Multilevel modeling in brms

Interfaces brms
1

I am working on a model in which I would like the coefficient of one variable to be modeled as explicitly dependent on other variables. Generally speaking, the scenario is one in which we have a dichotomous outcome Y, a three-level predictor of interest A (0, 1, 2), and multiple additional covariates (x1, x2, x3). I would like to estimate the overall effect of A on Y, but also allow this effect to vary with respect to the covariates. I run into an error when running the model included below (“Error: Factors with more than two levels are not allowed as covariates.”). Any thoughts on how to best proceed (or approach this problem in a different way)?

df <-
  tibble(
    a = rep(c(0, 1, 2), each = 50),
    x1 = rnorm(150),
    x2 = rnorm(150),
    x3 = rnorm(150),
    y = rbinom(150, size = 1, prob = 0.5)
  ) %>%
  mutate(
    a = factor(a)
  )

model <-
  brm(
    data = df,
    family = bernoulli,
    formula = bf(y ~ (b1 * a) + b2 + b3 + b4,
                 b1 ~ 1 + x1 + x2 + x3,
                 b2 ~ 0 + x1,
                 b3 ~ 0 + x2,
                 b4 ~ 0 + x3,
                 nl = TRUE),
    prior = c(prior(normal(0, 1.5), nlpar = "b1"),
              prior(normal(0, 1.5), nlpar = "b2"),
              prior(normal(0, 1.5), nlpar = "b3"),
              prior(normal(0, 1.5), nlpar = "b4")),
    iter = 1000, warmup = 200, chains = 1, cores = 1,
    seed = 19
  )
  • Operating System: macOS Mojave 10.4.3
  • brms Version: 2.8.0
2

Hi, not an expert on brms, but since others have not chimed in, I will give it a try.

This is a problem only because you are using the non-linear features of brms which work quite differently than the base version. In particular, there is no coefficient associated with the b1 term in the formula for y and so it doesn’t make sense to vary this coefficient for each level of the factor. If you want to do this, you IMHO should instead have something like y ~ b1 + b2 + b3 + b4 and b1 ~ a * (1 + x1 + x2 + x3)

But the main question is: Why do you want to use the non-linear features, why isn’t something like

y ~ a + a*x1 + a *x2 +a *x3

acceptable?

1 Like
3

Apologies for the delay - thanks so much for your response! I think your main question is absolutely right – I had run myself in circles trying to solve a problem that was actually more simple than I had thought.

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