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(lp0 = "logit", lmunb = "loge", lsize = "loge", ep0 = list(), emunb = list(), esize = list(), ipnb0 = NULL, isize = NULL, zero = -3, cutoff = 0.995, imethod = 1, shrinkage.init = 0.95)
lp0 |
Link function for the parameter p0, called |
lmunb |
Link function applied to the |
lsize |
Parameter link function applied to the reciprocal of the dispersion
parameter, called |
ep0, emunb, esize |
List. Extra argument for the respective links.
See |
ipnb0 |
Optional initial values for the probability p0. If given, they must be in (0,1), and it is ok to give one value each for each response/species. |
isize |
Optional initial values for |
zero |
Integer valued vector, usually assigned -3 or 3 if
used at all. Specifies which of the three linear predictors are
modelled as an intercept only. By default, the |
cutoff |
A numeric which is close to 1 but never exactly 1. Used to
specify how many terms of the infinite series are actually used.
The sum of the probabilites are added until they reach this value
or more. It is like specifying |
imethod, shrinkage.init |
See |
The response Y is zero with probability p0, or Y has a positive-negative binomial distribution with probability 1-p0. Thus 0 < p0 < 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 are (logit(p0), log(munb), log(k))^T. This vector is recycled for multiple species.
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 which is given by
mu = (1-p0) * munb / [1 - (k/(k+munb))^k].
Convergence for this VGAM family function seems to depend quite strongly on providing good initial values.
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 p0 to be modelled as functions of the covariates. It is a conditional model, not a mixture model.
This family function effectively combines
posnegbinomial
and 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.
dzanegbin
,
posnegbinomial
,
negbinomial
,
binomialff
,
rposnegbin
,
zinegbinomial
,
zipoisson
,
dnbinom
,
CommonVGAMffArguments
.
zdata <- data.frame(x = runif(nn <- 2000)) zdata <- transform(zdata, p0 = logit(-1 + 2*x, inverse = TRUE), y1 = rposnegbin(nn, munb = exp(0+2*x), size = exp(1)), y2 = rposnegbin(nn, munb = exp(1+2*x), size = exp(1))) zdata <- transform(zdata, y1 = ifelse(runif(nn) < p0, 0, y1), y2 = ifelse(runif(nn) < p0, 0, y2)) with(zdata, table(y1)) with(zdata, table(y2)) fit <- vglm(cbind(y1, y2) ~ x, zanegbinomial, zdata, trace = TRUE) coef(fit, matrix = TRUE) head(fitted(fit)) head(predict(fit))