tests/testthat/_snaps/lmerMod.md

In equatiomatic: Transform Models into 'LaTeX' Equations

colorizing works

$$
\begin{aligned}
  {\color{#FF00CC}{\operatorname{score}}}_{i}  &\sim N \left(\alpha_{j[i],k[i],l[i]} + \beta_{1j[i],k[i],l[i]}({\color{blue}{\operatorname{wave}}}), \sigma^2 \right) \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{j} \\
      &\beta_{1j}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\gamma_{0}^{\alpha} + \gamma_{1}^{\alpha}(\operatorname{group}{\color{orange}{_{\operatorname{low}}}}) + \gamma_{2}^{\alpha}(\operatorname{group}{\color{orange}{_{\operatorname{medium}}}}) + \gamma_{3l[i]}^{\alpha}({\color{red}{\operatorname{treatment}}}_{\operatorname{1}}) + \gamma_{4}^{\alpha}(\operatorname{group}{\color{orange}{_{\operatorname{low}}}} \times {\color{red}{\operatorname{treatment}}}_{\operatorname{1}}) + \gamma_{5}^{\alpha}(\operatorname{group}{\color{orange}{_{\operatorname{medium}}}} \times {\color{red}{\operatorname{treatment}}}_{\operatorname{1}}) \\
      &\gamma^{\beta_{1}}_{0} + \gamma^{\beta_{1}}_{1}(\operatorname{group}{\color{orange}{_{\operatorname{low}}}}) + \gamma^{\beta_{1}}_{2}(\operatorname{group}{\color{orange}{_{\operatorname{medium}}}}) + \gamma^{\beta_{1}}_{3}({\color{red}{\operatorname{treatment}}}_{\operatorname{1}}) + \gamma^{\beta_{1}}_{4}(\operatorname{group}{\color{orange}{_{\operatorname{low}}}} \times {\color{red}{\operatorname{treatment}}}_{\operatorname{1}}) + \gamma^{\beta_{1}}_{5}(\operatorname{group}{\color{orange}{_{\operatorname{medium}}}} \times {\color{red}{\operatorname{treatment}}}_{\operatorname{1}})
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     \sigma^2_{\alpha_{j}} & \rho_{\alpha_{j}\beta_{1j}} \\ 
     \rho_{\beta_{1j}\alpha_{j}} & \sigma^2_{\beta_{1j}}
  \end{array}
\right)
 \right)
    \text{, for sid j = 1,} \dots \text{,J} \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{k} \\
      &\beta_{1k}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\gamma_{0}^{\alpha} + \gamma_{1}^{\alpha}(\operatorname{prop\_low}) + \gamma_{2}^{\alpha}(\operatorname{prop\_low} \times {\color{red}{\operatorname{treatment}}}_{\operatorname{1}}) \\
      &\gamma^{\beta_{1}}_{0} + \gamma^{\beta_{1}}_{1}(\operatorname{prop\_low}) + \gamma^{\beta_{1}}_{1}(\operatorname{prop\_low} \times {\color{red}{\operatorname{treatment}}}_{\operatorname{1}})
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     \sigma^2_{\alpha_{k}} & \rho_{\alpha_{k}\beta_{1k}} \\ 
     \rho_{\beta_{1k}\alpha_{k}} & \sigma^2_{\beta_{1k}}
  \end{array}
\right)
 \right)
    \text{, for school k = 1,} \dots \text{,K} \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{l} \\
      &\beta_{1l} \\
      &\gamma_{3l}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\mu_{\alpha_{l}} \\
      &\mu_{\beta_{1l}} \\
      &\mu_{\gamma_{3l}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{ccc}
     \sigma^2_{\alpha_{l}} & \rho_{\alpha_{l}\beta_{1l}} & \rho_{\alpha_{l}\gamma_{3l}} \\ 
     \rho_{\beta_{1l}\alpha_{l}} & \sigma^2_{\beta_{1l}} & \rho_{\beta_{1l}\gamma_{3l}} \\ 
     \rho_{\gamma_{3l}\alpha_{l}} & \rho_{\gamma_{3l}\beta_{1l}} & \sigma^2_{\gamma_{3l}}
  \end{array}
\right)
 \right)
    \text{, for district l = 1,} \dots \text{,L}
\end{aligned}
$$

Math extraction works

Code
  extract_eq(m1)
Output
  $$
  \begin{aligned}
    \operatorname{Reaction}_{i}  &\sim N \left(\mu, \sigma^2 \right) \\
      \mu &=\alpha_{j[i]} + \beta_{1}(\operatorname{\log(Days\ +\ 1)}) + \beta_{2}(\operatorname{\exp(Days)}) + \beta_{3}(\operatorname{Days}) + \beta_{4}(\operatorname{Days^2}) + \beta_{5}(\operatorname{Days^3}) + \beta_{6}(\operatorname{Days^4}) \\
      \alpha_{j}  &\sim N \left(\mu_{\alpha_{j}}, \sigma^2_{\alpha_{j}} \right)
      \text{, for Subject j = 1,} \dots \text{,J}
  \end{aligned}
  $$

Code
  extract_eq(m2)
Output
  $$
  \begin{aligned}
    \operatorname{score}_{i}  &\sim N \left(\alpha_{j[i]} + \beta_{1}(\operatorname{\log(wave\ +\ 1)}), \sigma^2 \right) \\    
  \left(
    \begin{array}{c} 
      \begin{aligned}
        &\alpha_{j} \\
        &\beta_{1j}
      \end{aligned}
    \end{array}
  \right)
    &\sim N \left(
  \left(
    \begin{array}{c} 
      \begin{aligned}
        &\gamma_{0}^{\alpha} + \gamma_{1}^{\alpha}(\operatorname{\exp(prop\_low)}) \\
        &\mu_{\beta_{1j}}
      \end{aligned}
    \end{array}
  \right)
  , 
  \left(
    \begin{array}{cc}
       \sigma^2_{\alpha_{j}} & \rho_{\alpha_{j}\beta_{1j}} \\ 
       \rho_{\beta_{1j}\alpha_{j}} & \sigma^2_{\beta_{1j}}
    \end{array}
  \right)
   \right)
      \text{, for sid j = 1,} \dots \text{,J}
  \end{aligned}
  $$

Code
  extract_eq(m3)
Output
  $$
  \begin{aligned}
    \operatorname{score}_{i}  &\sim N \left(\alpha_{j[i],k[i],l[i]} + \beta_{1j[i],k[i],l[i]}(\operatorname{wave}), \sigma^2 \right) \\    
  \left(
    \begin{array}{c} 
      \begin{aligned}
        &\alpha_{j} \\
        &\beta_{1j}
      \end{aligned}
    \end{array}
  \right)
    &\sim N \left(
  \left(
    \begin{array}{c} 
      \begin{aligned}
        &\mu_{\alpha_{j}} \\
        &\mu_{\beta_{1j}}
      \end{aligned}
    \end{array}
  \right)
  , 
  \left(
    \begin{array}{cc}
       \sigma^2_{\alpha_{j}} & \rho_{\alpha_{j}\beta_{1j}} \\ 
       \rho_{\beta_{1j}\alpha_{j}} & \sigma^2_{\beta_{1j}}
    \end{array}
  \right)
   \right)
      \text{, for sid j = 1,} \dots \text{,J} \\    
  \left(
    \begin{array}{c} 
      \begin{aligned}
        &\alpha_{k} \\
        &\beta_{1k}
      \end{aligned}
    \end{array}
  \right)
    &\sim N \left(
  \left(
    \begin{array}{c} 
      \begin{aligned}
        &\gamma_{0}^{\alpha} + \gamma_{1}^{\alpha}(\operatorname{prop\_low}) + \gamma_{2}^{\alpha}(\operatorname{prop\_low^2}) + \gamma_{3}^{\alpha}(\operatorname{prop\_low^3}) + \gamma_{4}^{\alpha}(\operatorname{prop\_low^4}) \\
        &\mu_{\beta_{1k}}
      \end{aligned}
    \end{array}
  \right)
  , 
  \left(
    \begin{array}{cc}
       \sigma^2_{\alpha_{k}} & \rho_{\alpha_{k}\beta_{1k}} \\ 
       \rho_{\beta_{1k}\alpha_{k}} & \sigma^2_{\beta_{1k}}
    \end{array}
  \right)
   \right)
      \text{, for school k = 1,} \dots \text{,K} \\    
  \left(
    \begin{array}{c} 
      \begin{aligned}
        &\alpha_{l} \\
        &\beta_{1l}
      \end{aligned}
    \end{array}
  \right)
    &\sim N \left(
  \left(
    \begin{array}{c} 
      \begin{aligned}
        &\mu_{\alpha_{l}} \\
        &\mu_{\beta_{1l}}
      \end{aligned}
    \end{array}
  \right)
  , 
  \left(
    \begin{array}{cc}
       \sigma^2_{\alpha_{l}} & \rho_{\alpha_{l}\beta_{1l}} \\ 
       \rho_{\beta_{1l}\alpha_{l}} & \sigma^2_{\beta_{1l}}
    \end{array}
  \right)
   \right)
      \text{, for district l = 1,} \dots \text{,L}
  \end{aligned}
  $$

