VGAM (version 0.9-3)

zinegbinomial: Zero-Inflated Negative Binomial Distribution Family Function

Description

Fits a zero-inflated negative binomial distribution by full maximum likelihood estimation.

Usage

zinegbinomial(lpstr0 = "logit", lmunb = "loge", lsize = "loge",
              type.fitted = c("mean", "pobs0", "pstr0", "onempstr0"),
              ipstr0 = NULL, isize = NULL, zero = -3,
              imethod = 1, shrinkage.init = 0.95, nsimEIM = 250)
zinegbinomialff(lmunb = "loge", lsize = "loge", lonempstr0 = "logit",
                type.fitted = c("mean", "pobs0", "pstr0", "onempstr0"),
                isize = NULL, ionempstr0 = NULL, zero = c(-2, -3),
                imethod = 1, shrinkage.init = 0.95, nsimEIM = 250)

Arguments

lpstr0, lmunb, lsize

Link functions for the parameters $\phi$, the mean and $k$; see negbinomial for details, and Links for more choices. For the zero-deflated m

type.fitted

See CommonVGAMffArguments and fittedvlm for more information.

ipstr0, isize

Optional initial values for $\phi$ and $k$. The default is to compute an initial value internally for both. If a vector then recycling is used.

lonempstr0, ionempstr0

Corresponding arguments for the other parameterization. See details below.

imethod

An integer with value 1 or 2 or 3 which specifies the initialization method for the mean parameter. If failure to converge occurs try another value and/or else specify a value for shrinkage.init.

zero

Integers specifying which linear/additive predictor is modelled as intercepts only. If given, their absolute values must be either 1 or 2 or 3. The default is the $\phi$ and $k$ parameters (both for each response). See

shrinkage.init, nsimEIM

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.

Warning

Numerical problems can occur, e.g., when the probability of zero is actually less than, not more than, the nominal probability of zero. Half-stepping is not uncommon. If failure to converge occurs, try using combinations of arguments stepsize (in vglm.control), imethod, shrinkage.init, ipstr0, isize, and/or zero if there are explanatory variables.

An infinite loop might occur if some of the fitted values (the means) are too close to 0.

This VGAM family function is computationally expensive and usually runs slowly; setting trace = TRUE is useful for monitoring convergence.

Details

These functions are based on $$P(Y=0) = \phi + (1-\phi) (k/(k+\mu))^k,$$ and for $y=1,2,\ldots$, $$P(Y=y) = (1-\phi) \, dnbinom(y, \mu, k).$$ The parameter $\phi$ satisfies $0 < \phi < 1$. The mean of $Y$ is $(1-\phi) \mu$ (returned as the fitted values). By default, the three linear/additive predictors for zinegbinomial() are $(logit(\phi), \log(\mu), \log(k))^T$. See negbinomial, another VGAM family function, for the formula of the probability density function and other details of the negative binomial distribution.

Independent multivariate responses are handled. If so then arguments ipstr0 and isize may be vectors with length equal to the number of responses.

The VGAM family function zinegbinomialff() has a few changes compared to zinegbinomial(). These are: (i) the order of the linear/additive predictors is switched so the NB mean comes first; (ii) onempstr0 is now 1 minus the probability of a structural 0, i.e., the probability of the parent (NB) component, i.e., onempstr0 is 1-pstr0; (iii) argument zero has a new default so that the onempstr0 is intercept-only by default. Now zinegbinomialff() is generally recommended over zinegbinomial(). Both functions implement Fisher scoring and can handle multiple responses.

See Also

Zinegbin, negbinomial, rpois, CommonVGAMffArguments.

Examples

# Example 1
ndata <- data.frame(x2 = runif(nn <- 1000))
ndata <- transform(ndata, pstr0 = logit(-0.5 + 1 * x2, inverse = TRUE),
                          munb  =   exp( 3   + 1 * x2),
                          size  =   exp( 0   + 2 * x2))
ndata <- transform(ndata,
                   y1 = rzinegbin(nn, mu = munb, size = size, pstr0 = pstr0),
                   y2 = rzinegbin(nn, mu = munb, size = size, pstr0 = pstr0))
with(ndata, table(y1)["0"] / sum(table(y1)))
fit <- vglm(cbind(y1, y2) ~ x2, zinegbinomial(zero = NULL), data = ndata)
coef(fit, matrix = TRUE)
summary(fit)
head(cbind(fitted(fit), with(ndata, (1 - pstr0) * munb)))
round(vcov(fit), 3)


# Example 2: RR-ZINB could also be called a COZIVGLM-ZINB-2
ndata <- data.frame(x2 = runif(nn <- 2000))
ndata <- transform(ndata, x3 = runif(nn))
ndata <- transform(ndata, eta1 =          3   + 1   * x2 + 2 * x3)
ndata <- transform(ndata, pstr0  = logit(-1.5 + 0.5 * eta1, inverse = TRUE),
                          munb = exp(eta1),
                          size = exp(4))
ndata <- transform(ndata,
                   y1 = rzinegbin(nn, pstr0 = pstr0, mu = munb, size = size))
with(ndata, table(y1)["0"] / sum(table(y1)))
rrzinb <- rrvglm(y1 ~ x2 + x3, zinegbinomial(zero = NULL), data = ndata,
                 Index.corner = 2, str0 = 3, trace = TRUE)
coef(rrzinb, matrix = TRUE)
Coef(rrzinb)