Zero-Inflated Binomial Distribution Family Function
Fits a zero-inflated binomial distribution by maximum likelihood estimation.
zibinomial(lpstr0 = "logitlink", lprob = "logitlink",
type.fitted = c("mean", "prob", "pobs0", "pstr0", "onempstr0"),
ipstr0 = NULL, zero = NULL, multiple.responses = FALSE,
imethod = 1)
zibinomialff(lprob = "logitlink", lonempstr0 = "logitlink",
type.fitted = c("mean", "prob", "pobs0", "pstr0", "onempstr0"),
ionempstr0 = NULL, zero = "onempstr0",
multiple.responses = FALSE, imethod = 1)lpstr0, lprob |
Link functions for the parameter phi
and the usual binomial probability prob parameter.
See |
type.fitted |
See |
ipstr0 |
Optional initial values for phi, whose values must lie between 0 and 1. The default is to compute an initial value internally. If a vector then recyling is used. |
lonempstr0, ionempstr0 |
Corresponding arguments for the other parameterization. See details below. |
multiple.responses |
Logical. Currently it must be |
zero, imethod |
See |
These functions are based on
P(Y=0) = phi + (1- phi) * (1-prob)^N,
for y=0, and
P(Y=y) = (1-phi) * choose(N,Ny) * prob^(N*y) * (1-prob)^(N*(1-y)).
for y=1/N,2/N,…,1. That is, the response is a sample
proportion out of N trials, and the argument size in
rzibinom is N here.
The parameter phi is the probability of a structural zero,
and it satisfies 0 < phi < 1.
The mean of Y is E(Y) = (1-phi) * prob
and these are returned as the fitted values
by default.
By default, the two linear/additive predictors
for zibinomial()
are (logit(phi), logit(prob))^T.
The VGAM family function zibinomialff() has a few
changes compared to zibinomial().
These are:
(i) the order of the linear/additive predictors is switched so the
binomial probability comes first;
(ii) argument onempstr0 is now 1 minus
the probability of a structural zero, i.e.,
the probability of the parent (binomial) component,
i.e., onempstr0 is 1-pstr0;
(iii) argument zero has a new default so that the onempstr0
is intercept-only by default.
Now zibinomialff() is generally recommended over
zibinomial().
Both functions implement Fisher scoring.
An object of class "vglmff" (see vglmff-class).
The object is used by modelling functions such as vglm
and vgam.
Numerical problems can occur.
Half-stepping is not uncommon.
If failure to converge occurs, make use of the argument ipstr0
or ionempstr0,
or imethod.
The response variable must 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 needs large values of N and prob>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.
Setting stepsize = 0.5, say, may aid convergence.
Estimated probabilities of a structural zero and an
observed zero are returned, as in zipoisson.
The zero-deflated binomial distribution might
be fitted by setting lpstr0 = identitylink, albeit,
not entirely reliably. See zipoisson
for information that can be applied here. Else
try the zero-altered binomial distribution (see
zabinomial).
T. W. Yee
Welsh, A. H., Lindenmayer, D. B. and Donnelly, C. F. (2013). Fitting and interpreting occupancy models. PLOS One, 8, 1–21.
size <- 10 # Number of trials; N in the notation above
nn <- 200
zdata <- data.frame(pstr0 = logitlink( 0, inverse = TRUE), # 0.50
mubin = logitlink(-1, inverse = TRUE), # Mean of usual binomial
sv = rep(size, length = nn))
zdata <- transform(zdata,
y = rzibinom(nn, size = sv, prob = mubin, pstr0 = pstr0))
with(zdata, table(y))
fit <- vglm(cbind(y, sv - y) ~ 1, zibinomialff, data = zdata, trace = TRUE)
fit <- vglm(cbind(y, sv - y) ~ 1, zibinomialff, data = zdata, trace = TRUE,
stepsize = 0.5)
coef(fit, matrix = TRUE)
Coef(fit) # Useful for intercept-only models
head(fitted(fit, type = "pobs0")) # Estimate of P(Y = 0)
head(fitted(fit))
with(zdata, mean(y)) # Compare this with fitted(fit)
summary(fit)Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.