Implicit ID variables are handled

$$
\begin{aligned}
  \operatorname{score}_{i}  &\sim N \left(\alpha_{j[i],k[i]} + \beta_{1j[i],k[i]}(\operatorname{wave}), \sigma^2 \right) \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{j} \\
      &\beta_{1j}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\gamma_{0}^{\alpha} + \gamma_{1}^{\alpha}(\operatorname{treatment}_{\operatorname{1}}) \\
      &\mu_{\beta_{1j}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     \sigma^2_{\alpha_{j}} & \rho_{\alpha_{j}\beta_{1j}} \\ 
     \rho_{\beta_{1j}\alpha_{j}} & \sigma^2_{\beta_{1j}}
  \end{array}
\right)
 \right)
    \text{, for school j = 1,} \dots \text{,J} \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{k} \\
      &\beta_{1k}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\mu_{\alpha_{k}} \\
      &\mu_{\beta_{1k}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     \sigma^2_{\alpha_{k}} & \rho_{\alpha_{k}\beta_{1k}} \\ 
     \rho_{\beta_{1k}\alpha_{k}} & \sigma^2_{\beta_{1k}}
  \end{array}
\right)
 \right)
    \text{, for sid k = 1,} \dots \text{,K}
\end{aligned}
$$

Renaming Variables works

$$
\begin{aligned}
  \operatorname{Student\ Scores}_{i}  &\sim N \left(\alpha_{j[i],k[i],l[i]} + \beta_{1j[i],k[i],l[i]}(\operatorname{Wave}), \sigma^2 \right) \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{j} \\
      &\beta_{1j}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\gamma_{0}^{\alpha} + \gamma_{1k[i]}^{\alpha}(\operatorname{group}_{\operatorname{low}}) + \gamma_{2k[i]}^{\alpha}(\operatorname{group}_{\operatorname{medium}}) + \gamma_{3k[i],l[i]}^{\alpha}(\operatorname{treatment}) \\
      &\mu_{\beta_{1j}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     \sigma^2_{\alpha_{j}} & \rho_{\alpha_{j}\beta_{1j}} \\ 
     \rho_{\beta_{1j}\alpha_{j}} & \sigma^2_{\beta_{1j}}
  \end{array}
\right)
 \right)
    \text{, for sid j = 1,} \dots \text{,J} \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{k} \\
      &\beta_{1k} \\
      &\gamma_{1k} \\
      &\gamma_{2k} \\
      &\gamma_{3k}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\gamma_{0}^{\alpha} + \gamma_{1l[i]}^{\alpha}(\operatorname{P(low\ income)}) \\
      &\mu_{\beta_{1k}} \\
      &\mu_{\gamma_{1k}} \\
      &\mu_{\gamma_{2k}} \\
      &\mu_{\gamma_{3k}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{ccccc}
     \sigma^2_{\alpha_{k}} & \rho_{\alpha_{k}\beta_{1k}} & \rho_{\alpha_{k}\gamma_{1k}} & \rho_{\alpha_{k}\gamma_{2k}} & \rho_{\alpha_{k}\gamma_{3k}} \\ 
     \rho_{\beta_{1k}\alpha_{k}} & \sigma^2_{\beta_{1k}} & \rho_{\beta_{1k}\gamma_{1k}} & \rho_{\beta_{1k}\gamma_{2k}} & \rho_{\beta_{1k}\gamma_{3k}} \\ 
     \rho_{\gamma_{1k}\alpha_{k}} & \rho_{\gamma_{1k}\beta_{1k}} & \sigma^2_{\gamma_{1k}} & \rho_{\gamma_{1k}\gamma_{2k}} & \rho_{\gamma_{1k}\gamma_{3k}} \\ 
     \rho_{\gamma_{2k}\alpha_{k}} & \rho_{\gamma_{2k}\beta_{1k}} & \rho_{\gamma_{2k}\gamma_{1k}} & \sigma^2_{\gamma_{2k}} & \rho_{\gamma_{2k}\gamma_{3k}} \\ 
     \rho_{\gamma_{3k}\alpha_{k}} & \rho_{\gamma_{3k}\beta_{1k}} & \rho_{\gamma_{3k}\gamma_{1k}} & \rho_{\gamma_{3k}\gamma_{2k}} & \sigma^2_{\gamma_{3k}}
  \end{array}
\right)
 \right)
    \text{, for school k = 1,} \dots \text{,K} \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{l} \\
      &\beta_{1l} \\
      &\gamma_{3l} \\
      &\gamma_{1l}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\mu_{\alpha_{l}} \\
      &\mu_{\beta_{1l}} \\
      &\mu_{\gamma_{3l}} \\
      &\mu_{\gamma_{1l}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cccc}
     \sigma^2_{\alpha_{l}} & \rho_{\alpha_{l}\beta_{1l}} & \rho_{\alpha_{l}\gamma_{3l}} & \rho_{\alpha_{l}\gamma_{1l}} \\ 
     \rho_{\beta_{1l}\alpha_{l}} & \sigma^2_{\beta_{1l}} & \rho_{\beta_{1l}\gamma_{3l}} & \rho_{\beta_{1l}\gamma_{1l}} \\ 
     \rho_{\gamma_{3l}\alpha_{l}} & \rho_{\gamma_{3l}\beta_{1l}} & \sigma^2_{\gamma_{3l}} & \rho_{\gamma_{3l}\gamma_{1l}} \\ 
     \rho_{\gamma_{1l}\alpha_{l}} & \rho_{\gamma_{1l}\beta_{1l}} & \rho_{\gamma_{1l}\gamma_{3l}} & \sigma^2_{\gamma_{1l}}
  \end{array}
\right)
 \right)
    \text{, for district l = 1,} \dots \text{,L}
\end{aligned}
$$

