R: Zero-Inflated Binomial Distribution Family Function

zibinomial {VGAM}

R Documentation

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, imethod = 1)

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.

`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`.
`zero, imethod`	See `CommonVGAMffArguments` for information.

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) * choose(N,Ny) * mu^(N*y) * (1-mu)^(N*(1-y)).

for y=1/N,2/N,…,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.

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.

Note

The response variable must have one of the formats described by binomialff, e.g., a factor or two column matrix or a vector of sample proportions with the weights argument specifying the values of N.

To work well, one needs N>1 and mu>0, i.e., the larger N and mu are, the better.

For intercept-models and constant N over the n observations, the misc slot has a component called p0 which is the estimate of P(Y=0). This family function currently cannot handle a multivariate response (only mv = FALSE can be handled).

Author(s)

T. W. Yee

Examples

size = 10  # Number of trials; N in the notation above
nn = 200
zibdata = data.frame(phi   = logit( 0, inverse = TRUE), # 0.50
                     mubin = logit(-1, inverse = TRUE), # Mean of usual binomial
                     sv    = rep(size, length = 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)

[Package VGAM version 0.8-4 Index]