oalog: One-Altered Logarithmic Distribution

In VGAMdata: Data Supporting the 'VGAM' Package

One-Altered Logarithmic Distribution

Description

Fits a one-altered logarithmic distribution based on a conditional model involving a Bernoulli distribution and a 1-truncated logarithmic distribution.

Usage

oalog(lpobs1 = "logitlink", lshape = "logitlink",
      type.fitted = c("mean", "shape", "pobs1", "onempobs1"),
      ipobs1 = NULL, gshape = ppoints(8), zero = NULL)

Arguments

lpobs1	Link function for the parameter p_1 or \phi, called pobs1 or phi here. See Links for more choices.
lshape	See logff for details.
gshape, type.fitted	See CommonVGAMffArguments and fittedvlm for information.
ipobs1, zero	See CommonVGAMffArguments for information.

Details

The response Y is one with probability p_1, or Y has a 1-truncated logarithmic distribution with probability 1-p_1. Thus 0 < p_1 < 1, which is modelled as a function of the covariates. The one-altered logarithmic distribution differs from the one-inflated logarithmic distribution in that the former has ones coming from one source, whereas the latter has ones coming from the logarithmic distribution too. The one-inflated logarithmic distribution is implemented in the VGAM package. Some people call the one-altered logarithmic a hurdle model.

The input can be a matrix (multiple responses). By default, the two linear/additive predictors of oalog are (logit(\phi), logit(s))^T.

Value

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

The fitted.values slot of the fitted object, which should be extracted by the generic function fitted, returns the mean \mu (default) which is given by

\mu = \phi + (1-\phi) A

where A is the mean of the one-truncated logarithmic distribution. If type.fitted = "pobs1" then p_1 is returned.

Note

This family function effectively combines binomialff and otlog into one family function.

Author(s)

T. W. Yee

See Also

Gaitdlog, Oalog, logff, oilog, CommonVGAMffArguments, simulate.vlm.

Examples

## Not run: odata <- data.frame(x2 = runif(nn <- 1000))
odata <- transform(odata, pobs1  = logitlink(-1 + 2*x2, inv = TRUE),
                          shape  = logitlink(-2 + 3*x2, inv = TRUE))
odata <- transform(odata, y1 = roalog(nn, shape, pobs1 = pobs1),
                          y2 = roalog(nn, shape, pobs1 = pobs1))
with(odata, table(y1))

ofit <- vglm(cbind(y1, y2) ~ x2, oalog, data = odata, trace = TRUE)
coef(ofit, matrix = TRUE)
head(fitted(ofit))
head(predict(ofit))
summary(ofit)

## End(Not run)

VGAMdata documentation built on Sept. 17, 2024, 9:09 a.m.