theta.md
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
thetaknown). 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
Examples
# NOT RUN {
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)
# }