VGAM (version 1.0-6)

oiposbinomial: One-Inflated Positive Binomial Distribution Family Function

Description

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

Usage

oiposbinomial(lpstr1 = "logit", lprob = "logit",
              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 $\varphi$ 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 $$P(Y=y)=\varphi +(1-\varphi )N\mu (1-\mu {)}^N/(1-(1-\mu {)}^N),$$ for $y=1/N$, and $$P(Y=y)=(1-\varphi )(\genfrac{}{}{0ex}{}{N}{Ny}){\mu }^{Ny}(1-\mu {)}^{N(1-y)}/(1-(1-\mu {)}^N).$$ for $y=2/N,\dots ,1$. 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 $\varphi$ is the probability of a structural one, and it satisfies $0<\varphi <1$ (usually). The mean of $Y$ is $E(Y)=\varphi +(1-\varphi )\mu /(1-(1-\mu {)}^N)$ and these are returned as the default fitted values. By default, the two linear/additive predictors for oiposbinomial() are $(logit(\varphi ),logit(\mu ){)}^T$.

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  = logit( 0, inverse = TRUE),  # 0.50
                    mubin1 = logit(-1, inverse = TRUE),  # Mean of usual binomial
                    svec   = rep(size, length = nn),
                    x2     = runif(nn))
odata <- transform(odata,
                   mubin2 = logit(-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)
# }