mcmcsae (version 0.8.1)

f_binomial: Specify a binomial sampling distribution

Description

This function can be used in the family argument of create_sampler or generate_data to specify a binomial sampling distribution.

Usage

f_binomial(
  link = c("logit", "probit"),
  n.trial = NULL,
  control = binomial_control()
)

Value

A family object.

Arguments

link

the name of a link function. Currently the only allowed link functions for the binomial distribution are "logit" (default) and "probit".

n.trial

the number of binomial trials. This can be specified either as a formula for a variable number of trials, or as a scalar value for a common number of trials for all units.

control

a list with computational options. These options can be specified using function binomial_control.

Details

For the binomial family, the left hand side of the formula argument of create_sampler can be specified in several ways (similar to the options allowed by glm for binomial family):

1

as a factor, character, or boolean variable, say y. In this case the first level of as.factor(y) is interpreted as 'failures' and all other values as 'successes'. This option can only be used for binary data.

2a

as a numeric or integer vector with no values strictly between 0 and 1. The values are then interpreted as numbers of successes. This requires specifying the number of trials through argument n.trial, unless the data is binary (values 0 and 1 only). For non-integer values a warning is issued.

2b

as a numeric vector with values between 0 and 1. The values are then interpreted as the proportion of the number of successes. This requires specifying the number of trials through argument n.trial.

3

as a two-column integer matrix. The first column is interpreted as the number of successes, the second column as the number of failures.

Examples

y <- c(TRUE, FALSE, TRUE)
sampler <- create_sampler(y ~ 1, family=f_binomial())
# logistic binary regression is the default, and may also be
# specified as family="binomial"
sim <- MCMCsim(sampler, n.chain=2, n.iter=100, burnin=50, verbose=FALSE)
summary(predict(sim, newdata=data.frame(id=1)))

y <- c(0, 0, 1, 1, 0, 0, 0, 0, 1)
sampler <- create_sampler(y ~ 1, family=f_binomial(link="probit"))
sim <- MCMCsim(sampler, n.chain=2, n.iter=100, burnin=50, verbose=FALSE)
summary(predict(sim, newdata=data.frame(id=1)))

sampler <- create_sampler(c(0.2, 0.3, 0.5, 0.0) ~ 1, family=f_binomial(n.trial=10))
# is interpreted as
sampler <- create_sampler(c(2, 3, 5, 0) ~ 1, family=f_binomial(n.trial=10))
sim <- MCMCsim(sampler, n.chain=2, n.iter=100, burnin=50, verbose=FALSE)
summary(predict(sim, newdata=data.frame(id=1)))

n <- 1000
dat <- data.frame(
  x = runif(n),
  g = factor(sample(1:10, n, replace=TRUE)),
  trials = sample(1:5, n, replace=TRUE)
)
v <- rnorm(10)
dat$y <- rbinom(n, size=dat$trials, prob=1 / (1 + exp(-(1 - dat$x + v[dat$g]))))
sampler <- create_sampler(y ~ x + (1|g), data=dat, family=f_binomial(n.trial = ~ trials))
# alternatively:
sampler <- create_sampler(cbind(y, trials - y) ~ x + (1|g), data=dat, family="binomial")
sim <- MCMCsim(sampler, store.all=TRUE, burnin=200, n.iter=300, n.chain=2, verbose=FALSE)
summ <- summary(sim)
plot(v, summ$gen2[, "Mean"]); abline(0, 1)