zibinomial: Zero-Inflated Binomial Distribution Family Function

Description

Fits a zero-inflated binomial distribution by maximum likelihood estimation.

Usage

zibinomial(lphi="logit", link.mu="logit",
           ephi=list(), emu=list(),
           iphi=NULL, zero=1, mv=FALSE)

Arguments

lphi

Link function for the parameter $\phi$. See Links for more choices.

link.mu

Link function for the usual binomial probability $\mu$ parameter. See Links for more choices.

ephi, emu

List. Extra argument for the respective links. See earg in Links for general information.

iphi

Optional initial value for $\phi$, whose value must lie between 0 and 1. The default is to compute an initial value internally.

zero

An integer specifying which linear/additive predictor is modelled as intercepts only. If given, the value must be either 1 or 2, and the default is the first. Setting zero=NULL enables both $\phi$ and $\mu$ to be modelled as a function

Logical. Currently it must be FALSE to mean the function does not handle multivariate responses. This is to remain compatible with the same argument in binomialff.

Value

An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm and vgam.

Warning

Numerical problems can occur. Half-stepping is not uncommon. If failure to converge occurs, make use of the argument iphi.

Details

This function uses Fisher scoring and is based on

P (Y = 0) = ϕ + (1 - ϕ) (1 - μ)^{N},

for $y=0$, and

P (Y = y) = (1 - ϕ) (\binom{N}{N y}) μ^{N y} (1 - μ)^{N (1 - y)} .

for $y=1/N,2/N,\ldots,1$. That is, the response is a sample proportion out of $N$ trials, and the argument size in rzibinom is $N$ here. The parameter $\phi$ satisfies $0 < \phi < 1$. The mean of $Y$ is $E(Y)=(1-\phi) \mu$ and these are returned as the fitted values. By default, the two linear/additive predictors are $(logit(\phi), logit(\mu))^T$.

Examples

Run this code

size = 10  # number of trials; N in the notation above
n = 200
phi = 0.50
mubin = 0.3  # Mean of an ordinary binomial distribution
sv = rep(size, len=n)
y = rzibinom(n=n, size=sv, prob=mubin, phi=phi) / sv # A proportion
table(y)
fit = vglm(y ~ 1, zibinomial, weight=sv, trace=TRUE)
coef(fit, matrix=TRUE)
Coef(fit)
fit@misc$p0  # Estimate of P(Y=0)
fitted(fit)[1:4,]
mean(y) # Compare this with fitted(fit)
summary(fit)

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