npreg (version 1.1.0)

NegBin: Family Function for Negative Binomial

Description

Creates the functions needed to fit a Negative Binomial generalized smooth model via gsm with or without a known theta parameter. Adapted from the negative.binomial function in the MASS package.

Usage

NegBin(theta = NULL, link = "log")

Value

An object of class "family" with the functions and expressions needed to fit the gsm. In addition to the standard values (see family), this also produces the following:

logLik

function to evaluate the log-likelihood

canpar

function to compute the canonical parameter

cumulant

function to compute the cumulant function

theta

the specified theta parameter

fixed.theta

logical specifying if theta was provided

Arguments

theta

the size parameter for the Negative Binomial distribution. Default of NULL indicates that theta should be estimated from the data.

link

the link function. Must be log, sqrt, identity, or an object of class link-glm (as generated by make.link).

Author

Nathaniel E. Helwig <[e-mail]>

Details

The Negative Binomial distribution has mean \(\mu\) and variance \(\mu + \mu^2/\theta\), where the size parameter \(\theta\) is the inverse of the dispersion parameter. See NegBinomial for details.

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/stats/versions/3.6.2/topics/NegBinomial

See Also

gsm for fitting generalized smooth models with Negative Binomial responses

theta.mle for maximum likelihood estimation of theta

Examples

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

# negative binomial (size = 1/2, log link)
set.seed(1)
y <- rnbinom(n = n, size = 1/2, mu = exp(fx))

# fit model (known theta)
mod <- gsm(y ~ x, family = NegBin(theta = 1/2), knots = 10)
mean((mod$linear.predictors - fx)^2)
mod$family$theta   # fixed theta

# fit model (unknown theta)
mod <- gsm(y ~ x, family = NegBin, knots = 10)
mean((mod$linear.predictors - fx)^2)
mod$family$theta   # estimated theta