13 bookdown version 1.0.4--better \text{} solution

Author: ASKurz

13.Rmd

@@ -424,8 +424,8 @@ The statistical formula for our varying-intercepts logistic regression model fol
 
 \begin{align*}
 \text{admit}_i         & \sim \text{Binomial} (n_i, p_i) \\
-\text{logit} (p_i)     & = \alpha_{\text{dept\_id}_i} + \beta \text{male}_i \\
-\alpha_\text{dept\_id} & \sim \text{Normal} (\alpha, \sigma) \\
+\text{logit} (p_i)     & = \alpha_{\text{dept_id}_i} + \beta \text{male}_i \\
+\alpha_\text{dept_id} & \sim \text{Normal} (\alpha, \sigma) \\
 \alpha                 & \sim \text{Normal} (0, 10) \\
 \beta                  & \sim \text{Normal} (0, 1) \\
 \sigma                 & \sim \text{HalfCauchy} (0, 2) \\
@@ -526,8 +526,8 @@ Now we're ready to allow our `male` dummy to varies, too, the statistical model
 
 \begin{align*}
 \text{admit}_i     & \sim \text{Binomial} (n_i, p_i) \\
-\text{logit} (p_i) & = \alpha_{\text{dept\_id}_i} + \beta_{\text{dept\_id}_i} \text{male}_i \\
-\begin{bmatrix} \alpha_\text{dept\_id} \\ \beta_\text{dept\_id} \end{bmatrix} & \sim \text{MVNormal} \bigg (\begin{bmatrix} \alpha \\ \beta \end{bmatrix}, \mathbf{S}  \bigg ) \\
+\text{logit} (p_i) & = \alpha_{\text{dept_id}_i} + \beta_{\text{dept_id}_i} \text{male}_i \\
+\begin{bmatrix} \alpha_\text{dept_id} \\ \beta_\text{dept_id} \end{bmatrix} & \sim \text{MVNormal} \bigg (\begin{bmatrix} \alpha \\ \beta \end{bmatrix}, \mathbf{S}  \bigg ) \\
 \mathbf S & = \begin{pmatrix} \sigma_\alpha & 0 \\ 0 & \sigma_\beta \end{pmatrix} \mathbf R \begin{pmatrix} \sigma_\alpha & 0 \\ 0 & \sigma_\beta \end{pmatrix} \\
 \alpha                        & \sim \text{Normal} (0, 10) \\
 \beta                         & \sim \text{Normal} (0, 1) \\
@@ -776,24 +776,24 @@ d <-
 My math's aren't the best. But if I'm following along correctly, here's a fuller statistical expression of our cross-classified model.
 
