polr.md
In equatiomatic: Transform Models into 'LaTeX' Equations

colorizing works

$$
\begin{aligned}
\log\left[ \frac { P( \operatorname{rating}  \leq  \operatorname{1} ) }{ 1 - P( \operatorname{rating}  \leq  \operatorname{1} ) } \right] &= {\color{#1B9E77}{\alpha}}_{{\color{#666666}{1}}} + {\color{#D95F02}{\beta}}_{{\color{#A6761D}{1}}}({\color{blue}{\operatorname{temp}}}_{\operatorname{warm}})\ + \\
&\quad {\color{#7570B3}{\beta}}_{{\color{#E6AB02}{2}}}(\operatorname{contact}{\color{orange}{_{\operatorname{yes}}}}) + {\color{#E7298A}{\beta}}_{{\color{#66A61E}{3}}}({\color{blue}{\operatorname{temp}}}_{\operatorname{warm}} \times \operatorname{contact}{\color{orange}{_{\operatorname{yes}}}}) \\
\log\left[ \frac { P( \operatorname{rating}  \leq  \operatorname{2} ) }{ 1 - P( \operatorname{rating}  \leq  \operatorname{2} ) } \right] &= {\color{#1B9E77}{\alpha}}_{{\color{#666666}{2}}} + {\color{#D95F02}{\beta}}_{{\color{#A6761D}{1}}}({\color{blue}{\operatorname{temp}}}_{\operatorname{warm}})\ + \\
&\quad {\color{#7570B3}{\beta}}_{{\color{#E6AB02}{2}}}(\operatorname{contact}{\color{orange}{_{\operatorname{yes}}}}) + {\color{#E7298A}{\beta}}_{{\color{#66A61E}{3}}}({\color{blue}{\operatorname{temp}}}_{\operatorname{warm}} \times \operatorname{contact}{\color{orange}{_{\operatorname{yes}}}}) \\
\log\left[ \frac { P( \operatorname{rating}  \leq  \operatorname{3} ) }{ 1 - P( \operatorname{rating}  \leq  \operatorname{3} ) } \right] &= {\color{#1B9E77}{\alpha}}_{{\color{#666666}{3}}} + {\color{#D95F02}{\beta}}_{{\color{#A6761D}{1}}}({\color{blue}{\operatorname{temp}}}_{\operatorname{warm}})\ + \\
&\quad {\color{#7570B3}{\beta}}_{{\color{#E6AB02}{2}}}(\operatorname{contact}{\color{orange}{_{\operatorname{yes}}}}) + {\color{#E7298A}{\beta}}_{{\color{#66A61E}{3}}}({\color{blue}{\operatorname{temp}}}_{\operatorname{warm}} \times \operatorname{contact}{\color{orange}{_{\operatorname{yes}}}}) \\
\log\left[ \frac { P( \operatorname{rating}  \leq  \operatorname{4} ) }{ 1 - P( \operatorname{rating}  \leq  \operatorname{4} ) } \right] &= {\color{#1B9E77}{\alpha}}_{{\color{#666666}{4}}} + {\color{#D95F02}{\beta}}_{{\color{#A6761D}{1}}}({\color{blue}{\operatorname{temp}}}_{\operatorname{warm}})\ + \\
&\quad {\color{#7570B3}{\beta}}_{{\color{#E6AB02}{2}}}(\operatorname{contact}{\color{orange}{_{\operatorname{yes}}}}) + {\color{#E7298A}{\beta}}_{{\color{#66A61E}{3}}}({\color{blue}{\operatorname{temp}}}_{\operatorname{warm}} \times \operatorname{contact}{\color{orange}{_{\operatorname{yes}}}})
\end{aligned}
$$

