Generally Altered, Inflated, Truncated and Deflated Logarithmic Regression

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

gaitdlog(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 = "logitlink", 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(-7 * ppoints(12)), 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.

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 logffMlink 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 argument 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 and gaitdpoisson 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 Gaitdlog.

As alluded to above, when there are covariates it is much more interpretable to model the mean rather than the shape parameter. Hence logffMlink 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: gaitdlog() and logff(), gaitdlog(a.mix = 1) and oalog(zero = "pobs1"), gaitdlog(i.mix = 1) and oilog(zero = "pstr1"), gaitdlog(truncate = 1) and otlog(). The functions oalog, oilog and otlog 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)  avec <- c(5, 10)  # Alter these values parametrically
ivec <- c(3, 15)  # Inflate these values
tvec <- c(6, 7)   # Truncate these values
max.support <- 20; set.seed(1)
pobs.a <- pstr.i <- 0.1
gdata <- data.frame(x2 = runif(nn <- 1000))
gdata <- transform(gdata, shape.p = logitlink(2+0.5*x2, inverse = TRUE))
gdata <- transform(gdata,
  y1 = rgaitdlog(nn, shape.p, a.mix = avec, pobs.mix = pobs.a,
                i.mix = ivec, pstr.mix = pstr.i, truncate = tvec,
                max.support = max.support))
#> Error in eval(substitute(list(...)), `_data`, parent.frame()): object 'avec' not found
gaitdlog(a.mix = avec, i.mix = ivec, max.support = max.support)
#> Error: object 'avec' not found
with(gdata, table(y1))
#> Error in eval(substitute(expr), data, enclos = parent.frame()): object 'y1' not found
spikeplot(with(gdata, y1), las = 1)
#> Error in eval(substitute(expr), data, enclos = parent.frame()): object 'y1' not found
fit7 <- vglm(y1 ~ x2, trace = TRUE, data = gdata,
             gaitdlog(i.mix = ivec, truncate = tvec,
                      max.support = max.support, a.mix = avec,
                      eq.ap = TRUE, eq.ip = TRUE))
#> Error in eval(predvars, data, env): object 'y1' not found
head(fitted(fit7, type.fitted = "Pstr.mix"))
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'fitted': object 'fit7' not found
head(predict(fit7))
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'predict': object 'fit7' not found
t(coef(fit7, matrix = TRUE))  # Easier to see with t()
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'coef': object 'fit7' not found
summary(fit7)
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'summary': object 'fit7' not found
spikeplot(with(gdata, y1), lwd = 2, ylim = c(0, 0.4))
#> Error in eval(substitute(expr), data, enclos = parent.frame()): object 'y1' not found
plotdgaitd(fit7, new.plot = FALSE, offset.x = 0.2, all.lwd = 2)   # \dontrun{}
#> Error in h(simpleError(msg, call)): error in evaluating the argument 'object' in selecting a method for function 'plotdgaitd': object 'fit7' not found