Generally–Altered, –Inflated and –Truncated Logarithmic Regression Family Function (GAIT–Log–Log–Log Mixture Variant)

Description

Fits a generally–altered, –inflated and –truncated logarithmic regression (mixtures of logarithmic distributions on nested and/or partitioned supports).

Usage

gaitlog.mix(alter = NULL, inflate = NULL, truncate = NULL,
    max.support = Inf, zero = c("pobs.a", "pstr.i"),
    eq.ap = FALSE, eq.ip = FALSE, lshape.p = "logitlink",
    lpobs.a = "logitlink", lshape.a = "logitlink",
    lpstr.i = "logitlink", lshape.i = "logitlink",
    type.fitted = c("mean", "pobs.a", "pstr.i", "Pobs.a", "Pstr.i",
    "prob.a", "prob.i", "prob.t", "lhs.prob"),
    imethod = 1, gshape.p = -expm1(-7 * ppoints(12)), ishape.p = NULL,
    ishape.a = NULL, ishape.i = NULL,
    ipobs.a = NULL, ipstr.i = NULL, ishrinkage = 0.95, probs.y = 0.35)

Arguments

Details

Although the full GAIT–Log–Log–Log model may be fitted, the two submodels that may be fitted can be abbreviated GAT–Log–Log or GIT–Log–Log, which is where the inner distribution for ordinary values is the logarithmic distribution, and the outer distribution for the altered or inflated values is another logarithmic distribution with a different shape parameter by default. Thus for the GAT model the distribution being fitted is a (spliced) mixture of two logarithmic with differing (partitioned) support. Likewise, for the GIT model the distribution being fitted is a mixture of two logarithmic with nested support. Two shape parameters at a time may be constrained to be equal using eq.ap or eq.ip.

For the GIT model, by default, a logistic regression models the (structural) probability pstr.i that the response is inflated.

This function currently does not handle multiple responses. Further details are at Gaitlog.

For the GIT model, the ordering of the linear/additive predictors corresponds to length(inflate) equalling 0, 1, and more than 1; the dimension grows accordingly. The same idea holds for the GAT model.

Apart from the order of the linear/additive predictors, the following are (or should be) equivalent: gaitlog.mix() and logff(), gaitlog.mix(alter = 1) and oalog(zero = "pobs1"), gaitlog.mix(inflate = 1) and oilog(zero = "pstr1"), gaitlog.mix(truncate = 1) and otlog().

Value

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

Warning

See gaitpoisson.mix

Note

See gaitpoisson.mix

Author(s)

T. W. Yee

See Also

Gaitlog, gaitpoisson.mix, gaitpoisson.mlm, oalog, oilog, otlog, CommonVGAMffArguments, rootogram4, simulate.vlm.

Examples

avec <- c(5, 10)  # Alter these values
ivec <- c(3, 15)  # Inflate these values
tvec <- c(6, 7)   # Truncate these values
max.support <- 20; set.seed(1)
pobs.a <- logitlink(-1, inverse = TRUE)  # About 0.27
pstr.i <- logitlink(-1, inverse = TRUE)  # About 0.27
gdata <- data.frame(x2 = runif(nn <- 1000))
gdata <- transform(gdata, shape.p = logitlink(2+0.5*x2, inverse = TRUE))
gdata <- transform(gdata,
  y1 = rgaitlog(nn, shape.p, alter.mix = avec, pobs.mix.a = pobs.a,
                inflate.mix = ivec, pstr.mix.i = pstr.i, truncate = tvec,
                max.support = max.support))
gaitlog.mix(alter = avec, inflate = ivec, max.support = max.support)
with(gdata, table(y1))
gaitlxfit <- vglm(y1 ~ x2, crit = "coef", trace = TRUE, data = gdata,
                  gaitlog.mix(inflate = ivec, truncate = tvec,
                              max.support = max.support,
                              alter = avec, eq.ap = TRUE, eq.ip = TRUE))
head(fitted(gaitlxfit, type.fitted = "Pstr.i"))
head(predict(gaitlxfit))
coef(gaitlxfit, matrix = TRUE)
summary(gaitlxfit)