theta.md
From MASS v7.347
by Brian Ripley
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 chisquare
\(\sum (y\mu)^2/(\mu+\mu^2/\theta)\)
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
Examples
library(MASS)
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$Days, fitted(quine.nb), dfr = df.residual(quine.nb))
## weighted example
yeast < data.frame(cbind(numbers = 0:5, fr = c(213, 128, 37, 18, 3, 1)))
fit < glm.nb(numbers ~ 1, weights = fr, data = yeast)
summary(fit)
mu < fitted(fit)
theta.md(yeast$numbers, mu, dfr = 399, weights = yeast$fr)
theta.ml(yeast$numbers, mu, limit = 15, weights = yeast$fr)
theta.mm(yeast$numbers, mu, dfr = 399, weights = yeast$fr)
Community examples
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