[FR] Support for shared mixture model #1778
Description
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)).