{MASS}R Documentation

Estimate theta of the Negative Binomial


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

Usage, mu, dfr, weights, limit = 20, eps = .Machine$double.eps^0.25), mu, n, weights, limit = 10, eps = .Machine$double.eps^0.25,
         trace = FALSE), mu, dfr, weights, limit = 10, eps = .Machine$double.eps^0.25)


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 estimates by equating the deviance to the residual degrees of freedom, an analogue of a moment estimator. uses maximum likelihood. calculates the moment estimator of theta by equating the Pearson chi-square sum((y-μ)^2/(μ+μ^2/theta)) to the residual degrees of freedom.


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

See Also



quine.nb <- glm.nb(Days ~ .^2, data = quine)$Days, fitted(quine.nb), dfr = df.residual(quine.nb))$Days, fitted(quine.nb))$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)
mu <- fitted(fit), mu, dfr = 399, weights = fr), mu, weights = fr), mu, dfr = 399, weights = fr)

[Package MASS version 7.2-33 Index]