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