Renaming Variables works

$$
\begin{aligned}
P( \operatorname{outcome}  \leq  \operatorname{A} ) &= \Phi[\alpha_{1} + \beta_{1}(\operatorname{catty}_{\operatorname{b}})\ + \\
&\qquad\ \beta_{2}(\operatorname{catty}_{\operatorname{c}}) + \beta_{3}(\operatorname{catty}_{\operatorname{do\ do\ do}})\ + \\
&\qquad\ \beta_{4}(\operatorname{catty}_{\operatorname{e}}) + \beta_{5}(\operatorname{Cont\ Var})\ + \\
&\qquad\ \beta_{6}(\operatorname{catty}_{\operatorname{b}} \times \operatorname{Cont\ Var}) + \beta_{7}(\operatorname{catty}_{\operatorname{c}} \times \operatorname{Cont\ Var})\ + \\
&\qquad\ \beta_{8}(\operatorname{catty}_{\operatorname{do\ do\ do}} \times \operatorname{Cont\ Var}) + \beta_{9}(\operatorname{catty}_{\operatorname{e}} \times \operatorname{Cont\ Var})] \\
P( \operatorname{outcome}  \leq  \operatorname{B} ) &= \Phi[\alpha_{2} + \beta_{1}(\operatorname{catty}_{\operatorname{b}})\ + \\
&\qquad\ \beta_{2}(\operatorname{catty}_{\operatorname{c}}) + \beta_{3}(\operatorname{catty}_{\operatorname{do\ do\ do}})\ + \\
&\qquad\ \beta_{4}(\operatorname{catty}_{\operatorname{e}}) + \beta_{5}(\operatorname{Cont\ Var})\ + \\
&\qquad\ \beta_{6}(\operatorname{catty}_{\operatorname{b}} \times \operatorname{Cont\ Var}) + \beta_{7}(\operatorname{catty}_{\operatorname{c}} \times \operatorname{Cont\ Var})\ + \\
&\qquad\ \beta_{8}(\operatorname{catty}_{\operatorname{do\ do\ do}} \times \operatorname{Cont\ Var}) + \beta_{9}(\operatorname{catty}_{\operatorname{e}} \times \operatorname{Cont\ Var})]
\end{aligned}
$$

Math extraction works

$$
\begin{aligned}
\log\left[ \frac { P( \operatorname{outcome}  \leq  \operatorname{A} ) }{ 1 - P( \operatorname{outcome}  \leq  \operatorname{A} ) } \right] &= \alpha_{1} + \beta_{1}(\operatorname{continuous}) + \beta_{2}(\operatorname{continuous^2}) + \beta_{3}(\operatorname{continuous^3}) + \beta_{4}(\operatorname{\log(continuous)}) \\
\log\left[ \frac { P( \operatorname{outcome}  \leq  \operatorname{B} ) }{ 1 - P( \operatorname{outcome}  \leq  \operatorname{B} ) } \right] &= \alpha_{2} + \beta_{1}(\operatorname{continuous}) + \beta_{2}(\operatorname{continuous^2}) + \beta_{3}(\operatorname{continuous^3}) + \beta_{4}(\operatorname{\log(continuous)})
\end{aligned}
$$

$$
\begin{aligned}
P( \operatorname{outcome}  \leq  \operatorname{A} ) &= \Phi[\alpha_{1} + \beta_{1}(\operatorname{continuous}) + \beta_{2}(\operatorname{continuous^2}) + \beta_{3}(\operatorname{continuous^3}) + \beta_{4}(\operatorname{\log(continuous)})] \\
P( \operatorname{outcome}  \leq  \operatorname{B} ) &= \Phi[\alpha_{2} + \beta_{1}(\operatorname{continuous}) + \beta_{2}(\operatorname{continuous^2}) + \beta_{3}(\operatorname{continuous^3}) + \beta_{4}(\operatorname{\log(continuous)})]
\end{aligned}
$$

