VGAM (version 0.7-10)

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)

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(n=nn, size=sv, prob=mubin, phi=phi)/sv)
with(zibdata, table(y))
fit = vglm(y ~ 1, zibinomial, weight=sv, data=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)