zigeometric: Zero-Inflated Geometric Distribution Family Function

Description

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

Usage

zigeometric(lpstr0  = "logit", lprob = "logit",
            type.fitted = c("mean", "pobs0", "pstr0", "onempstr0"),
            ipstr0  = NULL, iprob = NULL,
            imethod = 1, bias.red = 0.5, zero = NULL)
zigeometricff(lprob = "logit", lonempstr0 = "logit",
              type.fitted = c("mean", "pobs0", "pstr0", "onempstr0"),
              iprob = NULL, ionempstr0 = NULL,
              imethod = 1, bias.red = 0.5, zero = -2)

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 mor

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.

Value

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

Details

Function zigeometric() is based on

P (Y = 0) = ϕ + (1 - ϕ) p,

for $y=0$, and

P (Y = y) = (1 - ϕ) 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.

Examples

Run this code

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 = logit(eta1, inverse = TRUE),
                          prob2 = logit(eta2, inverse = TRUE),
                          prob3 = logit(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)

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