Models 8.4 and 8.5

[ASKurz]

I've been unable to figure out the brms equivalent to McElreath’s:

#8.4
m8.4 <- map2stan(
    alist(
        y ~ dnorm( mu , sigma ) ,
        mu <- a1 + a2 ,
        sigma ~ dcauchy( 0 , 1 )
),
data=list(y=y) , start=list(a1=0,a2=0,sigma=1) , chains=2 , iter=4000 , warmup=1000 ) 

#8.5
m8.5 <- map2stan(
    alist(
        y ~ dnorm( mu , sigma ) ,
        mu <- a1 + a2 ,
        a1 ~ dnorm( 0 , 10 ) ,
        a2 ~ dnorm( 0 , 10 ) ,
        sigma ~ dcauchy( 0 , 1 )
),
data=list(y=y) , start=list(a1=0,a2=0,sigma=1) , chains=2 , iter=4000 , warmup=1000 ) 

It's the double intercept. It has me stumped.

[paul-buerkner]

Define two variables, name tham, say, intercept1 and intercept2 and set them to 1 for all observations. Then specify y ~ 0 + intercept1 + intercept2.

[ASKurz]

Ah; thanks for the idea, Paul! Along those lines, this works for model 8.5:

y <- rnorm(100, mean = 0, sd = 1)

b8.5 <-
  brm(data = list(y = y,
                  intercept1 = 1,
                  intercept2 = 1), 
      family = gaussian,
      y ~ 0 + intercept1 + intercept2,
      prior = c(set_prior("normal(0, 10)", class = "b"),
                set_prior("cauchy(0, 1)", class = "sigma")),
      inits = list(list(intercept1 = 0, intercept2 = 0, sigma = 1),
                   list(intercept1 = 0, intercept2 = 0, sigma = 1)),
      chains = 2, iter = 4000, warmup = 1000)

Is there a way to approach the challenge without altering the data?

[paul-buerkner]

Nope. To be honest, having two intercepts in the same model is pretty arcane and so there is not built-in solution for this. Please note that the "Intercept" inits won't work the way you specified them.

[ASKurz]

Ha. I caught the inits issue right around the time you responded.

Thanks, again, for the help.