rqbinom function

Sampling of overdispersed binomial data with constant overdispersion

rqbinom samples overdispersed binomial data with constant overdispersion from the beta-binomial distribution such that the quasi-binomial assumption is fulfilled.

rqbinom(n, size, prob, phi)

Arguments

• n: defines the number of clusters ($i$)
• size: integer vector defining the number of trials per cluster ($n_i$)
• prob: probability of success on each trial ($\pi$)
• phi: dispersion parameter ($\Phi$)

Returns

a data.frame with two columns (succ, fail)

Details

It is assumed that the dispersion parameter ($\Phi$) is constant for all $i=1, ... I$ clusters, such that the variance becomes

For the sampling $(a+b)_i$ is defined as

where $a_i=\pi (a+b)_i$ and $b_i=(a+b)_i-a_i$. Then, the binomial proportions for each cluster are sampled from the beta distribution

and the numbers of success for each cluster are sampled to be

In this parametrization $E(\pi_i)=\pi$ and $E(y_i)=n_i \pi$. Please note, the quasi-binomial assumption is not in contradiction with the beta-binomial distribution if all cluster sizes are the same.

Examples

# Sampling of example data
set.seed(456)
qb_dat1 <- rqbinom(n=10, size=50, prob=0.1, phi=3)
qb_dat1

set.seed(456)
qb_dat2 <- rqbinom(n=3, size=c(40, 50, 60), prob=0.1, phi=3)
qb_dat2