theta.md

0th

Percentile

Estimate theta of the Negative Binomial

Given the estimated mean vector, estimate theta of the Negative Binomial Distribution.

Keywords
models
Usage
theta.md(y, mu, dfr, weights, limit = 20, eps = .Machine$double.eps^0.25)

theta.ml(y, mu, n, weights, limit = 10, eps = .Machine$double.eps^0.25, trace = FALSE)

theta.mm(y, mu, dfr, weights, limit = 10, eps = .Machine$double.eps^0.25)

Arguments
y
Vector of observed values from the Negative Binomial.
mu
Estimated mean vector.
n
Number of data points (defaults to the sum of weights)
dfr
Residual degrees of freedom (assuming theta known). For a weighted fit this is the sum of the weights minus the number of fitted parameters.
weights
Case weights. If missing, taken as 1.
limit
Limit on the number of iterations.
eps
Tolerance to determine convergence.
trace
logical: should iteration progress be printed?
Details

theta.md estimates by equating the deviance to the residual degrees of freedom, an analogue of a moment estimator.

theta.ml uses maximum likelihood.

theta.mm calculates the moment estimator of theta by equating the Pearson chi-square $\sum (y-\mu)^2/(\mu+\mu^2/\theta)$ to the residual degrees of freedom.

Value

  • The required estimate of theta, as a scalar. For theta.ml, the standard error is given as attribute "SE".

See Also

glm.nb

Aliases
  • theta.md
  • theta.ml
  • theta.mm
Examples
quine.nb <- glm.nb(Days ~ .^2, data = quine)
theta.md(quine$Days, fitted(quine.nb), dfr = df.residual(quine.nb))
theta.ml(quine$Days, fitted(quine.nb))
theta.mm(quine$Days, fitted(quine.nb), dfr = df.residual(quine.nb))

## weighted example
yeast <- data.frame(cbind(numbers = 0:5, fr = c(213, 128, 37, 18, 3, 1)))
fit <- glm.nb(numbers ~ 1, weights = fr, data = yeast)
summary(fit)
attach(yeast)
mu <- fitted(fit)
theta.md(numbers, mu, dfr = 399, weights = fr)
theta.ml(numbers, mu, weights = fr)
theta.mm(numbers, mu, dfr = 399, weights = fr)
detach()
Documentation reproduced from package MASS, version 7.3-19, License: GPL-2 | GPL-3

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