VGAM (version 0.8-2)

zibinomial: Zero-Inflated Binomial Distribution Family Function

Description

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

Usage

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

Arguments

lphi, lmu

Link functions for the parameter $\phi$ and 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 values for $\phi$, whose values must lie between 0 and 1. The default is to compute an initial value internally. If a vector then recyling is used.

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

mv

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 $$P(Y=0) = \phi + (1-\phi) (1-\mu)^N,$$ for $y=0$, and $$P(Y=y) = (1-\phi) {N \choose Ny} \mu^{Ny} (1-\mu)^{N(1-y)}.$$ 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 $(logit(\phi), logit(\mu))^T$.

See Also

rzibinom, binomialff, posbinomial, rbinom.

Examples

size = 10  # number of trials; N in the notation above
nn = 200
zibdata = data.frame(phi   = logit( 0, inv = TRUE), # 0.50
                     mubin = logit(-1, inv = TRUE), # Mean of usual binomial
                     sv    = rep(size, len = nn))
zibdata = transform(zibdata, 
                    y = rzibinom(nn, size = sv, prob = mubin, phi = phi))
with(zibdata, table(y))
fit = vglm(cbind(y, sv - y) ~ 1, zibinomial, zibdata, trace = TRUE)

coef(fit, matrix = TRUE)
Coef(fit) # Useful for intercept-only models
fit@misc$p0  # Estimate of P(Y=0)
head(fitted(fit))
with(zibdata, mean(y)) # Compare this with fitted(fit)
summary(fit)