theta.md
Estimate theta of the Negative Binomial
Description
Given the estimated mean vector, estimate theta
of the Negative Binomial Distribution.
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$double.eps^0.25)
Arguments
y | Vector of observed values from the Negative Binomial. |
mu | Estimated mean vector. |
n | Number of data points (defaults to the sum of |
dfr | Residual degrees of freedom (assuming |
weights | Case weights. If missing, taken as 1. |
limit | Limit on the number of iterations. |
eps | Tolerance to determine convergence. |
trace | logical: should iteration progress be printed? |
Details
theta.md
estimates by equating the deviance to the residual degrees of freedom, an analogue of a moment estimator.
theta.ml
uses maximum likelihood.
theta.mm
calculates the moment estimator of theta
by equating the Pearson chi-square sum((y-mu)^2/(mu+mu^2/theta)) to the residual degrees of freedom.
Value
The required estimate of theta
, as a scalar. For theta.ml
, the standard error is given as attribute "SE"
.
See Also
Examples
quine.nb <- glm.nb(Days ~ .^2, data = quine) theta.md(quine$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) 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)
Copyright (©) 1999–2012 R Foundation for Statistical Computing.
Licensed under the GNU General Public License.