Hi everyone,
Can someone please help me with the appropriate mathematical notation for the model below?
brms code:
Outcome ~ 1 + A + F + mo(E) + mo(H) + P + S + (1 | id) + (1 | wave)
Where Outcome has 5 responses, E has 3, H has 4. Also, I have \approx 1000 individuals and 50 waves.
I have also specified the following priors (if any look fishy, please let me know):
prior(normal(0, 1.5), class = "Intercept")
prior(normal(0, 1), class = "b")
prior(exponential(2), class = "sd")
prior(dirichlet(rep(2, 2)), class = "simo", coef = "moedu1")
prior(dirichlet(rep(2, 3)), class = "simo", coef = "moinc1")
I think that this is almost correct, but I don’t know if I’ve include the varying intercepts properly:
Outcome_{i} \sim \text{Ordered-logit}(\phi_{i}, \kappa)
\phi_{i} = \beta_{A}A_{i} + \beta_{F}F_{i} + \beta_{E} \sum_{n = 1}^{E_{i}}\zeta_{n} + \beta_{H} \sum_{m = 1}^{H_{i}}\zeta_{m} + \beta_{P}P_{i} + \beta_{S}S_{i}
\beta_{A}, \beta_{F}, \beta_{E}, \beta_{H}, \beta_{P}, \beta_{S} \sim \text{Normal}(0, 1)
\zeta_{b} \sim \text{Dirichlet}(\alpha_{E})
\zeta_{m} \sim \text{Dirichlet}(\alpha_{H})
\alpha_{E} = \left \{ 2, 2 \right \}
\alpha_{H} = \left \{ 2, 2, 2 \right \}
\kappa_k = \gamma_{ID\left [ i \right ]} + \tau_{WAVE\left [ i \right ]}
\gamma_{j} \sim \text{Normal}(\bar{\gamma}, \sigma_{\gamma}), \text{for } j = 1..1000
\tau_{j} \sim \text{Normal}(\bar{\tau}, \sigma_{\gamma}), \sigma_{\gamma}), \text{for } j = 1..50
\bar{\gamma}, \bar{\tau} \sim \text{Normal}(0, 1.5)
\sigma_{\gamma}, \sigma_{\tau} \sim \text{Exponential}(2)
Thanks in advance!