zigeometric: Zero-Inflated Geometric Distribution Family Function

In VGAM: Vector Generalized Linear and Additive Models

Zero-Inflated Geometric Distribution Family Function

Description

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

Usage

zigeometric(lpstr0  = "logitlink", lprob = "logitlink",
            type.fitted = c("mean", "prob", "pobs0", "pstr0", "onempstr0"),
            ipstr0  = NULL, iprob = NULL,
            imethod = 1, bias.red = 0.5, zero = NULL)
zigeometricff(lprob = "logitlink", lonempstr0 = "logitlink",
              type.fitted = c("mean", "prob", "pobs0", "pstr0", "onempstr0"),
              iprob = NULL, ionempstr0 = NULL,
              imethod = 1, bias.red = 0.5, zero = "onempstr0")

Arguments

lpstr0, lprob

Link functions for the parameters \phi and p (prob). The usual geometric probability parameter is the latter. The probability of a structural zero is the former. See Links for more choices. For the zero-deflated model see below.

lonempstr0, ionempstr0	Corresponding arguments for the other parameterization. See details below.
bias.red	A constant used in the initialization process of pstr0. It should lie between 0 and 1, with 1 having no effect.
type.fitted	See CommonVGAMffArguments and fittedvlm for information.
ipstr0, iprob	See CommonVGAMffArguments for information.
zero, imethod	See CommonVGAMffArguments for information.

Details

Function zigeometric() is based on

P(Y=0) = \phi + (1-\phi) p,

for y=0, and

P(Y=y) = (1-\phi) p (1 - p)^{y}.

for y=1,2,\ldots. The parameter \phi satisfies 0 < \phi < 1. The mean of Y is E(Y)=(1-\phi) p / (1-p) and these are returned as the fitted values by default. By default, the two linear/additive predictors are (logit(\phi), logit(p))^T. Multiple responses are handled.

Estimated probabilities of a structural zero and an observed zero can be returned, as in zipoisson; see fittedvlm for information.

The VGAM family function zigeometricff() has a few changes compared to zigeometric(). These are: (i) the order of the linear/additive predictors is switched so the geometric probability comes first; (ii) argument onempstr0 is now 1 minus the probability of a structural zero, i.e., the probability of the parent (geometric) component, i.e., onempstr0 is 1-pstr0; (iii) argument zero has a new default so that the onempstr0 is intercept-only by default. Now zigeometricff() is generally recommended over zigeometric(). Both functions implement Fisher scoring and can handle multiple responses.

Value

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

Note

The zero-deflated geometric distribution might be fitted by setting lpstr0 = identitylink, albeit, not entirely reliably. See zipoisson for information that can be applied here. Else try the zero-altered geometric distribution (see zageometric).

Author(s)

T. W. Yee

See Also

rzigeom, geometric, zageometric, spikeplot, rgeom, simulate.vlm.

Examples

gdata <- data.frame(x2 = runif(nn <- 1000) - 0.5)
gdata <- transform(gdata, x3 = runif(nn) - 0.5,
                          x4 = runif(nn) - 0.5)
gdata <- transform(gdata, eta1 =  1.0 - 1.0 * x2 + 2.0 * x3,
                          eta2 = -1.0,
                          eta3 =  0.5)
gdata <- transform(gdata, prob1 = logitlink(eta1, inverse = TRUE),
                          prob2 = logitlink(eta2, inverse = TRUE),
                          prob3 = logitlink(eta3, inverse = TRUE))
gdata <- transform(gdata, y1 = rzigeom(nn, prob1, pstr0 = prob3),
                          y2 = rzigeom(nn, prob2, pstr0 = prob3),
                          y3 = rzigeom(nn, prob2, pstr0 = prob3))
with(gdata, table(y1))
with(gdata, table(y2))
with(gdata, table(y3))
head(gdata)

fit1 <- vglm(y1 ~ x2 + x3 + x4, zigeometric(zero = 1), data = gdata, trace = TRUE)
coef(fit1, matrix = TRUE)
head(fitted(fit1, type = "pstr0"))

fit2 <- vglm(cbind(y2, y3) ~ 1, zigeometric(zero = 1), data = gdata, trace = TRUE)
coef(fit2, matrix = TRUE)
summary(fit2)

VGAM documentation built on Sept. 19, 2023, 9:06 a.m.