One-Inflated Positive Binomial Distribution Family Function
Fits a one-inflated positive binomial distribution by maximum likelihood estimation.
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)lpstr1, lprob |
Link functions for the parameter phi
and the positive binomial probability prob parameter.
See |
type.fitted |
See |
iprob, gpstr1, gprob |
For initial values;
see |
multiple.responses |
Logical.
See |
zero |
See |
These functions are based on
P(Y=y) = phi + (1- phi) * N * prob * (1-prob)^N / (1-(1-prob)^N),
for y=1/N, and
P(Y=y) = (1-phi) * choose(N,Ny) * prob^(N*y) * (1-prob)^(N*(1-y)) / (1-(1-prob)^N).
for y=2/N,…,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) * prob / (1-(1-prob)^N)
and these are returned as the default fitted values.
By default, the two linear/additive predictors
for oiposbinomial()
are (logit(phi), logit(prob))^T.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm
and vgam.
The response variable should have one of the formats described by
binomialff, e.g., a factor or two column matrix or a
vector of sample proportions with the weights argument
specifying the values of N.
To work well, one ideally needs large values of N and prob much greater than 0, i.e., the larger N and prob are, the better. If N = 1 then the model is unidentifiable since the number of parameters is excessive.
Estimated probabilities of a structural one and an
observed one are returned, as in zipoisson.
The one-deflated positive binomial distribution might
be fitted by setting lpstr1 = "identitylink", albeit,
not entirely reliably. See zipoisson
for information that can be applied here.
T. W. Yee
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)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.