Set up a finite mixture family for use in brms.

mixture(..., flist = NULL, nmix = 1, order = NULL)

## Arguments

... One or more objects providing a description of the response distributions to be combined in the mixture model. These can be family functions, calls to family functions or character strings naming the families. For details of supported families see brmsfamily. Optional list of objects, which are treated in the same way as objects passed via the ... argument. Optional numeric vector specifying the number of times each family is repeated. If specified, it must have the same length as the number of families passed via ... and flist. Ordering constraint to identify mixture components. If 'mu' or TRUE, population-level intercepts of the mean parameters are ordered in non-ordinal models and fixed to the same value in ordinal models (see details). If 'none' or FALSE, no ordering constraint is applied. If NULL (the default), order is set to 'mu' if all families are the same and 'none' otherwise. Other ordering constraints may be implemented in the future.

## Value

An object of class mixfamily.

## Details

Most families supported by brms can be used to form mixtures. The response variable has to be valid for all components of the mixture family. Currently, the number of mixture components has to be specified by the user. It is not yet possible to estimate the number of mixture components from the data.

Ordering intercepts in mixtures of ordinal families is not possible as each family has itself a set of vector of intercepts (i.e. ordinal thresholds). Instead, brms will fix the vector of intercepts across components in ordinal mixtures, if desired, so that users can try to identify the mixture model via selective inclusion of predictors.

For most mixture models, you may want to specify priors on the population-level intercepts via set_prior to improve convergence. In addition, it is sometimes necessary to set inits = 0 in the call to brm to allow chains to initialize properly.

For more details on the specification of mixture models, see brmsformula.

## Examples

if (FALSE) {
## simulate some data
set.seed(1234)
dat <- data.frame(
y = c(rnorm(200), rnorm(100, 6)),
x = rnorm(300),
z = sample(0:1, 300, TRUE)
)

## fit a simple normal mixture model
mix <- mixture(gaussian, gaussian)
prior <- c(
prior(normal(0, 7), Intercept, dpar = mu1),
prior(normal(5, 7), Intercept, dpar = mu2)
)
fit1 <- brm(bf(y ~ x + z), dat, family = mix,
prior = prior, chains = 2)
summary(fit1)
pp_check(fit1)

## use different predictors for the components
fit2 <- brm(bf(y ~ 1, mu1 ~ x, mu2 ~ z), dat, family = mix,
prior = prior, chains = 2)
summary(fit2)

## fix the mixing proportions
fit3 <- brm(bf(y ~ x + z, theta1 = 1, theta2 = 2),
dat, family = mix, prior = prior,
inits = 0, chains = 2)
summary(fit3)
pp_check(fit3)

## predict the mixing proportions
fit4 <- brm(bf(y ~ x + z, theta2 ~ x),
dat, family = mix, prior = prior,
inits = 0, chains = 2)
summary(fit4)
pp_check(fit4)

## compare model fit
LOO(fit1, fit2, fit3, fit4)
}