Generally Altered, Inflated, Truncated and Deflated Zeta Regression

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.

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

truncate, max.support

See gaitdpoisson. Only max.support = Inf is allowed because some equations are intractable.

a.mix, i.mix, d.mix

See gaitdpoisson.

a.mlm, i.mlm, d.mlm

See gaitdpoisson.

lshape.p, lshape.a, lshape.i, lshape.d

Link functions. See gaitdpoisson and Links for more choices and information. Actually, it is usually a good idea to set these arguments equal to zetaffMlink because the log-mean is the first linear/additive predictor so it is like a Poisson regression.

eq.ap, eq.ip, eq.dp

Single logical each. See gaitdpoisson

parallel.a, parallel.i, parallel.d

Single logical each. See gaitdpoisson.

type.fitted, mux.init

See gaitdpoisson.

imethod, ipobs.mix, ipstr.mix, ipdip.mix

See CommonVGAMffArguments and gaitdpoisson for information.

ipobs.mlm, ipstr.mlm, ipdip.mlm, byrow.aid

See CommonVGAMffArguments and gaitdpoisson for information.

gpstr.mix, gpstr.mlm

See CommonVGAMffArguments and gaitdpoisson for information.

gshape.p, ishape.p

See CommonVGAMffArguments and gaitdpoisson for information. The former is used only if the latter is not given. Practical experience has shown that good initial values are needed, so if convergence is not obtained then try a finer grid.

ishape.a, ishape.i, ishape.d

See CommonVGAMffArguments and gaitdpoisson for information.

probs.y, ishrinkage

See CommonVGAMffArguments for information.

zero

See gaitdpoisson and CommonVGAMffArguments for information.

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.

Value

An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm, rrvglm and vgam.

Warning

See gaitdpoisson.

Author

T. W. Yee

Note

See gaitdpoisson.

Examples

if (FALSE) { # \dontrun{
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)
} # }