Really big models work

Code
  extract_eq(big_mod)
Output
  $$
  \begin{aligned}
    \operatorname{rt}_{i}  &\sim N \left(\mu, \sigma^2 \right) \\
      \mu &=\beta_{1j[i]}(\operatorname{n1\_intercept}) + \beta_{2j[i]}(\operatorname{n1\_warning1}) + \beta_{3j[i]}(\operatorname{n1\_cuing1}) + \beta_{4j[i]}(\operatorname{x1\_intercept}) + \beta_{5j[i]}(\operatorname{x1\_warning1}) + \beta_{6j[i]}(\operatorname{x1\_cuing1}) + \beta_{7j[i]}(\operatorname{n2\_intercept}) + \beta_{8j[i]}(\operatorname{n2\_warning1}) + \beta_{9j[i]}(\operatorname{n2\_cuing1}) + \beta_{10j[i]}(\operatorname{x2\_intercept}) + \beta_{11j[i]}(\operatorname{x2\_warning1}) + \beta_{12j[i]}(\operatorname{x2\_cuing1}) \\    
  \left(
    \begin{array}{c} 
      \begin{aligned}
        &\beta_{1j} \\
        &\beta_{2j} \\
        &\beta_{3j} \\
        &\beta_{4j} \\
        &\beta_{5j} \\
        &\beta_{6j} \\
        &\beta_{7j} \\
        &\beta_{8j} \\
        &\beta_{9j} \\
        &\beta_{10j} \\
        &\beta_{11j} \\
        &\beta_{12j}
      \end{aligned}
    \end{array}
  \right)
    &\sim N \left(
  \left(
    \begin{array}{c} 
      \begin{aligned}
        &\mu_{\beta_{1j}} \\
        &\mu_{\beta_{2j}} \\
        &\mu_{\beta_{3j}} \\
        &\mu_{\beta_{4j}} \\
        &\mu_{\beta_{5j}} \\
        &\mu_{\beta_{6j}} \\
        &\mu_{\beta_{7j}} \\
        &\mu_{\beta_{8j}} \\
        &\mu_{\beta_{9j}} \\
        &\mu_{\beta_{10j}} \\
        &\mu_{\beta_{11j}} \\
        &\mu_{\beta_{12j}}
      \end{aligned}
    \end{array}
  \right)
  , 
  \left(
    \begin{array}{cccccccccccc}
       \sigma^2_{\beta_{1j}} & \rho_{\beta_{1j}\beta_{2j}} & \rho_{\beta_{1j}\beta_{3j}} & \rho_{\beta_{1j}\beta_{4j}} & \rho_{\beta_{1j}\beta_{5j}} & \rho_{\beta_{1j}\beta_{6j}} & \rho_{\beta_{1j}\beta_{7j}} & \rho_{\beta_{1j}\beta_{8j}} & \rho_{\beta_{1j}\beta_{9j}} & \rho_{\beta_{1j}\beta_{10j}} & \rho_{\beta_{1j}\beta_{11j}} & \rho_{\beta_{1j}\beta_{12j}} \\ 
       \rho_{\beta_{2j}\beta_{1j}} & \sigma^2_{\beta_{2j}} & \rho_{\beta_{2j}\beta_{3j}} & \rho_{\beta_{2j}\beta_{4j}} & \rho_{\beta_{2j}\beta_{5j}} & \rho_{\beta_{2j}\beta_{6j}} & \rho_{\beta_{2j}\beta_{7j}} & \rho_{\beta_{2j}\beta_{8j}} & \rho_{\beta_{2j}\beta_{9j}} & \rho_{\beta_{2j}\beta_{10j}} & \rho_{\beta_{2j}\beta_{11j}} & \rho_{\beta_{2j}\beta_{12j}} \\ 
       \rho_{\beta_{3j}\beta_{1j}} & \rho_{\beta_{3j}\beta_{2j}} & \sigma^2_{\beta_{3j}} & \rho_{\beta_{3j}\beta_{4j}} & \rho_{\beta_{3j}\beta_{5j}} & \rho_{\beta_{3j}\beta_{6j}} & \rho_{\beta_{3j}\beta_{7j}} & \rho_{\beta_{3j}\beta_{8j}} & \rho_{\beta_{3j}\beta_{9j}} & \rho_{\beta_{3j}\beta_{10j}} & \rho_{\beta_{3j}\beta_{11j}} & \rho_{\beta_{3j}\beta_{12j}} \\ 
       \rho_{\beta_{4j}\beta_{1j}} & \rho_{\beta_{4j}\beta_{2j}} & \rho_{\beta_{4j}\beta_{3j}} & \sigma^2_{\beta_{4j}} & \rho_{\beta_{4j}\beta_{5j}} & \rho_{\beta_{4j}\beta_{6j}} & \rho_{\beta_{4j}\beta_{7j}} & \rho_{\beta_{4j}\beta_{8j}} & \rho_{\beta_{4j}\beta_{9j}} & \rho_{\beta_{4j}\beta_{10j}} & \rho_{\beta_{4j}\beta_{11j}} & \rho_{\beta_{4j}\beta_{12j}} \\ 
       \rho_{\beta_{5j}\beta_{1j}} & \rho_{\beta_{5j}\beta_{2j}} & \rho_{\beta_{5j}\beta_{3j}} & \rho_{\beta_{5j}\beta_{4j}} & \sigma^2_{\beta_{5j}} & \rho_{\beta_{5j}\beta_{6j}} & \rho_{\beta_{5j}\beta_{7j}} & \rho_{\beta_{5j}\beta_{8j}} & \rho_{\beta_{5j}\beta_{9j}} & \rho_{\beta_{5j}\beta_{10j}} & \rho_{\beta_{5j}\beta_{11j}} & \rho_{\beta_{5j}\beta_{12j}} \\ 
       \rho_{\beta_{6j}\beta_{1j}} & \rho_{\beta_{6j}\beta_{2j}} & \rho_{\beta_{6j}\beta_{3j}} & \rho_{\beta_{6j}\beta_{4j}} & \rho_{\beta_{6j}\beta_{5j}} & \sigma^2_{\beta_{6j}} & \rho_{\beta_{6j}\beta_{7j}} & \rho_{\beta_{6j}\beta_{8j}} & \rho_{\beta_{6j}\beta_{9j}} & \rho_{\beta_{6j}\beta_{10j}} & \rho_{\beta_{6j}\beta_{11j}} & \rho_{\beta_{6j}\beta_{12j}} \\ 
       \rho_{\beta_{7j}\beta_{1j}} & \rho_{\beta_{7j}\beta_{2j}} & \rho_{\beta_{7j}\beta_{3j}} & \rho_{\beta_{7j}\beta_{4j}} & \rho_{\beta_{7j}\beta_{5j}} & \rho_{\beta_{7j}\beta_{6j}} & \sigma^2_{\beta_{7j}} & \rho_{\beta_{7j}\beta_{8j}} & \rho_{\beta_{7j}\beta_{9j}} & \rho_{\beta_{7j}\beta_{10j}} & \rho_{\beta_{7j}\beta_{11j}} & \rho_{\beta_{7j}\beta_{12j}} \\ 
       \rho_{\beta_{8j}\beta_{1j}} & \rho_{\beta_{8j}\beta_{2j}} & \rho_{\beta_{8j}\beta_{3j}} & \rho_{\beta_{8j}\beta_{4j}} & \rho_{\beta_{8j}\beta_{5j}} & \rho_{\beta_{8j}\beta_{6j}} & \rho_{\beta_{8j}\beta_{7j}} & \sigma^2_{\beta_{8j}} & \rho_{\beta_{8j}\beta_{9j}} & \rho_{\beta_{8j}\beta_{10j}} & \rho_{\beta_{8j}\beta_{11j}} & \rho_{\beta_{8j}\beta_{12j}} \\ 
       \rho_{\beta_{9j}\beta_{1j}} & \rho_{\beta_{9j}\beta_{2j}} & \rho_{\beta_{9j}\beta_{3j}} & \rho_{\beta_{9j}\beta_{4j}} & \rho_{\beta_{9j}\beta_{5j}} & \rho_{\beta_{9j}\beta_{6j}} & \rho_{\beta_{9j}\beta_{7j}} & \rho_{\beta_{9j}\beta_{8j}} & \sigma^2_{\beta_{9j}} & \rho_{\beta_{9j}\beta_{10j}} & \rho_{\beta_{9j}\beta_{11j}} & \rho_{\beta_{9j}\beta_{12j}} \\ 
       \rho_{\beta_{10j}\beta_{1j}} & \rho_{\beta_{10j}\beta_{2j}} & \rho_{\beta_{10j}\beta_{3j}} & \rho_{\beta_{10j}\beta_{4j}} & \rho_{\beta_{10j}\beta_{5j}} & \rho_{\beta_{10j}\beta_{6j}} & \rho_{\beta_{10j}\beta_{7j}} & \rho_{\beta_{10j}\beta_{8j}} & \rho_{\beta_{10j}\beta_{9j}} & \sigma^2_{\beta_{10j}} & \rho_{\beta_{10j}\beta_{11j}} & \rho_{\beta_{10j}\beta_{12j}} \\ 
       \rho_{\beta_{11j}\beta_{1j}} & \rho_{\beta_{11j}\beta_{2j}} & \rho_{\beta_{11j}\beta_{3j}} & \rho_{\beta_{11j}\beta_{4j}} & \rho_{\beta_{11j}\beta_{5j}} & \rho_{\beta_{11j}\beta_{6j}} & \rho_{\beta_{11j}\beta_{7j}} & \rho_{\beta_{11j}\beta_{8j}} & \rho_{\beta_{11j}\beta_{9j}} & \rho_{\beta_{11j}\beta_{10j}} & \sigma^2_{\beta_{11j}} & \rho_{\beta_{11j}\beta_{12j}} \\ 
       \rho_{\beta_{12j}\beta_{1j}} & \rho_{\beta_{12j}\beta_{2j}} & \rho_{\beta_{12j}\beta_{3j}} & \rho_{\beta_{12j}\beta_{4j}} & \rho_{\beta_{12j}\beta_{5j}} & \rho_{\beta_{12j}\beta_{6j}} & \rho_{\beta_{12j}\beta_{7j}} & \rho_{\beta_{12j}\beta_{8j}} & \rho_{\beta_{12j}\beta_{9j}} & \rho_{\beta_{12j}\beta_{10j}} & \rho_{\beta_{12j}\beta_{11j}} & \sigma^2_{\beta_{12j}}
    \end{array}
  \right)
   \right)
      \text{, for id j = 1,} \dots \text{,J}
  \end{aligned}
  $$

