theta.mle: MLE of Theta for Negative Binomial

In npreg: Nonparametric Regression via Smoothing Splines

MLE of Theta for Negative Binomial

Description

Computes the maximum likelihood estimate of the size (theta) parameter for the Negative Binomial distribution via a Newton-Raphson algorithm.

Usage

theta.mle(y, mu, theta, wt = 1, 
          maxit = 100, maxth = .Machine$double.xmax,
          tol = .Machine$double.eps^0.5)

Arguments

y	response vector
mu	mean vector
theta	initial theta (optional)
wt	weight vector
maxit	max number of iterations
maxth	max possible value of theta
tol	convergence tolerance

Details

Based on the glm.nb function in the MASS package. If theta is missing, the initial estimate of theta is given by

theta <- 1 / mean(wt * (y / mu - 1)^2)

which is motivated by the method of moments estimator for the dispersion parameter in a quasi-Poisson model.

Value

Returns estimated theta with attributes

SE	standard error estimate
iter	number of iterations

Author(s)

Nathaniel E. Helwig <[e-mail]>

References

Venables, W. N. and Ripley, B. D. (1999) Modern Applied Statistics with S-PLUS. Third Edition. Springer.

https://www.rdocumentation.org/packages/MASS/versions/7.3-51.6/topics/negative.binomial

https://www.rdocumentation.org/packages/MASS/versions/7.3-51.6/topics/glm.nb

See Also

NegBin for details on the Negative Binomial distribution

Examples

# generate data
n <- 1000
x <- seq(0, 1, length.out = n)
fx <- 3 * x + sin(2 * pi * x) - 1.5
mu <- exp(fx)

# simulate negative binomial data
set.seed(1)
y <- rnbinom(n = n, size = 1/2, mu = mu)

# estimate theta
theta.mle(y, mu)

npreg documentation built on May 29, 2024, 4:17 a.m.