zigeometric {VGAM} | R Documentation

## 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", "prob", "pobs0", "pstr0", "onempstr0"),
                ipstr0  = NULL, iprob = NULL,
                imethod = 1, bias.red = 0.5, zero = NULL)
    zigeometricff(lprob = "logit", lonempstr0 = "logit",
                  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 prob (`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) * prob,

for y=0, and

P(Y=y) = (1-phi) * prob * (1 - prob)^y.

for y=1,2,…. The parameter phi satisfies 0 < phi < 1. The mean of Y is E(Y) = (1-phi) * prob / (1-prob) and these are returned as the fitted values by default. By default, the two linear/additive predictors are (logit(phi), logit(prob))^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`, `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 = 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)

[Package VGAM version 1.0-3 Index]