Nonlinear syntax with a multinomial model?

Interfaces brms
3

Thanks for the nudge, @paul.buerkner. I think I have it. For the sake of continuity, I’m going to switch to the Fishing data used in GitHub issue #560. For anyone else following, that example was based on a conditional logistic model, which I’m not totally up on but I believe is an alternative parameterization of what I’m calling the multinomial model. Anyway, the code below fits an intercepts-only multinomial model for the 4-category response variable mode. In this example, the reference category will be "boat". I’ll show how to fit the model with three styles of syntax, what I’m going to call

  • the conventional syntax (fish1a),
  • the verbose syntax (fish1b), and
  • the nonlinear syntax (fish1c).
library(brms)
data("Fishing", package = "mlogit")

# conventional syntax
fish1a <-
  brm(data = Fishing, 
      family = categorical(link = logit, refcat = "boat"),
      mode ~ 1,
      prior = c(prior(normal(0, 1), class = Intercept, dpar = mubeach),
                prior(normal(0, 1), class = Intercept, dpar = mucharter),
                prior(normal(0, 1), class = Intercept, dpar = mupier)))

# verbose syntax
fish1b <-
  brm(data = Fishing, 
      family = categorical(link = logit, refcat = "boat"),
      bf(mode ~ 1,
         mubeach ~ 1,
         mucharter ~ 1,
         mupier ~ 1),
      prior = c(prior(normal(0, 1), class = Intercept, dpar = mubeach),
                prior(normal(0, 1), class = Intercept, dpar = mucharter),
                prior(normal(0, 1), class = Intercept, dpar = mupier)))

# nonlinear syntax 
fish1c <-
  brm(data = Fishing, 
      family = categorical(link = logit, refcat = "boat"),
      bf(mode ~ 1,
         nlf(mubeach ~ abeach),
         nlf(mucharter ~ acharter),
         nlf(mupier ~ apier),
         abeach + acharter + apier ~ 1),
      prior = c(prior(normal(0, 1), class = b, nlpar = abeach),
                prior(normal(0, 1), class = b, nlpar = acharter),
                prior(normal(0, 1), class = b, nlpar = apier)))

The results are the same for all.

                    Estimate Est.Error  Q2.5 Q97.5
mubeach_Intercept      -1.13      0.10 -1.32 -0.94
mupier_Intercept       -0.85      0.09 -1.02 -0.67
mucharter_Intercept     0.08      0.07 -0.05  0.21
                    Estimate Est.Error  Q2.5 Q97.5
mubeach_Intercept      -1.13      0.10 -1.32 -0.94
mupier_Intercept       -0.85      0.09 -1.02 -0.67
mucharter_Intercept     0.08      0.07 -0.05  0.21
                   Estimate Est.Error  Q2.5 Q97.5
abeach_Intercept      -1.13      0.10 -1.33 -0.94
acharter_Intercept     0.08      0.07 -0.04  0.22
apier_Intercept       -0.85      0.09 -1.02 -0.68