Fits a zero-inflated Poisson distribution based on Yip (1988).
yip88(link = "loglink", n.arg = NULL, imethod = 1)
Link function for the usual
The total number of observations in the data set. Needed when the response variable has all the zeros deleted from it, so that the number of zeros can be determined.
The method implemented here, Yip (1988), maximizes
likelihood. Consequently, the methodology used here
zeros from the data set, and is thus related to the
P(Y=0) = 0).
The probability function of
Y is 0 with probability
P(Y=0) =\phi + (1-\phi) P(W=0)
W is Poisson(
can be obtained
by the extractor function
fitted applied to the object.
This family function treats
\phi as a scalar.
If you want
to model both
as a function
of covariates, try
An object of class
The object is used by modelling functions
Under- or over-flow may occur if the data is
Yip (1988) only considered
being a scalar and not
modelled as a function of covariates. To get
around this limitation,
Inference obtained from
may or may not be correct. In particular,
the p-values, standard
errors and degrees of freedom may need adjustment.
Use simulation on
artificial data to check that these are reasonable.
The data may be inputted in two ways.
The first is when the response is
a vector of positive values, with the
specifying the total number of observations.
The second is simply
include all the data in the response.
In this case, the zeros are
trimmed off during the computation, and
slots of the object, if assigned, will reflect this.
The estimate of
\phi is placed in
misc slot as
@misc$pstr0. However, this estimate is
computed only for intercept
models, i.e., the formula is of the form
y ~ 1.
Thomas W. Yee
Yip, P. (1988). Inference about the mean of a Poisson distribution in the presence of a nuisance parameter. The Australian Journal of Statistics, 30, 299–306.
Angers, J-F. and Biswas, A. (2003). A Bayesian analysis of zero-inflated generalized Poisson model. Computational Statistics & Data Analysis, 42, 37–46.
phi <- 0.35; lambda <- 2 # Generate some artificial data y <- rzipois(n <- 1000, lambda, phi) table(y) # Two equivalent ways of fitting the same model fit1 <- vglm(y ~ 1, yip88(n = length(y)), subset = y > 0) fit2 <- vglm(y ~ 1, yip88, trace = TRUE, crit = "coef") (true.mean <- (1-phi) * lambda) mean(y) head(fitted(fit1)) fit1@misc$pstr0 # The estimate of phi # Compare the ZIP with the positive Poisson distribution pp <- vglm(y ~ 1, pospoisson, subset = y > 0, crit = "c") coef(pp) Coef(pp) coef(fit1) - coef(pp) # Same head(fitted(fit1) - fitted(pp)) # Different # Another example (Angers and Biswas, 2003) --------------------- abdata <- data.frame(y = 0:7, w = c(182, 41, 12, 2, 2, 0, 0, 1)) abdata <- subset(abdata, w > 0) yy <- with(abdata, rep(y, w)) fit3 <- vglm(yy ~ 1, yip88(n = length(yy)), subset = yy > 0) fit3@misc$pstr0 # phi estimate (they get 0.5154 with SE 0.0707) coef(fit3, matrix = TRUE) Coef(fit3) # Estimate of lambda (they get 0.6997 with SE 0.1520) head(fitted(fit3)) mean(yy) # Compare this with fitted(fit3)
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