NegBin | R Documentation |
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.
NegBin(theta = NULL, link = "log")
theta |
the |
link |
the link function. Must be |
The Negative Binomial distribution has mean μ and variance μ + μ^2/θ, where the size
parameter θ is the inverse of the dispersion parameter. See NegBinomial
for details.
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 |
fixed.theta |
logical specifying if |
Nathaniel E. Helwig <helwig@umn.edu>
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
gsm
for fitting generalized smooth models with Negative Binomial responses
theta.mle
for maximum likelihood estimation of theta
# 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
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