Categorical variable level parsing works (from issue #140)

$$
\begin{aligned}
  \operatorname{error}_{i}  &\sim N \left(\mu, \sigma^2 \right) \\
    \mu &=\alpha_{j[i]} + \beta_{1}(\operatorname{brochure}_{\operatorname{standard}}) + \beta_{2}(\operatorname{disease}_{\operatorname{DS}}) + \beta_{3}(\operatorname{brochure}_{\operatorname{standard}} \times \operatorname{disease}_{\operatorname{DS}}) \\
    \alpha_{j}  &\sim N \left(\mu_{\alpha_{j}}, \sigma^2_{\alpha_{j}} \right)
    \text{, for ID j = 1,} \dots \text{,J}
\end{aligned}
$$

Unconditional lmer models work

$$
\begin{aligned}
  \operatorname{score}_{i}  &\sim N \left(\alpha_{j[i]}, \sigma^2 \right) \\
    \alpha_{j}  &\sim N \left(\mu_{\alpha_{j}}, \sigma^2_{\alpha_{j}} \right)
    \text{, for sid j = 1,} \dots \text{,J}
\end{aligned}
$$

$$
\begin{aligned}
  \operatorname{score}_{i}  &\sim N \left(\alpha_{j[i],k[i]}, \sigma^2 \right) \\
    \alpha_{j}  &\sim N \left(\mu_{\alpha_{j}}, \sigma^2_{\alpha_{j}} \right)
    \text{, for sid j = 1,} \dots \text{,J} \\
    \alpha_{k}  &\sim N \left(\mu_{\alpha_{k}}, \sigma^2_{\alpha_{k}} \right)
    \text{, for school k = 1,} \dots \text{,K}
\end{aligned}
$$

$$
\begin{aligned}
  \operatorname{score}_{i}  &\sim N \left(\alpha_{j[i],k[i],l[i]}, \sigma^2 \right) \\
    \alpha_{j}  &\sim N \left(\mu_{\alpha_{j}}, \sigma^2_{\alpha_{j}} \right)
    \text{, for sid j = 1,} \dots \text{,J} \\
    \alpha_{k}  &\sim N \left(\mu_{\alpha_{k}}, \sigma^2_{\alpha_{k}} \right)
    \text{, for school k = 1,} \dots \text{,K} \\
    \alpha_{l}  &\sim N \left(\mu_{\alpha_{l}}, \sigma^2_{\alpha_{l}} \right)
    \text{, for district l = 1,} \dots \text{,L}
\end{aligned}
$$

Level 1 predictors work

$$
\begin{aligned}
  \operatorname{math}_{i}  &\sim N \left(\mu, \sigma^2 \right) \\
    \mu &=\alpha_{j[i]} + \beta_{1}(\operatorname{female}) + \beta_{2}(\operatorname{ses}) + \beta_{3}(\operatorname{minority}) \\
    \alpha_{j}  &\sim N \left(\mu_{\alpha_{j}}, \sigma^2_{\alpha_{j}} \right)
    \text{, for sch.id j = 1,} \dots \text{,J}
\end{aligned}
$$

$$
\begin{aligned}
  \operatorname{score}_{i}  &\sim N \left(\alpha_{j[i],k[i],l[i]} + \beta_{1}(\operatorname{wave}), \sigma^2 \right) \\
    \alpha_{j}  &\sim N \left(\mu_{\alpha_{j}}, \sigma^2_{\alpha_{j}} \right)
    \text{, for sid j = 1,} \dots \text{,J} \\
    \alpha_{k}  &\sim N \left(\mu_{\alpha_{k}}, \sigma^2_{\alpha_{k}} \right)
    \text{, for school k = 1,} \dots \text{,K} \\
    \alpha_{l}  &\sim N \left(\mu_{\alpha_{l}}, \sigma^2_{\alpha_{l}} \right)
    \text{, for district l = 1,} \dots \text{,L}
\end{aligned}
$$

Mean separate works as expected

$$
\begin{aligned}
  \operatorname{math}_{i}  &\sim N \left(\alpha_{j[i]} + \beta_{1}(\operatorname{female}) + \beta_{2}(\operatorname{ses}) + \beta_{3}(\operatorname{minority}), \sigma^2 \right) \\
    \alpha_{j}  &\sim N \left(\mu_{\alpha_{j}}, \sigma^2_{\alpha_{j}} \right)
    \text{, for sch.id j = 1,} \dots \text{,J}
\end{aligned}
$$

$$
\begin{aligned}
  \operatorname{score}_{i}  &\sim N \left(\mu, \sigma^2 \right) \\
    \mu &=\alpha_{j[i],k[i],l[i]} + \beta_{1}(\operatorname{wave}) \\
    \alpha_{j}  &\sim N \left(\mu_{\alpha_{j}}, \sigma^2_{\alpha_{j}} \right)
    \text{, for sid j = 1,} \dots \text{,J} \\
    \alpha_{k}  &\sim N \left(\mu_{\alpha_{k}}, \sigma^2_{\alpha_{k}} \right)
    \text{, for school k = 1,} \dots \text{,K} \\
    \alpha_{l}  &\sim N \left(\mu_{\alpha_{l}}, \sigma^2_{\alpha_{l}} \right)
    \text{, for district l = 1,} \dots \text{,L}
\end{aligned}
$$

Wrapping works as expected

$$
\begin{aligned}
  \operatorname{math}_{i}  &\sim N \left(\mu, \sigma^2 \right) \\
    \mu &=\alpha_{j[i]} + \beta_{1}(\operatorname{female})\ + \\
&\quad \beta_{2}(\operatorname{ses}) + \beta_{3}(\operatorname{minority}) \\
    \alpha_{j}  &\sim N \left(\mu_{\alpha_{j}}, \sigma^2_{\alpha_{j}} \right)
    \text{, for sch.id j = 1,} \dots \text{,J}
\end{aligned}
$$

Unstructured variance-covariances work as expected

$$
\begin{aligned}
  \operatorname{math}_{i}  &\sim N \left(\mu, \sigma^2 \right) \\
    \mu &=\alpha_{j[i]} + \beta_{1}(\operatorname{female}) + \beta_{2}(\operatorname{ses}) + \beta_{3j[i]}(\operatorname{minority}) \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{j} \\
      &\beta_{3j}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\mu_{\alpha_{j}} \\
      &\mu_{\beta_{3j}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     \sigma^2_{\alpha_{j}} & \rho_{\alpha_{j}\beta_{3j}} \\ 
     \rho_{\beta_{3j}\alpha_{j}} & \sigma^2_{\beta_{3j}}
  \end{array}
\right)
 \right)
    \text{, for sch.id j = 1,} \dots \text{,J}
\end{aligned}
$$

$$
\begin{aligned}
  \operatorname{math}_{i}  &\sim N \left(\mu, \sigma^2 \right) \\
    \mu &=\alpha_{j[i]} + \beta_{1j[i]}(\operatorname{female}) + \beta_{2j[i]}(\operatorname{ses}) + \beta_{3}(\operatorname{minority}) \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{j} \\
      &\beta_{1j} \\
      &\beta_{2j}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\mu_{\alpha_{j}} \\
      &\mu_{\beta_{1j}} \\
      &\mu_{\beta_{2j}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{ccc}
     \sigma^2_{\alpha_{j}} & \rho_{\alpha_{j}\beta_{1j}} & \rho_{\alpha_{j}\beta_{2j}} \\ 
     \rho_{\beta_{1j}\alpha_{j}} & \sigma^2_{\beta_{1j}} & \rho_{\beta_{1j}\beta_{2j}} \\ 
     \rho_{\beta_{2j}\alpha_{j}} & \rho_{\beta_{2j}\beta_{1j}} & \sigma^2_{\beta_{2j}}
  \end{array}
\right)
 \right)
    \text{, for sch.id j = 1,} \dots \text{,J}
\end{aligned}
$$

$$
\begin{aligned}
  \operatorname{math}_{i}  &\sim N \left(\mu, \sigma^2 \right) \\
    \mu &=\alpha_{j[i]} + \beta_{1j[i]}(\operatorname{female}) + \beta_{2j[i]}(\operatorname{ses}) + \beta_{3}(\operatorname{minority}) + \beta_{4j[i]}(\operatorname{female} \times \operatorname{ses}) \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{j} \\
      &\beta_{1j} \\
      &\beta_{2j} \\
      &\beta_{4j}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\mu_{\alpha_{j}} \\
      &\mu_{\beta_{1j}} \\
      &\mu_{\beta_{2j}} \\
      &\mu_{\beta_{4j}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cccc}
     \sigma^2_{\alpha_{j}} & \rho_{\alpha_{j}\beta_{1j}} & \rho_{\alpha_{j}\beta_{2j}} & \rho_{\alpha_{j}\beta_{4j}} \\ 
     \rho_{\beta_{1j}\alpha_{j}} & \sigma^2_{\beta_{1j}} & \rho_{\beta_{1j}\beta_{2j}} & \rho_{\beta_{1j}\beta_{4j}} \\ 
     \rho_{\beta_{2j}\alpha_{j}} & \rho_{\beta_{2j}\beta_{1j}} & \sigma^2_{\beta_{2j}} & \rho_{\beta_{2j}\beta_{4j}} \\ 
     \rho_{\beta_{4j}\alpha_{j}} & \rho_{\beta_{4j}\beta_{1j}} & \rho_{\beta_{4j}\beta_{2j}} & \sigma^2_{\beta_{4j}}
  \end{array}
\right)
 \right)
    \text{, for sch.id j = 1,} \dots \text{,J}
\end{aligned}
$$

