VGAMdata (version 1.1-9)

# oilog: One-inflated Logarithmic Distribution Family Function

## Description

Fits a 1-inflated logarithmic distribution.

## Usage

type.fitted = c("mean", "shape", "pobs1", "pstr1",
"onempstr1"), ishape = NULL, gpstr1 = ppoints(8), gshape =
ppoints(8), zero = NULL)

## Value

An object of class "vglmff"

(see vglmff-class). The object is used by modelling functions such as vglm,

rrvglm and vgam.

## Arguments

lpstr1, lshape

Link functions. For lpstr1: the same idea as zipoisson except it applies to a structural 1.

gpstr1, gshape, ishape

For initial values. See CommonVGAMffArguments for information.

type.fitted, zero

See CommonVGAMffArguments for information.

Thomas W. Yee

## Details

The 1-inflated logarithmic distribution is a mixture distribution of the logarithmic distribution with some probability of obtaining a (structural) 1. Thus there are two sources for obtaining the value 1. This distribution is written here in a way that retains a similar notation to the one-inflated positive-Poisson, i.e., the probability $$P[Y=1]$$ involves another parameter $$\phi$$. See oipospoisson.

This family function can handle multiple responses.

Gaitdlog, Oilog, logff, Oizeta.

## Examples

Run this code
if (FALSE)  odata <- data.frame(x2 = runif(nn <- 1000))  # Artificial data
odata <- transform(odata, pstr1 = logitlink(-1 + x2, inv = TRUE),
shape = 0.5)
odata <- transform(odata, y1 = roilog(nn, shape, pstr1 = pstr1))
with(odata, table(y1))
fit1 <- vglm(y1 ~ x2, oilog(zero = "shape"), odata, trace = TRUE)
coef(fit1, matrix = TRUE)

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