VGAM (version 1.1-2)

oazeta: One-Altered Zeta Distribution

Description

Fits a one-altered zeta distribution based on a conditional model involving a Bernoulli distribution and a 1-truncated zeta distribution.

Usage

oazeta(lpobs1 = "logitlink", lshape = "loglink",
       type.fitted = c("mean", "shape", "pobs1", "onempobs1"),
       gshape = exp((-4:3)/4), ishape = NULL, ipobs1 = NULL, zero = NULL)

Arguments

lpobs1

Link function for the parameter \(p_1\) or \(\phi\), called pobs1 or phi here. See Links for more choices.

lshape

See zeta for details.

type.fitted

See CommonVGAMffArguments and fittedvlm for information.

gshape, ishape, ipobs1, zero

See CommonVGAMffArguments for information.

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 $$\mu = \phi + (1-\phi) A$$ where \(A\) is the mean of the one-truncated zeta distribution. If type.fitted = "pobs1" then \(p_1\) is returned.

Details

The response \(Y\) is one with probability \(p_1\), or \(Y\) has a 1-truncated zeta distribution with probability \(1-p_1\). Thus \(0 < p_1 < 1\), which is modelled as a function of the covariates. The one-altered zeta distribution differs from the one-inflated zeta distribution in that the former has ones coming from one source, whereas the latter has ones coming from the zeta distribution too. The one-inflated zeta distribution is implemented in the VGAM package. Some people call the one-altered zeta a hurdle model.

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

See Also

Oazeta, zetaff, oizeta, otzeta, CommonVGAMffArguments, simulate.vlm.

Examples

# NOT RUN {
odata <- data.frame(x2 = runif(nn <- 1000))
odata <- transform(odata, pobs1 = logitlink(-1 + 2*x2, inverse = TRUE),
                          shape =  loglink( 1 + 1*x2, inverse = TRUE))
odata <- transform(odata, y1 = roazeta(nn, shape = shape, pobs1 = pobs1),
                          y2 = roazeta(nn, shape = shape, pobs1 = pobs1))
with(odata, table(y1))

ofit <- vglm(cbind(y1, y2) ~ x2, oazeta, data = odata, trace = TRUE)
coef(ofit, matrix = TRUE)
head(fitted(ofit))
head(predict(ofit))
summary(ofit)
# }