &= \color{orchid}{b_{13}}+\color{gray}{r_{12}b_{23}}\\
-r_{14} &= \color{orchid}{b_{14}}+\color{forestgreen}{b_{13}b_{34}}+\color{gray}{r_{12}b_{24}}+\color{gray}{r_{12}b_{23}b_{34}}\\
-r_{23} &= \color{orchid}{b_{23}}+\color{gray}{r_{12}b_{13}}\\
-r_{24} &= \color{orchid}{b_{24}}+\color{forestgreen}{b_{23}b_{34}}+\color{gray}{r_{12}b_{14}}+\color{gray}{r_{12}b_{13}b_{34}}\\
-r_{34} &= \color{orchid}{b_{34}}+\color{dodgerblue}{b_{23}b_{24}}+\color{dodgerblue}{b_{13}b_{14}}+\color{gray}{b_{13}r_{12}b_{24}}+\color{gray}{b_{13}r_{12}b_{23}b_{34}}\\
-\text{Key: }&\color{orchid}{\text{Direct effect}},\, \color{forestgreen}{\text{Indirect effect}},\,\color{dodgerblue}{\text{Spurious effect}},\,\color{gray}{\text{Unanalyzed effect}}
-\end{align}
-$$
 
 ## Path Diagrams for Exploratory Factor Analysis