Collapsing polr factors works

Code
  extract_eq(model_logit)
Output
  $$
  \begin{aligned}
  \log\left[ \frac { P( \operatorname{outcome}  \leq  \operatorname{A} ) }{ 1 - P( \operatorname{outcome}  \leq  \operatorname{A} ) } \right] &= \alpha_{1} + \beta_{1}(\operatorname{categorical}_{\operatorname{b}}) + \beta_{2}(\operatorname{categorical}_{\operatorname{c}}) + \beta_{3}(\operatorname{categorical}_{\operatorname{d}}) + \beta_{4}(\operatorname{categorical}_{\operatorname{e}}) + \beta_{5}(\operatorname{continuous}) + \beta_{6}(\operatorname{categorical}_{\operatorname{b}} \times \operatorname{continuous}) + \beta_{7}(\operatorname{categorical}_{\operatorname{c}} \times \operatorname{continuous}) + \beta_{8}(\operatorname{categorical}_{\operatorname{d}} \times \operatorname{continuous}) + \beta_{9}(\operatorname{categorical}_{\operatorname{e}} \times \operatorname{continuous}) \\
  \log\left[ \frac { P( \operatorname{outcome}  \leq  \operatorname{B} ) }{ 1 - P( \operatorname{outcome}  \leq  \operatorname{B} ) } \right] &= \alpha_{2} + \beta_{1}(\operatorname{categorical}_{\operatorname{b}}) + \beta_{2}(\operatorname{categorical}_{\operatorname{c}}) + \beta_{3}(\operatorname{categorical}_{\operatorname{d}}) + \beta_{4}(\operatorname{categorical}_{\operatorname{e}}) + \beta_{5}(\operatorname{continuous}) + \beta_{6}(\operatorname{categorical}_{\operatorname{b}} \times \operatorname{continuous}) + \beta_{7}(\operatorname{categorical}_{\operatorname{c}} \times \operatorname{continuous}) + \beta_{8}(\operatorname{categorical}_{\operatorname{d}} \times \operatorname{continuous}) + \beta_{9}(\operatorname{categorical}_{\operatorname{e}} \times \operatorname{continuous})
  \end{aligned}
  $$

Code
  extract_eq(model_probit)
Output
  $$
  \begin{aligned}
  P( \operatorname{outcome}  \leq  \operatorname{A} ) &= \Phi[\alpha_{1} + \beta_{1}(\operatorname{categorical}_{\operatorname{b}}) + \beta_{2}(\operatorname{categorical}_{\operatorname{c}}) + \beta_{3}(\operatorname{categorical}_{\operatorname{d}}) + \beta_{4}(\operatorname{categorical}_{\operatorname{e}}) + \beta_{5}(\operatorname{continuous}) + \beta_{6}(\operatorname{categorical}_{\operatorname{b}} \times \operatorname{continuous}) + \beta_{7}(\operatorname{categorical}_{\operatorname{c}} \times \operatorname{continuous}) + \beta_{8}(\operatorname{categorical}_{\operatorname{d}} \times \operatorname{continuous}) + \beta_{9}(\operatorname{categorical}_{\operatorname{e}} \times \operatorname{continuous})] \\
  P( \operatorname{outcome}  \leq  \operatorname{B} ) &= \Phi[\alpha_{2} + \beta_{1}(\operatorname{categorical}_{\operatorname{b}}) + \beta_{2}(\operatorname{categorical}_{\operatorname{c}}) + \beta_{3}(\operatorname{categorical}_{\operatorname{d}}) + \beta_{4}(\operatorname{categorical}_{\operatorname{e}}) + \beta_{5}(\operatorname{continuous}) + \beta_{6}(\operatorname{categorical}_{\operatorname{b}} \times \operatorname{continuous}) + \beta_{7}(\operatorname{categorical}_{\operatorname{c}} \times \operatorname{continuous}) + \beta_{8}(\operatorname{categorical}_{\operatorname{d}} \times \operatorname{continuous}) + \beta_{9}(\operatorname{categorical}_{\operatorname{e}} \times \operatorname{continuous})]
  \end{aligned}
  $$

Code
  extract_eq(model_logit, index_factors = TRUE)
Output
  $$
  \log\left[ \frac { P( \operatorname{outcome}  \leq  \operatorname{A} ) }{ 1 - P( \operatorname{outcome}  \leq  \operatorname{A} ) } \right] = \alpha + \operatorname{categorical}_{\operatorname{i}} + \operatorname{continuous} + \left(\operatorname{categorical}_{\operatorname{i}} \times \operatorname{continuous}\right) \\
  \log\left[ \frac { P( \operatorname{outcome}  \leq  \operatorname{B} ) }{ 1 - P( \operatorname{outcome}  \leq  \operatorname{B} ) } \right] = \alpha + \operatorname{categorical}_{\operatorname{i}} + \operatorname{continuous} + \left(\operatorname{categorical}_{\operatorname{i}} \times \operatorname{continuous}\right)
  $$