 \begin{align*}
-\text{pulled\_left}_i      & \sim \text{Binomial} (n = 1, p_i) \\
-\text{logit} (p_i)         & = \alpha_i + (\beta_{1i} + \beta_{2i} \text{condition}_i) \text{prosoc\_left}_i  \\
-\alpha_i                   & = \alpha + \alpha_{\text{actor}_i} + \alpha_{\text{block\_id}_i} \\
-\beta_{1i}                 & = \beta_1 + \beta_{1, \text{actor}_i} + \beta_{1, \text{block\_id}_i} \\
-\beta_{2i}                 & = \beta_2 + \beta_{2, \text{actor}_i} + \beta_{2, \text{block\_id}_i} \\
+\text{pulled_left}_i       & \sim \text{Binomial} (n = 1, p_i) \\
+\text{logit} (p_i)         & = \alpha_i + (\beta_{1i} + \beta_{2i} \text{condition}_i) \text{prosoc_left}_i  \\
+\alpha_i                   & = \alpha + \alpha_{\text{actor}_i} + \alpha_{\text{block_id}_i} \\
+\beta_{1i}                 & = \beta_1 + \beta_{1, \text{actor}_i} + \beta_{1, \text{block_id}_i} \\
+\beta_{2i}                 & = \beta_2 + \beta_{2, \text{actor}_i} + \beta_{2, \text{block_id}_i} \\
 \begin{bmatrix} \alpha_\text{actor} \\ \beta_{1, \text{actor}} \\ \beta_{2, \text{actor}} \end{bmatrix} & \sim \text{MVNormal} \begin{pmatrix} \begin{bmatrix}0 \\ 0 \\ 0 \end{bmatrix} , \mathbf{S}_\text{actor} \end{pmatrix} \\
-\begin{bmatrix} \alpha_\text{block\_id} \\ \beta_{1, \text{block\_id}} \\ \beta_{2, \text{block\_id}} \end{bmatrix} & \sim \text{MVNormal} \begin{pmatrix} \begin{bmatrix}0 \\ 0 \\ 0 \end{bmatrix} , \mathbf{S}_\text{block\_id} \end{pmatrix} \\
+\begin{bmatrix} \alpha_\text{block_id} \\ \beta_{1, \text{block_id}} \\ \beta_{2, \text{block_id}} \end{bmatrix} & \sim \text{MVNormal} \begin{pmatrix} \begin{bmatrix}0 \\ 0 \\ 0 \end{bmatrix} , \mathbf{S}_\text{block_id} \end{pmatrix} \\
 \mathbf S_\text{actor}     & = \begin{pmatrix} \sigma_{\alpha_\text{actor}} & 0 & 0 \\ 0 & \sigma_{\beta_{1_\text{actor}}} & 0 \\ 0 & 0 & \sigma_{\beta_{2_\text{actor}}} \end{pmatrix} 
 \mathbf R_\text{actor} \begin{pmatrix} \sigma_{\alpha_\text{actor}} & 0 & 0 \\ 0 & \sigma_{\beta_{1_\text{actor}}} & 0 \\ 0 & 0 & \sigma_{\beta_{2_\text{actor}}} \end{pmatrix} \\
-\mathbf S_\text{block\_id} & = \begin{pmatrix} \sigma_{\alpha_\text{block\_id}} & 0 & 0 \\ 0 & \sigma_{\beta_{1_\text{block\_id}}} & 0 \\ 0 & 0 & \sigma_{\beta_{2_\text{block\_id}}} \end{pmatrix} 
-\mathbf R_\text{block\_id} \begin{pmatrix} \sigma_{\alpha_\text{block\_id}} & 0 & 0 \\ 0 & \sigma_{\beta_{1_\text{block\_id}}} & 0 \\ 0 & 0 & \sigma_{\beta_{2_\text{block\_id}}} \end{pmatrix} \\
+\mathbf S_\text{block_id}  & = \begin{pmatrix} \sigma_{\alpha_\text{block_id}} & 0 & 0 \\ 0 & \sigma_{\beta_{1_\text{block_id}}} & 0 \\ 0 & 0 & \sigma_{\beta_{2_\text{block_id}}} \end{pmatrix} 
+\mathbf R_\text{block_id} \begin{pmatrix} \sigma_{\alpha_\text{block_id}} & 0 & 0 \\ 0 & \sigma_{\beta_{1_\text{block_id}}} & 0 \\ 0 & 0 & \sigma_{\beta_{2_\text{block_id}}} \end{pmatrix} \\
 \alpha                     & \sim \text{Normal} (0, 1) \\
 \beta_1                    & \sim \text{Normal} (0, 1) \\
 \beta_2                    & \sim \text{Normal} (0, 1) \\
 (\sigma_{\alpha_\text{actor}}, \sigma_{\beta_{1_\text{actor}}}, \sigma_{\beta_{2_\text{actor}}}) & \sim \text{HalfCauchy} (0, 2) \\
-(\sigma_{\alpha_\text{block\_id}}, \sigma_{\beta_{1_\text{block\_id}}}, \sigma_{\beta_{2_\text{block\_id}}}) & \sim \text{HalfCauchy} (0, 2) \\
+(\sigma_{\alpha_\text{block_id}}, \sigma_{\beta_{1_\text{block_id}}}, \sigma_{\beta_{2_\text{block_id}}}) & \sim \text{HalfCauchy} (0, 2) \\
 \mathbf R_\text{actor}     & \sim \text{LKJcorr} (4) \\
-\mathbf R_\text{block\_id} & \sim \text{LKJcorr} (4)
+\mathbf R_\text{block_id}  & \sim \text{LKJcorr} (4)
 \end{align*}
 
 And now each $\mathbf R$ is a $3 \times 3$ correlation matrix.