VGAM (version 1.1-1)

oiposbinomial: One-Inflated Positive Binomial Distribution Family Function

Description

Fits a one-inflated positive binomial distribution by maximum likelihood estimation.

Usage

oiposbinomial(lpstr1 = "logitlink", lprob = "logitlink",
              type.fitted = c("mean", "prob", "pobs1", "pstr1", "onempstr1"),
              iprob = NULL, gpstr1 = ppoints(9), gprob  = ppoints(9),
              multiple.responses = FALSE, zero = NULL)

Arguments

lpstr1, lprob

Link functions for the parameter \(\phi\) and the positive binomial probability \(\mu\) parameter. See Links for more choices. See CommonVGAMffArguments also. For the one-deflated model see below.

type.fitted

See CommonVGAMffArguments and fittedvlm.

iprob, gpstr1, gprob

For initial values; see CommonVGAMffArguments.

multiple.responses

Logical. See binomialff and posbinomial.

zero

See CommonVGAMffArguments for information.

Value

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

Details

These functions are based on $$P(Y=y) = \phi + (1-\phi) N \mu (1-\mu)^N / (1-(1-\mu)^N),$$ for \(y=1/N\), and $$P(Y=y) = (1-\phi) {N \choose Ny} \mu^{Ny} (1-\mu)^{N(1-y)} / (1-(1-\mu)^N).$$ for \(y=2/N,\ldots,1\). That is, the response is a sample proportion out of \(N\) trials, and the argument size in roiposbinom is \(N\) here. Ideally \(N > 2\) is needed. The parameter \(\phi\) is the probability of a structural one, and it satisfies \(0 < \phi < 1\) (usually). The mean of \(Y\) is \(E(Y)=\phi + (1-\phi) \mu / (1-(1-\mu)^N)\) and these are returned as the default fitted values. By default, the two linear/additive predictors for oiposbinomial() are \((logit(\phi), logit(\mu))^T\).

See Also

roiposbinom, posbinomial, binomialff, rbinom.

Examples

# NOT RUN {
size <- 10  # Number of trials; N in the notation above
nn <- 200
odata <- data.frame(pstr1  = logitlink( 0, inverse = TRUE),  # 0.50
                    mubin1 = logitlink(-1, inverse = TRUE),  # Mean of usual binomial
                    svec   = rep(size, length = nn),
                    x2     = runif(nn))
odata <- transform(odata,
                   mubin2 = logitlink(-1 + x2, inverse = TRUE))
odata <- transform(odata,
                   y1 = roiposbinom(nn, svec, pr = mubin1, pstr1 = pstr1),
                   y2 = roiposbinom(nn, svec, pr = mubin2, pstr1 = pstr1))
with(odata, table(y1))
fit1 <- vglm(y1 / svec ~  1, oiposbinomial, data = odata,
             weights = svec, trace = TRUE, crit = "coef")
fit2 <- vglm(y2 / svec ~ x2, oiposbinomial, data = odata,
             weights = svec, trace = TRUE)

coef(fit1, matrix = TRUE)
Coef(fit1)  # Useful for intercept-only models
head(fitted(fit1, type = "pobs1"))  # Estimate of P(Y = 1)
head(fitted(fit1))
with(odata, mean(y1))  # Compare this with fitted(fit1)
summary(fit1)
# }