$$
\begin{aligned}
  \operatorname{math}_{i}  &\sim N \left(\mu, \sigma^2 \right) \\
    \mu &=\alpha_{j[i]} + \beta_{1j[i]}(\operatorname{female}) + \beta_{2j[i]}(\operatorname{ses}) + \beta_{3j[i]}(\operatorname{minority}) + \beta_{4j[i]}(\operatorname{female} \times \operatorname{ses}) \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{j} \\
      &\beta_{1j} \\
      &\beta_{2j} \\
      &\beta_{3j} \\
      &\beta_{4j}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\mu_{\alpha_{j}} \\
      &\mu_{\beta_{1j}} \\
      &\mu_{\beta_{2j}} \\
      &\mu_{\beta_{3j}} \\
      &\mu_{\beta_{4j}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{ccccc}
     \sigma^2_{\alpha_{j}} & \rho_{\alpha_{j}\beta_{1j}} & \rho_{\alpha_{j}\beta_{2j}} & \rho_{\alpha_{j}\beta_{3j}} & \rho_{\alpha_{j}\beta_{4j}} \\ 
     \rho_{\beta_{1j}\alpha_{j}} & \sigma^2_{\beta_{1j}} & \rho_{\beta_{1j}\beta_{2j}} & \rho_{\beta_{1j}\beta_{3j}} & \rho_{\beta_{1j}\beta_{4j}} \\ 
     \rho_{\beta_{2j}\alpha_{j}} & \rho_{\beta_{2j}\beta_{1j}} & \sigma^2_{\beta_{2j}} & \rho_{\beta_{2j}\beta_{3j}} & \rho_{\beta_{2j}\beta_{4j}} \\ 
     \rho_{\beta_{3j}\alpha_{j}} & \rho_{\beta_{3j}\beta_{1j}} & \rho_{\beta_{3j}\beta_{2j}} & \sigma^2_{\beta_{3j}} & \rho_{\beta_{3j}\beta_{4j}} \\ 
     \rho_{\beta_{4j}\alpha_{j}} & \rho_{\beta_{4j}\beta_{1j}} & \rho_{\beta_{4j}\beta_{2j}} & \rho_{\beta_{4j}\beta_{3j}} & \sigma^2_{\beta_{4j}}
  \end{array}
\right)
 \right)
    \text{, for sch.id j = 1,} \dots \text{,J}
\end{aligned}
$$

$$
\begin{aligned}
  \operatorname{score}_{i}  &\sim N \left(\alpha_{j[i],k[i],l[i]} + \beta_{1j[i],k[i],l[i]}(\operatorname{wave}), \sigma^2 \right) \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{j} \\
      &\beta_{1j}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\mu_{\alpha_{j}} \\
      &\mu_{\beta_{1j}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     \sigma^2_{\alpha_{j}} & \rho_{\alpha_{j}\beta_{1j}} \\ 
     \rho_{\beta_{1j}\alpha_{j}} & \sigma^2_{\beta_{1j}}
  \end{array}
\right)
 \right)
    \text{, for sid j = 1,} \dots \text{,J} \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{k} \\
      &\beta_{1k}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\mu_{\alpha_{k}} \\
      &\mu_{\beta_{1k}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     \sigma^2_{\alpha_{k}} & \rho_{\alpha_{k}\beta_{1k}} \\ 
     \rho_{\beta_{1k}\alpha_{k}} & \sigma^2_{\beta_{1k}}
  \end{array}
\right)
 \right)
    \text{, for school k = 1,} \dots \text{,K} \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{l} \\
      &\beta_{1l}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\mu_{\alpha_{l}} \\
      &\mu_{\beta_{1l}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     \sigma^2_{\alpha_{l}} & \rho_{\alpha_{l}\beta_{1l}} \\ 
     \rho_{\beta_{1l}\alpha_{l}} & \sigma^2_{\beta_{1l}}
  \end{array}
\right)
 \right)
    \text{, for district l = 1,} \dots \text{,L}
\end{aligned}
$$

Group-level predictors work as expected

$$
\begin{aligned}
  \operatorname{score}_{i}  &\sim N \left(\alpha_{j[i],k[i],l[i]} + \beta_{1j[i],k[i],l[i]}(\operatorname{wave}), \sigma^2 \right) \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{j} \\
      &\beta_{1j}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\gamma_{0}^{\alpha} + \gamma_{1k[i]}^{\alpha}(\operatorname{group}_{\operatorname{low}}) + \gamma_{2k[i]}^{\alpha}(\operatorname{group}_{\operatorname{medium}}) + \gamma_{3k[i],l[i]}^{\alpha}(\operatorname{treatment}_{\operatorname{1}}) \\
      &\mu_{\beta_{1j}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     \sigma^2_{\alpha_{j}} & \rho_{\alpha_{j}\beta_{1j}} \\ 
     \rho_{\beta_{1j}\alpha_{j}} & \sigma^2_{\beta_{1j}}
  \end{array}
\right)
 \right)
    \text{, for sid j = 1,} \dots \text{,J} \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{k} \\
      &\beta_{1k} \\
      &\gamma_{1k} \\
      &\gamma_{2k} \\
      &\gamma_{3k}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\mu_{\alpha_{k}} \\
      &\mu_{\beta_{1k}} \\
      &\mu_{\gamma_{1k}} \\
      &\mu_{\gamma_{2k}} \\
      &\mu_{\gamma_{3k}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{ccccc}
     \sigma^2_{\alpha_{k}} & \rho_{\alpha_{k}\beta_{1k}} & \rho_{\alpha_{k}\gamma_{1k}} & \rho_{\alpha_{k}\gamma_{2k}} & \rho_{\alpha_{k}\gamma_{3k}} \\ 
     \rho_{\beta_{1k}\alpha_{k}} & \sigma^2_{\beta_{1k}} & \rho_{\beta_{1k}\gamma_{1k}} & \rho_{\beta_{1k}\gamma_{2k}} & \rho_{\beta_{1k}\gamma_{3k}} \\ 
     \rho_{\gamma_{1k}\alpha_{k}} & \rho_{\gamma_{1k}\beta_{1k}} & \sigma^2_{\gamma_{1k}} & \rho_{\gamma_{1k}\gamma_{2k}} & \rho_{\gamma_{1k}\gamma_{3k}} \\ 
     \rho_{\gamma_{2k}\alpha_{k}} & \rho_{\gamma_{2k}\beta_{1k}} & \rho_{\gamma_{2k}\gamma_{1k}} & \sigma^2_{\gamma_{2k}} & \rho_{\gamma_{2k}\gamma_{3k}} \\ 
     \rho_{\gamma_{3k}\alpha_{k}} & \rho_{\gamma_{3k}\beta_{1k}} & \rho_{\gamma_{3k}\gamma_{1k}} & \rho_{\gamma_{3k}\gamma_{2k}} & \sigma^2_{\gamma_{3k}}
  \end{array}
\right)
 \right)
    \text{, for school k = 1,} \dots \text{,K} \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{l} \\
      &\beta_{1l} \\
      &\gamma_{3l}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\mu_{\alpha_{l}} \\
      &\mu_{\beta_{1l}} \\
      &\mu_{\gamma_{3l}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{ccc}
     \sigma^2_{\alpha_{l}} & \rho_{\alpha_{l}\beta_{1l}} & \rho_{\alpha_{l}\gamma_{3l}} \\ 
     \rho_{\beta_{1l}\alpha_{l}} & \sigma^2_{\beta_{1l}} & \rho_{\beta_{1l}\gamma_{3l}} \\ 
     \rho_{\gamma_{3l}\alpha_{l}} & \rho_{\gamma_{3l}\beta_{1l}} & \sigma^2_{\gamma_{3l}}
  \end{array}
\right)
 \right)
    \text{, for district l = 1,} \dots \text{,L}
\end{aligned}
$$

