Could you please clarify how to interpret the theta2_covar coefficient (I know model fit is very poor)? Is it the log odds of being in mixture 2?

## simulate some data

set.seed(1234)

dat ← data.frame(

y = c(rnorm(100), rnorm(50, 2)),

x = rnorm(150),

covar = rnorm(150)

)

## fit a simple normal mixture model

fit1 ← brm(bf(y ~ x,

theta2 ~ covar),

data = dat,

family = mixture(gaussian, nmix = 2),

chains = 2, init = 0)

summary(fit1)

Family: mixture(gaussian, gaussian)

Links: mu1 = identity; sigma1 = identity; mu2 = identity; sigma2 = identity; theta1 = identity; theta2 = identity

Formula: y ~ x

theta2 ~ covar

Data: dat (Number of observations: 150)

Draws: 2 chains, each with iter = 2000; warmup = 1000; thin = 1;

total post-warmup draws = 2000

Population-Level Effects:

Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS

mu1_Intercept 0.33 0.38 -0.50 0.74 1.21 7 22

mu2_Intercept 0.70 0.16 0.42 1.06 1.03 61 139

theta2_Intercept 2.91 6.05 -8.29 13.70 1.17 31 117

mu1_x -0.03 0.33 -0.56 0.57 1.10 15 73

mu2_x -0.03 0.25 -0.52 0.45 1.02 31 156

theta2_covar 57.77 133.76 -177.65 299.19 1.14 25 130

Family Specific Parameters:

Estimate Est.Error l-95% CI u-95% CI Rhat Bulk_ESS Tail_ESS

sigma1 1.33 0.34 0.54 1.76 1.19 12 16

sigma2 1.40 0.15 1.13 1.73 1.06 41 171