[FR] Support for shared mixture model

[trinhdhk]

Currently when specifying a multivariate mixture model, the model assumes 3 independent sets of mixtures (theta_y1, theta_y2, theta_y3). Is there any plan for supporting the shared mixture model, as in constraining theta_y1 = theta_y2 = theta_y3 = theta.

x <- rnorm(1000)
x2 <- rpois(1000,2)
u <- rnorm(1000)
lp <- -.5+x+0.2*x2
mu1 <- c(0.5, -0.2, 0) |> sapply('+', 0.5 * x)
mu2 <- c(-1.5, -1, -0.5)

y <- sapply(seq_along(z),
            function(i){
              if (z[i] == 1) {
                return(sapply(plogis(mu1[i,]), rbinom, n=1, size=1))
              }
              sapply(plogis(mu2), rbinom, n=1, size=1)
            }) |> t()
colnames(y) <- paste0('y', 1:3)

dataset <-
  data.frame(x=x, x2=x2,) |> cbind(y)

# demonstration, I don't think this is identifiable
model <-
  brm(
    bf(y1 ~ 1,
       theta1 ~ x+x2,
       mu1 ~ x,
       mu2 ~ 1) +
      bf(y2 ~ 1,
         theta1 ~ x+x2,
         mu1 ~ x,
         mu2 ~ 1) +
      bf(y3 ~ 1,
         theta1 ~ x+x2,
         mu1 ~ x,
         mu2 ~ 1) +
      set_rescor(FALSE),
    algorithm='fullrank',
    tol_rel_obj = 1e-4,
    iter=4000,
    cores=2, chains=2,
    family = mixture(bernoulli, bernoulli),
    data = dataset
  )

model

Family: MV(mixture(bernoulli, bernoulli), mixture(bernoulli, bernoulli), mixture(bernoulli, bernoulli)) 
  Links: mu1 = logit; mu2 = logit; theta1 = identity; theta2 = identity
         mu1 = logit; mu2 = logit; theta1 = identity; theta2 = identity
         mu1 = logit; mu2 = logit; theta1 = identity; theta2 = identity 
Formula: y1 ~ 1 
         theta1 ~ x + x2
         mu1 ~ x
         mu2 ~ 1
         y2 ~ 1 
         theta1 ~ x + x2
         mu1 ~ x
         mu2 ~ 1
         y3 ~ 1 
         theta1 ~ x + x2
         mu1 ~ x
         mu2 ~ 1
   Data: dataset (Number of observations: 1000) 
  Draws: 1 chains, each with iter = 1000; warmup = 0; thin = 1;
         total post-warmup draws = 1000

Regression Coefficients:
<...>

I find this type of model not very useful in many cases, as we can model them independently. Rather than MV(mixture(bernoulli, bernoulli), mixture(bernoulli, bernoulli), mixture(bernoulli, bernoulli), I believe there are more needs for mixture(MV(bernoulli, bernoulli, bernoulli), MV(bernoulli, bernoulli, bernoulli)).

[paul-buerkner]

In the formula, you should be able to do something like bf(..., theta2 = "theta1") I believe, which should do the trick, I hope.

[trinhdhk]

Thanks for the immediate response
Sorry, it was my typo, I meant theta1_y1 = theta1_y2 = theta1_y3, i.e. cross-outcome constraint.

Also,

In the formula, you should be able to do something like bf(..., theta2 = "theta1") I believe, which should do the trick, I hope.

model <-
  brm(
    bf(y1 ~ 1,
       theta1 ~ x+x2,
       mu1 ~ x,
       mu2 ~ 1) +
      bf(y2 ~ 1,
         # theta1 = 'theta1_y1',
         mu1 ~ x,
         mu2 ~ 1) +
      bf(y3 ~ 1,
         theta2 = 'theta1',
         mu1 ~ x,
         mu2 ~ 1) +
      set_rescor(FALSE),
    algorithm='fullrank',
    tol_rel_obj = 1e-4,
    iter=4000,
    cores=2, chains=2,
    family = mixture(bernoulli, bernoulli),
    data = dataset
  )

sum(unlist(fix_theta)) : invalid 'type' (character) of argument

[paul-buerkner]

Cross outcome will only be possible with brms 3.0.

[trinhdhk]

Cross outcome will only be possible with brms 3.0.

Thanks a lot. That is clear.
Any estimated timeline for that? I am in struggling between waiting for brms and implement the model in raw Stan.

[paul-buerkner]

I try to make it this year but with so much other stuff going on I am not sure. Trinh Dong ***@***.***> schrieb am Do., 15. Mai 2025, 11:49:

…

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