$$
\begin{aligned}
  \operatorname{score}_{i}  &\sim N \left(\alpha_{j[i],k[i],l[i]} + \beta_{1j[i],k[i],l[i]}(\operatorname{wave}), \sigma^2 \right) \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{j} \\
      &\beta_{1j}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\gamma_{0}^{\alpha} + \gamma_{1k[i]}^{\alpha}(\operatorname{group}_{\operatorname{low}}) + \gamma_{2k[i]}^{\alpha}(\operatorname{group}_{\operatorname{medium}}) + \gamma_{3k[i],l[i]}^{\alpha}(\operatorname{treatment}_{\operatorname{1}}) \\
      &\mu_{\beta_{1j}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     \sigma^2_{\alpha_{j}} & \rho_{\alpha_{j}\beta_{1j}} \\ 
     \rho_{\beta_{1j}\alpha_{j}} & \sigma^2_{\beta_{1j}}
  \end{array}
\right)
 \right)
    \text{, for sid j = 1,} \dots \text{,J} \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{k} \\
      &\beta_{1k} \\
      &\gamma_{1k} \\
      &\gamma_{2k} \\
      &\gamma_{3k}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\gamma_{0}^{\alpha} + \gamma_{1l[i]}^{\alpha}(\operatorname{prop\_low}) \\
      &\mu_{\beta_{1k}} \\
      &\mu_{\gamma_{1k}} \\
      &\mu_{\gamma_{2k}} \\
      &\mu_{\gamma_{3k}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{ccccc}
     \sigma^2_{\alpha_{k}} & \rho_{\alpha_{k}\beta_{1k}} & \rho_{\alpha_{k}\gamma_{1k}} & \rho_{\alpha_{k}\gamma_{2k}} & \rho_{\alpha_{k}\gamma_{3k}} \\ 
     \rho_{\beta_{1k}\alpha_{k}} & \sigma^2_{\beta_{1k}} & \rho_{\beta_{1k}\gamma_{1k}} & \rho_{\beta_{1k}\gamma_{2k}} & \rho_{\beta_{1k}\gamma_{3k}} \\ 
     \rho_{\gamma_{1k}\alpha_{k}} & \rho_{\gamma_{1k}\beta_{1k}} & \sigma^2_{\gamma_{1k}} & \rho_{\gamma_{1k}\gamma_{2k}} & \rho_{\gamma_{1k}\gamma_{3k}} \\ 
     \rho_{\gamma_{2k}\alpha_{k}} & \rho_{\gamma_{2k}\beta_{1k}} & \rho_{\gamma_{2k}\gamma_{1k}} & \sigma^2_{\gamma_{2k}} & \rho_{\gamma_{2k}\gamma_{3k}} \\ 
     \rho_{\gamma_{3k}\alpha_{k}} & \rho_{\gamma_{3k}\beta_{1k}} & \rho_{\gamma_{3k}\gamma_{1k}} & \rho_{\gamma_{3k}\gamma_{2k}} & \sigma^2_{\gamma_{3k}}
  \end{array}
\right)
 \right)
    \text{, for school k = 1,} \dots \text{,K} \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{l} \\
      &\beta_{1l} \\
      &\gamma_{3l} \\
      &\gamma_{1l}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\mu_{\alpha_{l}} \\
      &\mu_{\beta_{1l}} \\
      &\mu_{\gamma_{3l}} \\
      &\mu_{\gamma_{1l}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cccc}
     \sigma^2_{\alpha_{l}} & \rho_{\alpha_{l}\beta_{1l}} & \rho_{\alpha_{l}\gamma_{3l}} & \rho_{\alpha_{l}\gamma_{1l}} \\ 
     \rho_{\beta_{1l}\alpha_{l}} & \sigma^2_{\beta_{1l}} & \rho_{\beta_{1l}\gamma_{3l}} & \rho_{\beta_{1l}\gamma_{1l}} \\ 
     \rho_{\gamma_{3l}\alpha_{l}} & \rho_{\gamma_{3l}\beta_{1l}} & \sigma^2_{\gamma_{3l}} & \rho_{\gamma_{3l}\gamma_{1l}} \\ 
     \rho_{\gamma_{1l}\alpha_{l}} & \rho_{\gamma_{1l}\beta_{1l}} & \rho_{\gamma_{1l}\gamma_{3l}} & \sigma^2_{\gamma_{1l}}
  \end{array}
\right)
 \right)
    \text{, for district l = 1,} \dots \text{,L}
\end{aligned}
$$

$$
\begin{aligned}
  \operatorname{score}_{i}  &\sim N \left(\alpha_{j[i],k[i],l[i]} + \beta_{1j[i],k[i],l[i]}(\operatorname{wave}), \sigma^2 \right) \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{j} \\
      &\beta_{1j}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\gamma_{0}^{\alpha} + \gamma_{1}^{\alpha}(\operatorname{group}_{\operatorname{low}}) + \gamma_{2}^{\alpha}(\operatorname{group}_{\operatorname{medium}}) + \gamma_{3k[i]}^{\alpha}(\operatorname{treatment}_{\operatorname{1}}) \\
      &\mu_{\beta_{1j}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     \sigma^2_{\alpha_{j}} & \rho_{\alpha_{j}\beta_{1j}} \\ 
     \rho_{\beta_{1j}\alpha_{j}} & \sigma^2_{\beta_{1j}}
  \end{array}
\right)
 \right)
    \text{, for sid j = 1,} \dots \text{,J} \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{k} \\
      &\beta_{1k} \\
      &\gamma_{3k}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\gamma_{0}^{\alpha} + \gamma_{1}^{\alpha}(\operatorname{prop\_low}) \\
      &\mu_{\beta_{1k}} \\
      &\mu_{\gamma_{3k}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{ccc}
     \sigma^2_{\alpha_{k}} & \rho_{\alpha_{k}\beta_{1k}} & \rho_{\alpha_{k}\gamma_{3k}} \\ 
     \rho_{\beta_{1k}\alpha_{k}} & \sigma^2_{\beta_{1k}} & \rho_{\beta_{1k}\gamma_{3k}} \\ 
     \rho_{\gamma_{3k}\alpha_{k}} & \rho_{\gamma_{3k}\beta_{1k}} & \sigma^2_{\gamma_{3k}}
  \end{array}
\right)
 \right)
    \text{, for school k = 1,} \dots \text{,K} \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{l} \\
      &\beta_{1l}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\gamma_{0}^{\alpha} + \gamma_{1}^{\alpha}(\operatorname{dist\_mean}) \\
      &\mu_{\beta_{1l}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     \sigma^2_{\alpha_{l}} & \rho_{\alpha_{l}\beta_{1l}} \\ 
     \rho_{\beta_{1l}\alpha_{l}} & \sigma^2_{\beta_{1l}}
  \end{array}
\right)
 \right)
    \text{, for district l = 1,} \dots \text{,L}
\end{aligned}
$$

Interactions work as expected

$$
\begin{aligned}
  \operatorname{math}_{i}  &\sim N \left(\mu, \sigma^2 \right) \\
    \mu &=\alpha_{j[i]} + \beta_{1}(\operatorname{minority}) + \beta_{2}(\operatorname{female}) + \beta_{3}(\operatorname{female} \times \operatorname{minority}) \\
    \alpha_{j}  &\sim N \left(\mu_{\alpha_{j}}, \sigma^2_{\alpha_{j}} \right)
    \text{, for sch.id j = 1,} \dots \text{,J}
\end{aligned}
$$

