VGAM: gaitzeta – R documentation

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gaitzeta

Generally–Altered, –Inflated and –Truncated Zeta Regression

Description

Fits a generally–altered, –inflated and –truncated zeta regression by MLE. The GAIT combo model having 5 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 and inflated values.

Usage

gaitzeta(alt.mix = NULL, inf.mix = NULL, alt.mlm = NULL,
     inf.mlm = NULL, truncate = NULL, max.support = Inf,
     zero = c("pobs", "pstr"), eq.ap = FALSE, eq.ip = FALSE,
     parallel.ap = FALSE, parallel.ip = FALSE, lshape.p = "loglink",
     lshape.a = lshape.p, lshape.i = lshape.p,
     type.fitted = c("mean", "shapes", "pobs.mlm", "pstr.mlm",
     "pobs.mix", "pstr.mix", "Pobs.mix", "Pstr.mix", "nonspecial",
     "Numer", "Denom.p", "sum.mlm.i", "sum.mix.i", "ptrunc.p",
     "cdf.max.s"), gshape.p = 1 + exp(-seq(7)),
     gpstr.mix = ppoints(7) / 3,
     gpstr.mlm = ppoints(7) / (3 + length(inf.mlm)), imethod = 1,
     imux = 0.5, ishape.p = NULL, ishape.a = ishape.p,
     ishape.i = ishape.p, ipobs.mix = NULL, ipstr.mix = NULL,
     ipobs.mlm = NULL, ipstr.mlm = NULL, byrow.ai = FALSE,
     ishrinkage = 0.95, probs.y = 0.35)

Arguments

`truncate, max.support`	See `gaitpoisson`. Only `max.support = Inf` is allowed because some equations are intractable.
`alt.mix, inf.mix`	See `gaitpoisson`.
`alt.mlm, inf.mlm`	See `gaitpoisson`.
`lshape.p, lshape.a, lshape.i`	Link functions. See `gaitpoisson` and `Links` for more choices and information.
`eq.ap, eq.ip`	Single logical each. See `gaitpoisson`
`parallel.ap, parallel.ip`	Single logical each. See `gaitpoisson`.
`type.fitted, imux`	See `gaitpoisson`.
`imethod, ipobs.mix, ipstr.mix`	See `CommonVGAMffArguments` and `gaitpoisson` for information.
`ipobs.mlm, ipstr.mlm, byrow.ai`	See `CommonVGAMffArguments` and `gaitpoisson` for information.
`gpstr.mix, gpstr.mlm`	See `CommonVGAMffArguments` and `gaitpoisson` for information.
`gshape.p, ishape.p`	See `CommonVGAMffArguments` and `gaitpoisson` 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`	See `CommonVGAMffArguments` and `gaitpoisson` for information.
`probs.y, ishrinkage`	See `CommonVGAMffArguments` for information.
`zero`	See `gaitpoisson` and `CommonVGAMffArguments` for information.

Details

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

Apart from the order of the linear/additive predictors, the following are (or should be) equivalent: gaitzeta() and zetaff(), gaitzeta(alt.mix = 1) and oazeta(zero = "pobs1"), gaitzeta(inf.mix = 1) and oizeta(zero = "pstr1"), gaitzeta(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 gaitpoisson.

Note

See gaitpoisson.

Author(s)

T. W. Yee

Examples

## Not run: 
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.mix <- pstr.mix <- 0.1
gdata <- data.frame(x2 = runif(nn <- 1000))
gdata <- transform(gdata, shape.p = loglink(0.1+0.1*x2, inverse = TRUE))
gdata <- transform(gdata,
  y1 = rgaitzeta(nn, shape.p, alt.mix = avec, pobs.mix = pobs.mix,
                 inf.mix = ivec, pstr.mix = pstr.mix, truncate = tvec))
gaitzeta(alt.mix = avec, inf.mix = ivec, max.support = max.support)
with(gdata, table(y1))
spikeplot(with(gdata, y1), col = "pink2", log = "x")
gaitzxfit <- vglm(y1 ~ x2, crit = "coef", trace = TRUE, data = gdata,
                  gaitzeta(inf.mix = ivec, truncate = tvec,
                           alt.mix = avec, eq.ap = TRUE, eq.ip = TRUE))
head(fitted(gaitzxfit, type.fitted = "Pstr.mix"))
head(predict(gaitzxfit))
t(coef(gaitzxfit, matrix = TRUE))  # Easier to see with t()
summary(gaitzxfit, HDEtest = FALSE)  # summary(gaitzxfit) is better

## End(Not run)

VGAM

Vector Generalized Linear and Additive Models

v1.1-5

GPL-3

Authors

Thomas Yee [aut, cre], Cleve Moler [ctb] (author of several LINPACK routines)

Initial release

2021-01-13