Model definitions

Formal math

\[ \begin{aligned} &\ \textbf{Multinomial probability of selection of choice}_i \textbf{ in respondent}_j \\ \text{Choice}_{i_j} \sim&\ \operatorname{Categorical}(\{\mu_{1,i_j}, \mu_{2,i_j}, \mu_{3,i_j}\}) \\[10pt] &\ \textbf{Model for probability of each option} \\ \{\mu_{1,i_j}, \mu_{2,i_j}, \mu_{3,i_j}\} =&\ (\beta_0 + b_{0_j}) + \beta_1 \text{Organization[Greenpeace]}_{i_j} + \beta_2 \text{Organization[Oxfam]}_{i_j} + \\ &\ \beta_3 \text{Organization[Red Cross]}_{i_j} + \beta_4 \text{Issue[Environment]}_{i_j} + \\ &\ \beta_5 \text{Issue[Human rights]}_{i_j} + \beta_6 \text{Issue[Refugee relief]}_{i_j} + \\ &\ \beta_7 \text{Transparency[Yes]}_{i_j} + \beta_8 \text{Accountability[Yes]}_{i_j} + \\ &\ \beta_9 \text{Funding[Few wealthy donors]}_{i_j} + \beta_{10} \text{Funding[Government grants]}_{i_j} + \\ &\ \beta_{11} \text{Government relationship[Criticized]}_{i_j} + \\ &\ \beta_{12} \text{Government relationship[Under crackdown]}_{i_j} \\[5pt] b_{0_j} \sim&\ \mathcal{N}(0, \sigma_0) \qquad\quad\quad \text{Respondent-specific offsets from global probability} \\[10pt] &\ \textbf{Priors} \\ \beta_{0 \dots 12} \sim&\ \mathcal{N} (0, 3) \qquad\qquad\ \ \text{Prior for choice-level coefficients} \\ \sigma_0 \sim&\ \operatorname{Exponential}(1) \quad \text{Prior for between-respondent variability} \end{aligned} \]

R code

R/funs_models.R

f_treatment_only <- function(dat) {
  BAYES_SEED <- 706615  # From random.org

  categorical_priors <- c(
    prior(normal(0, 3), class = b, dpar = mu1),
    prior(normal(0, 3), class = b, dpar = mu2),
    prior(normal(0, 3), class = b, dpar = mu3),
    prior(exponential(1), class = sd, dpar = mu1),
    prior(exponential(1), class = sd, dpar = mu2),
    prior(exponential(1), class = sd, dpar = mu3) # ,
  )

  model <- brm(
    bf(choice_alt ~
      # Conjoint attributes (treatment variables)
      feat_org + feat_issue + feat_transp + feat_acc + feat_funding + feat_govt +
      # Respondent-specific intercepts
      (1 | id)),
    data = dat,
    family = categorical(refcat = "0"),
    prior = categorical_priors,
    chains = 4, warmup = 1000, iter = 5000, seed = BAYES_SEED, refresh = 10
  )

  return(model)
}