gaitdzeta: Generally Altered, Inflated, Truncated and Deflated Zeta Regression

Description

Fits a generally altered, inflated, truncated and deflated zeta regression by MLE. The GAITD combo model having 7 types of special values is implemented. This allows mixtures of zetas on nested and/or partitioned support as well as a multinomial logit model for altered, inflated and deflated values.

Usage

gaitdzeta(a.mix = NULL, i.mix = NULL, d.mix = NULL,
         a.mlm = NULL, i.mlm = NULL, d.mlm = NULL,
         truncate = NULL, max.support = Inf,
         zero = c("pobs", "pstr", "pdip"), eq.ap = TRUE, eq.ip = TRUE,
         eq.dp = TRUE, parallel.a = FALSE,
         parallel.i = FALSE, parallel.d = FALSE,
         lshape.p = "loglink", lshape.a = lshape.p,
         lshape.i = lshape.p, lshape.d = lshape.p,
         type.fitted = c("mean", "shapes", "pobs.mlm", "pstr.mlm",
         "pdip.mlm", "pobs.mix", "pstr.mix", "pdip.mix", "Pobs.mix",
         "Pstr.mix", "Pdip.mix", "nonspecial",
         "Numer", "Denom.p", "sum.mlm.i", "sum.mix.i", "sum.mlm.d",
         "sum.mix.d", "ptrunc.p", "cdf.max.s"),
         gshape.p = -expm1(-ppoints(7)), gpstr.mix = ppoints(7) / 3,
         gpstr.mlm = ppoints(7) / (3 + length(i.mlm)),
         imethod = 1, mux.init = c(0.75, 0.5, 0.75),
         ishape.p = NULL, ishape.a = ishape.p,
         ishape.i = ishape.p, ishape.d = ishape.p,
         ipobs.mix = NULL, ipstr.mix = NULL, ipdip.mix = NULL,
         ipobs.mlm = NULL, ipstr.mlm = NULL, ipdip.mlm = NULL,
         byrow.aid = FALSE, ishrinkage = 0.95, probs.y = 0.35)

Arguments

Value

An object of class "vglmff"

(see vglmff-class). The object is used by modelling functions such as vglm,

rrvglm

and vgam.

Details

Many details to this family function can be found in gaitdpoisson because it is also a 1-parameter discrete distribution. This function currently does not handle multiple responses. Further details are at Gaitdzeta.

As alluded to above, when there are covariates it is much more interpretable to model the mean rather than the shape parameter. Hence zetaffMlink is recommended. (This might become the default in the future.) So installing VGAMextra is a good idea.

Apart from the order of the linear/additive predictors, the following are (or should be) equivalent: gaitdzeta() and zetaff(), gaitdzeta(a.mix = 1) and oazeta(zero = "pobs1"), gaitdzeta(i.mix = 1) and oizeta(zero = "pstr1"), gaitdzeta(truncate = 1) and otzeta(). The functions oazeta, oizeta and otzeta have been placed in VGAMdata.

Examples

Run this code

if (FALSE) {
avec <- c(5, 10)  # Alter these values parametrically
ivec <- c(3, 15)  # Inflate these values
tvec <- c(6, 7)   # Truncate these values
set.seed(1); pobs.a <- pstr.i <- 0.1
gdata <- data.frame(x2 = runif(nn <- 1000))
gdata <- transform(gdata, shape.p = logitlink(2, inverse = TRUE))
gdata <- transform(gdata,
  y1 = rgaitdzeta(nn, shape.p, a.mix = avec, pobs.mix = pobs.a,
                  i.mix = ivec, pstr.mix = pstr.i, truncate = tvec))
gaitdzeta(a.mix = avec, i.mix = ivec)
with(gdata, table(y1))
spikeplot(with(gdata, y1), las = 1)
fit7 <- vglm(y1 ~ 1, trace = TRUE, data = gdata, crit = "coef",
             gaitdzeta(i.mix = ivec, truncate = tvec,
                       a.mix = avec, eq.ap = TRUE, eq.ip = TRUE))
head(fitted(fit7, type.fitted = "Pstr.mix"))
head(predict(fit7))
t(coef(fit7, matrix = TRUE))  # Easier to see with t()
summary(fit7)
spikeplot(with(gdata, y1), lwd = 2, ylim = c(0, 0.6), xlim = c(0, 20))
plotdgaitd(fit7, new.plot = FALSE, offset.x = 0.2, all.lwd = 2)
}