Hi everyone,

I have a logistic hierarchical model that I ran using `brms`

:

`correct ~ 1 + experiment * phase + (1 + experiment * phase | strategy/subject)`

Here, I wanted to predict the probability of getting a correct response, having experiment (categorical 2 levels) and phase (categorical 2 levels) as predictors; also, I have participants clustered within groups, and I wanted to get varying intercepts and effects for them, I used the following priors:

`priors_logistic <- c(prior(normal(2, 2), class = b), prior(normal(2, 2), class = Intercept), prior(lkj(2), class = cor), prior(normal(0, 2), class = sd))`

I want to report this model, and I am struggling to find an example similar to this to write the equation (having both varying intercept, effects and the interaction for nested clusters). So far this is what I think it should look like:

\begin{align*} \text{correct}_i & \sim \operatorname{Binomial}(n_i, p_i) \\ logit(p_i) & = \alpha_{jk[i]} + \beta_{1jk[i]}experiment + \beta_{2jk[i]}phase + \beta_{3jk[i]}experiment \times phase \\ \begin{bmatrix} \alpha_{jk} \\ \beta_{1jk} \\ \beta_{2jk} \\ \beta_{3jk}\end{bmatrix} & \sim \text{MVNormal} \left (\begin{bmatrix} \alpha \\ \beta_{1} \\ \beta_{2} \\ \beta_{3}\end{bmatrix}, \mathbf{S} \right ) \\ \mathbf{S} & = \begin{bmatrix} \sigma_\alpha & 0 & 0 & 0 \\ 0 & \sigma_{\beta_{1}} & 0 & 0 \\ 0 & 0 & \sigma_{\beta_{2}} & 0 \\ 0 & 0 & 0 & \sigma_{\beta_{3}} \end{bmatrix} \mathbf R \begin{bmatrix} \sigma_\alpha & 0 & 0 & 0 \\ 0 & \sigma_{\beta_{1}} & 0 & 0 \\ 0 & 0 & \sigma_{\beta_{2}} & 0 \\ 0 & 0 & 0 & \sigma_{\beta_{3}} \end{bmatrix} \\ \alpha & \sim \operatorname{Normal}(2,2) \\ \beta_{1}, \beta_{2} \ and\ \beta_{3} & \sim \operatorname{Normal}(2,2) \\ \sigma_{\alpha}, \sigma_{\beta_{1}}, \sigma_{\beta_{2}} \ and \ \sigma_{\beta_{3}} & \sim \operatorname{HalfNormal}(0,2) \\ R & \sim \operatorname{LKJcorr}(2) \end{align*}

But I am not sure if these lay out the model correctly. Thanks for your help!