Code
  extract_eq(model_probit, index_factors = TRUE)
Output
  $$
  P( \operatorname{outcome}  \leq  \operatorname{A} ) = \Phi[\alpha + \operatorname{categorical}_{\operatorname{i}} + \operatorname{continuous} + \left(\operatorname{categorical}_{\operatorname{i}} \times \operatorname{continuous}\right)] \\
  P( \operatorname{outcome}  \leq  \operatorname{B} ) = \Phi[\alpha + \operatorname{categorical}_{\operatorname{i}} + \operatorname{continuous} + \left(\operatorname{categorical}_{\operatorname{i}} \times \operatorname{continuous}\right)]
  $$

Ordered logistic regression works

$$
\begin{aligned}
\log\left[ \frac { P( \operatorname{outcome}  \leq  \operatorname{A} ) }{ 1 - P( \operatorname{outcome}  \leq  \operatorname{A} ) } \right] &= \alpha_{1} + \beta_{1}(\operatorname{continuous\_1}) + \beta_{2}(\operatorname{continuous\_2}) \\
\log\left[ \frac { P( \operatorname{outcome}  \leq  \operatorname{B} ) }{ 1 - P( \operatorname{outcome}  \leq  \operatorname{B} ) } \right] &= \alpha_{2} + \beta_{1}(\operatorname{continuous\_1}) + \beta_{2}(\operatorname{continuous\_2})
\end{aligned}
$$

$$
\begin{aligned}
\log\left[ \frac { P( \operatorname{outcome}  \leq  \operatorname{A} ) }{ 1 - P( \operatorname{outcome}  \leq  \operatorname{A} ) } \right] &= \alpha_{1} + \beta_{1}(\operatorname{continuous\_1})\ + \\
&\quad \beta_{2}(\operatorname{continuous\_2}) \\
\log\left[ \frac { P( \operatorname{outcome}  \leq  \operatorname{B} ) }{ 1 - P( \operatorname{outcome}  \leq  \operatorname{B} ) } \right] &= \alpha_{2} + \beta_{1}(\operatorname{continuous\_1})\ + \\
&\quad \beta_{2}(\operatorname{continuous\_2})
\end{aligned}
$$

$$
\begin{aligned}
P( \operatorname{outcome}  \leq  \operatorname{A} ) &= \Phi[\alpha_{1} + \beta_{1}(\operatorname{continuous\_1}) + \beta_{2}(\operatorname{continuous\_2})] \\
P( \operatorname{outcome}  \leq  \operatorname{B} ) &= \Phi[\alpha_{2} + \beta_{1}(\operatorname{continuous\_1}) + \beta_{2}(\operatorname{continuous\_2})]
\end{aligned}
$$

$$
\begin{aligned}
P( \operatorname{outcome}  \leq  \operatorname{A} ) &= \Phi[\alpha_{1} + \beta_{1}(\operatorname{continuous\_1})\ + \\
&\qquad\ \beta_{2}(\operatorname{continuous\_2})] \\
P( \operatorname{outcome}  \leq  \operatorname{B} ) &= \Phi[\alpha_{2} + \beta_{1}(\operatorname{continuous\_1})\ + \\
&\qquad\ \beta_{2}(\operatorname{continuous\_2})]
\end{aligned}
$$

$$
\begin{aligned}
\log\left[ \frac { P( \operatorname{outcome}  \leq  \operatorname{A} ) }{ 1 - P( \operatorname{outcome}  \leq  \operatorname{A} ) } \right] &= 1.09 + 0.03(\operatorname{continuous\_1}) - 0.03(\operatorname{continuous\_2}) \\
\log\left[ \frac { P( \operatorname{outcome}  \leq  \operatorname{B} ) }{ 1 - P( \operatorname{outcome}  \leq  \operatorname{B} ) } \right] &= 2.48 + 0.03(\operatorname{continuous\_1}) - 0.03(\operatorname{continuous\_2})
\end{aligned}
$$