$$
\begin{aligned}
  \operatorname{score}_{i}  &\sim N \left(\alpha_{j[i],k[i],l[i]}, \sigma^2 \right) \\    \alpha_{j}  &\sim N \left(\gamma_{0}^{\alpha} + \gamma_{1k[i],l[i]}^{\alpha}(\operatorname{treatment}_{\operatorname{1}}) + \gamma_{2l[i]}^{\alpha}(\operatorname{group}_{\operatorname{low}}) + \gamma_{3l[i]}^{\alpha}(\operatorname{group}_{\operatorname{medium}}) + \gamma_{4l[i]}^{\alpha}(\operatorname{group}_{\operatorname{low}} \times \operatorname{treatment}_{\operatorname{1}}) + \gamma_{5l[i]}^{\alpha}(\operatorname{group}_{\operatorname{medium}} \times \operatorname{treatment}_{\operatorname{1}}), \sigma^2_{\alpha_{j}} \right)
    \text{, for sid j = 1,} \dots \text{,J} \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{k} \\
      &\gamma_{1k}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\mu_{\alpha_{k}} \\
      &\mu_{\gamma_{1k}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     \sigma^2_{\alpha_{k}} & \rho_{\alpha_{k}\gamma_{1k}} \\ 
     \rho_{\gamma_{1k}\alpha_{k}} & \sigma^2_{\gamma_{1k}}
  \end{array}
\right)
 \right)
    \text{, for school k = 1,} \dots \text{,K} \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{l} \\
      &\gamma_{1l} \\
      &\gamma_{2l} \\
      &\gamma_{3l} \\
      &\gamma_{4l} \\
      &\gamma_{5l}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\mu_{\alpha_{l}} \\
      &\mu_{\gamma_{1l}} \\
      &\mu_{\gamma_{2l}} \\
      &\mu_{\gamma_{3l}} \\
      &\mu_{\gamma_{4l}} \\
      &\mu_{\gamma_{5l}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cccccc}
     \sigma^2_{\alpha_{l}} & \rho_{\alpha_{l}\gamma_{1l}} & \rho_{\alpha_{l}\gamma_{2l}} & \rho_{\alpha_{l}\gamma_{3l}} & \rho_{\alpha_{l}\gamma_{4l}} & \rho_{\alpha_{l}\gamma_{5l}} \\ 
     \rho_{\gamma_{1l}\alpha_{l}} & \sigma^2_{\gamma_{1l}} & \rho_{\gamma_{1l}\gamma_{2l}} & \rho_{\gamma_{1l}\gamma_{3l}} & \rho_{\gamma_{1l}\gamma_{4l}} & \rho_{\gamma_{1l}\gamma_{5l}} \\ 
     \rho_{\gamma_{2l}\alpha_{l}} & \rho_{\gamma_{2l}\gamma_{1l}} & \sigma^2_{\gamma_{2l}} & \rho_{\gamma_{2l}\gamma_{3l}} & \rho_{\gamma_{2l}\gamma_{4l}} & \rho_{\gamma_{2l}\gamma_{5l}} \\ 
     \rho_{\gamma_{3l}\alpha_{l}} & \rho_{\gamma_{3l}\gamma_{1l}} & \rho_{\gamma_{3l}\gamma_{2l}} & \sigma^2_{\gamma_{3l}} & \rho_{\gamma_{3l}\gamma_{4l}} & \rho_{\gamma_{3l}\gamma_{5l}} \\ 
     \rho_{\gamma_{4l}\alpha_{l}} & \rho_{\gamma_{4l}\gamma_{1l}} & \rho_{\gamma_{4l}\gamma_{2l}} & \rho_{\gamma_{4l}\gamma_{3l}} & \sigma^2_{\gamma_{4l}} & \rho_{\gamma_{4l}\gamma_{5l}} \\ 
     \rho_{\gamma_{5l}\alpha_{l}} & \rho_{\gamma_{5l}\gamma_{1l}} & \rho_{\gamma_{5l}\gamma_{2l}} & \rho_{\gamma_{5l}\gamma_{3l}} & \rho_{\gamma_{5l}\gamma_{4l}} & \sigma^2_{\gamma_{5l}}
  \end{array}
\right)
 \right)
    \text{, for district l = 1,} \dots \text{,L}
\end{aligned}
$$

$$
\begin{aligned}
  \operatorname{score}_{i}  &\sim N \left(\alpha_{j[i],k[i],l[i]} + \beta_{1j[i]}(\operatorname{wave}), \sigma^2 \right) \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{j} \\
      &\beta_{1j}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\gamma_{0}^{\alpha} + \gamma_{1}^{\alpha}(\operatorname{treatment}_{\operatorname{1}}) \\
      &\gamma^{\beta_{1}}_{0} + \gamma^{\beta_{1}}_{1}(\operatorname{treatment}_{\operatorname{1}})
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     \sigma^2_{\alpha_{j}} & \rho_{\alpha_{j}\beta_{1j}} \\ 
     \rho_{\beta_{1j}\alpha_{j}} & \sigma^2_{\beta_{1j}}
  \end{array}
\right)
 \right)
    \text{, for sid j = 1,} \dots \text{,J} \\    \alpha_{k}  &\sim N \left(\mu_{\alpha_{k}}, \sigma^2_{\alpha_{k}} \right)
    \text{, for school k = 1,} \dots \text{,K} \\    \alpha_{l}  &\sim N \left(\mu_{\alpha_{l}}, \sigma^2_{\alpha_{l}} \right)
    \text{, for district l = 1,} \dots \text{,L}
\end{aligned}
$$

$$
\begin{aligned}
  \operatorname{score}_{i}  &\sim N \left(\alpha_{j[i],k[i],l[i]} + \beta_{1}(\operatorname{wave}), \sigma^2 \right) \\
    \alpha_{j}  &\sim N \left(\gamma_{0}^{\alpha} + \gamma_{1}^{\alpha}(\operatorname{treatment}_{\operatorname{1}}) + \gamma_{2}^{\alpha}(\operatorname{treatment}_{\operatorname{1}} \times \operatorname{wave}), \sigma^2_{\alpha_{j}} \right)
    \text{, for sid j = 1,} \dots \text{,J} \\
    \alpha_{k}  &\sim N \left(\mu_{\alpha_{k}}, \sigma^2_{\alpha_{k}} \right)
    \text{, for school k = 1,} \dots \text{,K} \\
    \alpha_{l}  &\sim N \left(\mu_{\alpha_{l}}, \sigma^2_{\alpha_{l}} \right)
    \text{, for district l = 1,} \dots \text{,L}
\end{aligned}
$$

$$
\begin{aligned}
  \operatorname{score}_{i}  &\sim N \left(\alpha_{j[i],k[i],l[i]} + \beta_{1j[i],k[i],l[i]}(\operatorname{wave}), \sigma^2 \right) \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{j} \\
      &\beta_{1j}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\gamma_{0}^{\alpha} + \gamma_{1}^{\alpha}(\operatorname{group}_{\operatorname{low}}) + \gamma_{2}^{\alpha}(\operatorname{group}_{\operatorname{medium}}) + \gamma_{3l[i]}^{\alpha}(\operatorname{treatment}_{\operatorname{1}}) + \gamma_{4}^{\alpha}(\operatorname{group}_{\operatorname{low}} \times \operatorname{treatment}_{\operatorname{1}}) + \gamma_{5}^{\alpha}(\operatorname{group}_{\operatorname{medium}} \times \operatorname{treatment}_{\operatorname{1}}) \\
      &\gamma^{\beta_{1}}_{0} + \gamma^{\beta_{1}}_{1}(\operatorname{group}_{\operatorname{low}}) + \gamma^{\beta_{1}}_{2}(\operatorname{group}_{\operatorname{medium}}) + \gamma^{\beta_{1}}_{3}(\operatorname{treatment}_{\operatorname{1}}) + \gamma^{\beta_{1}}_{4}(\operatorname{group}_{\operatorname{low}} \times \operatorname{treatment}_{\operatorname{1}}) + \gamma^{\beta_{1}}_{5}(\operatorname{group}_{\operatorname{medium}} \times \operatorname{treatment}_{\operatorname{1}})
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     \sigma^2_{\alpha_{j}} & \rho_{\alpha_{j}\beta_{1j}} \\ 
     \rho_{\beta_{1j}\alpha_{j}} & \sigma^2_{\beta_{1j}}
  \end{array}
\right)
 \right)
    \text{, for sid j = 1,} \dots \text{,J} \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{k} \\
      &\beta_{1k}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\gamma_{0}^{\alpha} + \gamma_{1}^{\alpha}(\operatorname{prop\_low}) + \gamma_{2}^{\alpha}(\operatorname{prop\_low} \times \operatorname{treatment}_{\operatorname{1}}) \\
      &\gamma^{\beta_{1}}_{0} + \gamma^{\beta_{1}}_{2}(\operatorname{prop\_low}) + \gamma^{\beta_{1}}_{1}(\operatorname{prop\_low} \times \operatorname{treatment}_{\operatorname{1}})
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     \sigma^2_{\alpha_{k}} & \rho_{\alpha_{k}\beta_{1k}} \\ 
     \rho_{\beta_{1k}\alpha_{k}} & \sigma^2_{\beta_{1k}}
  \end{array}
\right)
 \right)
    \text{, for school k = 1,} \dots \text{,K} \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{l} \\
      &\beta_{1l} \\
      &\gamma_{3l}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\mu_{\alpha_{l}} \\
      &\mu_{\beta_{1l}} \\
      &\mu_{\gamma_{3l}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{ccc}
     \sigma^2_{\alpha_{l}} & \rho_{\alpha_{l}\beta_{1l}} & \rho_{\alpha_{l}\gamma_{3l}} \\ 
     \rho_{\beta_{1l}\alpha_{l}} & \sigma^2_{\beta_{1l}} & \rho_{\beta_{1l}\gamma_{3l}} \\ 
     \rho_{\gamma_{3l}\alpha_{l}} & \rho_{\gamma_{3l}\beta_{1l}} & \sigma^2_{\gamma_{3l}}
  \end{array}
\right)
 \right)
    \text{, for district l = 1,} \dots \text{,L}
\end{aligned}
$$

