Estimate theta of the Negative Binomial

Given the estimated mean vector, estimate theta overdispersion parameter of the negative binomial distribution.

Usage

nb_theta(
  y,
  mu,
  n,
  weights,
  left = -10,
  right = 20,
  tol = .Machine$double.eps^0.25
)

Arguments

y

vector of observed values from the negative binomial.

mu

estimated mean vector from generalized linear model

n

number of data points (defaults to the sum of weights)

weights

sample weights. If missing, set to 1

left

left boundary for estimating theta on a log scale. So -10 corresponds to a minimum theta value of exp(-10)

right

right boundary for estimating theta on a log scale

tol

tolerance of optimization

Details

Estimate overdispersion parameter for negative binomial distribution using univariate optimization with Brent's method. For very large datasets, this can be much faster than the Newton-Raphson method used by MASS::theta.ml(). This is faster since the lgamma() function used in the likelihood is faster than the digamma() and trigamma() functions used in the score and information steps. Also, the univariate optimization is performed on log(theta), while the Newton-Raphson approach is performed on the original scale of theta.

See also

MASS::theta.ml()

Examples

library(MASS)

quine.nb <- glm.nb(Days ~ .^2, data = quine)
# estimate from MASS package
theta.ml(quine$Days, fitted(quine.nb), limit=200, eps=1e-6)
#> [1] 1.603641
#> attr(,"SE")
#> [1] 0.2138379

# faster for large-scale data
nb_theta(quine$Days, fitted(quine.nb))
#> [1] 1.603654