zageometric: Zero-Altered Geometric Distribution

Description

Fits a zero-altered geometric distribution based on a conditional model involving a Bernoulli distribution and a positive-geometric distribution.

Usage

zageometric(lpobs0 = "logitlink", lprob = "logitlink",
     type.fitted = c("mean", "prob", "pobs0", "onempobs0"),
     imethod = 1, ipobs0 = NULL, iprob = NULL, zero = NULL)
zageometricff(lprob = "logitlink", lonempobs0 = "logitlink",
     type.fitted = c("mean", "prob", "pobs0", "onempobs0"),
     imethod = 1, iprob = NULL, ionempobs0 = NULL, zero = "onempobs0")

Arguments

Value

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

The fitted.values slot of the fitted object, which should be extracted by the generic function fitted, returns the mean $\mu$ (default) which is given by

$$\mu = (1-\phi) / p.$$

If type.fitted = "pobs0" then $p_0$ is returned.

Details

The response $Y$ is zero with probability $p_0$, or $Y$ has a positive-geometric distribution with probability $1-p_0$. Thus $0 < p_0 < 1$, which is modelled as a function of the covariates. The zero-altered geometric distribution differs from the zero-inflated geometric distribution in that the former has zeros coming from one source, whereas the latter has zeros coming from the geometric distribution too. The zero-inflated geometric distribution is implemented in the VGAM package. Some people call the zero-altered geometric a hurdle model.

The input can be a matrix (multiple responses). By default, the two linear/additive predictors of zageometric are $(logit(\phi), logit(p))^T$.

The VGAM family function zageometricff() has a few changes compared to zageometric(). These are: (i) the order of the linear/additive predictors is switched so the geometric probability comes first; (ii) argument onempobs0 is now 1 minus the probability of an observed 0, i.e., the probability of the positive geometric distribution, i.e., onempobs0 is 1-pobs0; (iii) argument zero has a new default so that the pobs0 is intercept-only by default. Now zageometricff() is generally recommended over zageometric(). Both functions implement Fisher scoring and can handle multiple responses.

Examples

Run this code

zdata <- data.frame(x2 = runif(nn <- 1000))
zdata <- transform(zdata, pobs0 = logitlink(-1 + 2*x2, inverse = TRUE),
                          prob  = logitlink(-2 + 3*x2, inverse = TRUE))
zdata <- transform(zdata, y1 = rzageom(nn, prob = prob, pobs0 = pobs0),
                          y2 = rzageom(nn, prob = prob, pobs0 = pobs0))
with(zdata, table(y1))

fit <- vglm(cbind(y1, y2) ~ x2, zageometric, data = zdata, trace = TRUE)
coef(fit, matrix = TRUE)
head(fitted(fit))
head(predict(fit))
summary(fit)