Beta-Binomial Residuals

This parameterization of the beta-binomial distribution uses an expected probability parameter, prob, and a dispersion parameter, theta. The parameters of the underlying beta mixture are alpha = (2 * prob) / theta and beta = (2 * (1 - prob)) / theta. This parameterization of theta is unconventional, but has useful properties when modelling. When theta = 0, the beta-binomial reverts to the binomial distribution. When theta = 1 and prob = 0.5, the parameters of the beta distribution become alpha = 1 and beta = 1, which correspond to a uniform distribution for the beta-binomial probability parameter.

Usage

res_beta_binom(
  x,
  size = 1,
  prob = 0.5,
  theta = 0,
  type = "dev",
  simulate = FALSE
)

Arguments

x

A non-negative whole numeric vector of values.

size

A non-negative whole numeric vector of the number of trials.

prob

A numeric vector of values between 0 and 1 of the probability of success.

theta

A non-negative numeric vector of the dispersion for the mixture models (student, gamma-Poisson and beta-binomial).

type

A string of the residual type. 'raw' for raw residuals 'dev' for deviance residuals and 'data' for the data.

simulate

A flag specifying whether to simulate residuals.

Value

An numeric vector of the corresponding residuals.

See also

Other res_dist: res_bern(), res_binom(), res_gamma(), res_gamma_pois(), res_gamma_pois_zi(), res_lnorm(), res_neg_binom(), res_norm(), res_pois(), res_pois_zi(), res_skewnorm(), res_student()

Examples

res_beta_binom(c(0, 1, 2), 4, 0.5, 0.1)
#> [1] -2.2434148 -0.9346019  0.0000000