zanegbinomial {VGAM} | R Documentation |

Fits a zero-altered negative binomial distribution based on a conditional model involving a binomial distribution and a positive-negative binomial distribution.

zanegbinomial(lpobs0 = "logit", lmunb = "loge", lsize = "loge", type.fitted = c("mean", "pobs0"), ipobs0 = NULL, isize = NULL, zero = -3, imethod = 1, nsimEIM = 250, shrinkage.init = 0.95) zanegbinomialff(lmunb = "loge", lsize = "loge", lonempobs0 = "logit", type.fitted = c("mean", "pobs0", "onempobs0"), isize = NULL, ionempobs0 = NULL, zero = c(-2, -3), imethod = 1, nsimEIM = 250, shrinkage.init = 0.95)

`lpobs0` |
Link function for the parameter |

`lmunb` |
Link function applied to the |

`lsize` |
Parameter link function applied to the reciprocal of the dispersion
parameter, called |

`type.fitted` |
See |

`lonempobs0, ionempobs0` |
Corresponding argument for the other parameterization. See details below. |

`ipobs0, isize` |
Optional initial values for |

`zero` |
Specifies which of the three linear predictors are
modelled as an intercept only.
All parameters can be modelled as a
function of the explanatory variables by setting |

`nsimEIM, imethod` |
See |

`shrinkage.init` |
See |

The response *Y* is zero with probability *pobs0*,
or *Y* has a positive-negative binomial distribution with
probability *1-pobs0*. Thus *0 < pobs0 < 1*,
which is modelled as a function of the covariates. The zero-altered
negative binomial distribution differs from the zero-inflated negative
binomial distribution in that the former has zeros coming from one
source, whereas the latter has zeros coming from the negative binomial
distribution too. The zero-inflated negative binomial distribution
is implemented in the VGAM package. Some people
call the zero-altered negative binomial a *hurdle* model.

For one response/species, by default, the three linear/additive
predictors
for `zanegbinomial()`

are *(logit(pobs0),
log(munb), log(k))^T*. This vector is recycled for multiple species.

The VGAM family function `zanegbinomialff()`

has a few
changes compared to `zanegbinomial()`

.
These are:
(i) the order of the linear/additive predictors is switched so the
negative binomial mean comes first;
(ii) argument `onempobs0`

is now 1 minus the probability of an observed 0,
i.e., the probability of the positive negative binomial distribution,
i.e., `onempobs0`

is `1-pobs0`

;
(iii) argument `zero`

has a new default so that the `pobs0`

is intercept-only by default.
Now `zanegbinomialff()`

is generally recommended over
`zanegbinomial()`

.
Both functions implement Fisher scoring and can handle
multiple responses.

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-pobs0) * munb / [1 - (k/(k+munb))^k].*

If `type.fitted = "pobs0"`

then *pobs0* is returned.

Convergence for this VGAM family function seems to depend quite strongly on providing good initial values.

This VGAM family function is computationally expensive
and usually runs slowly;
setting `trace = TRUE`

is useful for monitoring convergence.

Inference obtained from `summary.vglm`

and `summary.vgam`

may or may not be correct. In particular, the p-values, standard errors
and degrees of freedom may need adjustment. Use simulation on artificial
data to check that these are reasonable.

Note this family function allows *pobs0* to be modelled as
functions of the covariates provided `zero`

is set correctly.
It is a conditional model, not a mixture model.
Simulated Fisher scoring is the algorithm.

This family function effectively combines
`binomialff`

into
one family function.

This family function can handle a multivariate response, e.g., more than one species.

T. W. Yee

Welsh, A. H., Cunningham, R. B., Donnelly, C. F. and Lindenmayer,
D. B. (1996)
Modelling the abundances of rare species: statistical models
for counts with extra zeros.
*Ecological Modelling*,
**88**,
297–308.

Yee, T. W. (2014)
Reduced-rank vector generalized linear models with two linear predictors.
*Computational Statistics and Data Analysis*.

`dzanegbin`

,
`posnegbinomial`

,
`negbinomial`

,
`binomialff`

,
`rposnegbin`

,
`zinegbinomial`

,
`zipoisson`

,
`dnbinom`

,
`CommonVGAMffArguments`

.

## Not run: zdata <- data.frame(x2 = runif(nn <- 2000)) zdata <- transform(zdata, pobs0 = logit(-1 + 2*x2, inverse = TRUE)) zdata <- transform(zdata, y1 = rzanegbin(nn, munb = exp(0+2*x2), size = exp(1), pobs0 = pobs0), y2 = rzanegbin(nn, munb = exp(1+2*x2), size = exp(1), pobs0 = pobs0)) with(zdata, table(y1)) with(zdata, table(y2)) fit <- vglm(cbind(y1, y2) ~ x2, zanegbinomial, data = zdata, trace = TRUE) coef(fit, matrix = TRUE) head(fitted(fit)) head(predict(fit)) ## End(Not run)

[Package *VGAM* version 0.9-3 Index]