Alternate random effect VCV structures work

$$
\begin{aligned}
  \operatorname{math}_{i}  &\sim N \left(\mu, \sigma^2 \right) \\
    \mu &=\alpha_{j[i]} + \beta_{1j[i]}(\operatorname{minority}) + \beta_{2j[i]}(\operatorname{female}) + \beta_{3j[i]}(\operatorname{female} \times \operatorname{minority}) \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{j} \\
      &\beta_{1j} \\
      &\beta_{2j} \\
      &\beta_{3j}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\mu_{\alpha_{j}} \\
      &\mu_{\beta_{1j}} \\
      &\mu_{\beta_{2j}} \\
      &\mu_{\beta_{3j}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cccc}
     \sigma^2_{\alpha_{j}} & 0 & 0 & 0 \\ 
     0 & \sigma^2_{\beta_{1j}} & 0 & 0 \\ 
     0 & 0 & \sigma^2_{\beta_{2j}} & 0 \\ 
     0 & 0 & 0 & \sigma^2_{\beta_{3j}}
  \end{array}
\right)
 \right)
    \text{, for sch.id j = 1,} \dots \text{,J}
\end{aligned}
$$

$$
\begin{aligned}
  \operatorname{math}_{i}  &\sim N \left(\mu, \sigma^2 \right) \\
    \mu &=\alpha_{j[i]} + \beta_{1j[i]}(\operatorname{minority}) + \beta_{2j[i]}(\operatorname{female}) + \beta_{3j[i]}(\operatorname{female} \times \operatorname{minority}) \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{j} \\
      &\beta_{1j} \\
      &\beta_{2j} \\
      &\beta_{3j}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\mu_{\alpha_{j}} \\
      &\mu_{\beta_{1j}} \\
      &\mu_{\beta_{2j}} \\
      &\mu_{\beta_{3j}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cccc}
     \sigma^2_{\alpha_{j}} & 0 & 0 & 0 \\ 
     0 & \sigma^2_{\beta_{1j}} & 0 & 0 \\ 
     0 & 0 & \sigma^2_{\beta_{2j}} & 0 \\ 
     0 & 0 & 0 & \sigma^2_{\beta_{3j}}
  \end{array}
\right)
 \right)
    \text{, for sch.id j = 1,} \dots \text{,J}
\end{aligned}
$$

$$
\begin{aligned}
  \operatorname{score}_{i}  &\sim N \left(\alpha_{j[i],k[i],l[i],m[i]} + \beta_{1j[i],k[i],m[i]}(\operatorname{wave}), \sigma^2 \right) \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{j} \\
      &\beta_{1j}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\mu_{\alpha_{j}} \\
      &\mu_{\beta_{1j}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     \sigma^2_{\alpha_{j}} & 0 \\ 
     0 & \sigma^2_{\beta_{1j}}
  \end{array}
\right)
 \right)
    \text{, for sid j = 1,} \dots \text{,J} \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{k} \\
      &\beta_{1k}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\mu_{\alpha_{k}} \\
      &\mu_{\beta_{1k}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     \sigma^2_{\alpha_{k}} & \rho_{\alpha_{k}\beta_{1k}} \\ 
     \rho_{\beta_{1k}\alpha_{k}} & \sigma^2_{\beta_{1k}}
  \end{array}
\right)
 \right)
    \text{, for school k = 1,} \dots \text{,K} \\    \alpha_{l}  &\sim N \left(\mu_{\alpha_{l}}, \sigma^2_{\alpha_{l}} \right)
    \text{, for school.1 l = 1,} \dots \text{,L} \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{m} \\
      &\beta_{1m}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\mu_{\alpha_{m}} \\
      &\mu_{\beta_{1m}}
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     \sigma^2_{\alpha_{m}} & 0 \\ 
     0 & \sigma^2_{\beta_{1m}}
  \end{array}
\right)
 \right)
    \text{, for district m = 1,} \dots \text{,M}
\end{aligned}
$$

Nested model syntax works

$$
\begin{aligned}
  \operatorname{score}_{i}  &\sim N \left(\alpha_{j[i],k[i]}, \sigma^2 \right) \\
    \alpha_{j}  &\sim N \left(\mu_{\alpha_{j}}, \sigma^2_{\alpha_{j}} \right)
    \text{, for school:sid j = 1,} \dots \text{,J} \\
    \alpha_{k}  &\sim N \left(\mu_{\alpha_{k}}, \sigma^2_{\alpha_{k}} \right)
    \text{, for sid k = 1,} \dots \text{,K}
\end{aligned}
$$

$$
\begin{aligned}
  \operatorname{score}_{i}  &\sim N \left(\alpha_{j[i],k[i]}, \sigma^2 \right) \\
    \alpha_{j}  &\sim N \left(\mu_{\alpha_{j}}, \sigma^2_{\alpha_{j}} \right)
    \text{, for school:sid j = 1,} \dots \text{,J} \\
    \alpha_{k}  &\sim N \left(\mu_{\alpha_{k}}, \sigma^2_{\alpha_{k}} \right)
    \text{, for sid k = 1,} \dots \text{,K}
\end{aligned}
$$

$$
\begin{aligned}
  \operatorname{score}_{i}  &\sim N \left(\alpha_{j[i],k[i]}, \sigma^2 \right) \\
    \alpha_{j}  &\sim N \left(\mu_{\alpha_{j}}, \sigma^2_{\alpha_{j}} \right)
    \text{, for school:sid j = 1,} \dots \text{,J} \\
    \alpha_{k}  &\sim N \left(\mu_{\alpha_{k}}, \sigma^2_{\alpha_{k}} \right)
    \text{, for sid k = 1,} \dots \text{,K}
\end{aligned}
$$

use_coef works

$$
\begin{aligned}
  \operatorname{\widehat{score}}_{i}  &\sim N \left(98.18_{\alpha_{j[i],k[i],l[i]}} + 0.17_{\beta_{1j[i],k[i]}}(\operatorname{wave}), \sigma^2 \right) \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{j} \\
      &\beta_{1j}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &-2.1_{\gamma_{1}^{\alpha}}(\operatorname{treatment}_{\operatorname{1}}) \\
      &0
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     9.26 & -0.2 \\ 
     -0.2 & 0.29
  \end{array}
\right)
 \right)
    \text{, for sid j = 1,} \dots \text{,J} \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{k} \\
      &\beta_{1k}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &0 \\
      &0
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     3.24 & 1 \\ 
     1 & 0.01
  \end{array}
\right)
 \right)
    \text{, for school k = 1,} \dots \text{,K} \\    \alpha_{l}  &\sim N \left(0, 0 \right)
    \text{, for district l = 1,} \dots \text{,L}
\end{aligned}
$$

return variances works

$$
\begin{aligned}
  \operatorname{\widehat{score}}_{i}  &\sim N \left(98.18_{\alpha_{j[i],k[i],l[i]}} + 0.17_{\beta_{1j[i],k[i]}}(\operatorname{wave}), \sigma^2 \right) \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{j} \\
      &\beta_{1j}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &-2.1_{\gamma_{1}^{\alpha}}(\operatorname{treatment}_{\operatorname{1}}) \\
      &0
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     85.78 & -0.53 \\ 
     -0.53 & 0.09
  \end{array}
\right)
 \right)
    \text{, for sid j = 1,} \dots \text{,J} \\    
\left(
  \begin{array}{c} 
    \begin{aligned}
      &\alpha_{k} \\
      &\beta_{1k}
    \end{aligned}
  \end{array}
\right)
  &\sim N \left(
\left(
  \begin{array}{c} 
    \begin{aligned}
      &0 \\
      &0
    \end{aligned}
  \end{array}
\right)
, 
\left(
  \begin{array}{cc}
     10.47 & 0.02 \\ 
     0.02 & 0
  \end{array}
\right)
 \right)
    \text{, for school k = 1,} \dots \text{,K} \\    \alpha_{l}  &\sim N \left(0, 0 \right)
    \text{, for district l = 1,} \dots \text{,L}
\end{aligned}
$$

equatiomatic documentation built on Jan. 31, 2022, 1:06 a.m.