Family Object for the Zero-Truncated Poisson Distribution

Description

Family object for specification of zero-truncated Poisson models as a glm.

Usage

ztpoisson()

Details

The ztpoisson family allows to estimate zero-truncated Poisson regression models as generalized linear models. As in the zerotrunc function, the link function is a log-link between the mean \(\lambda\) of the untruncated Poisson distribution and the linear predictor. This corresponds to a non-canonical link between for the mean of the zero-truncated Poisson distribution which does not have a closed-form representation.

Note that for new family objects ‘glm()’ estimates a dispersion parameter by default. Thus, unlike for the poisson family the dispersion parameter is not fixed, unless dispersion = 1 is set explicitly .

Value

An object of class “family”.

See Also

dztpois, poisson, zerotrunc

Examples

library("countreg")

## data
data("CrabSatellites", package = "countreg")
cs <- subset(CrabSatellites, subset = satellites > 0)
cs$color <- as.numeric(cs$color)

## model
ztp1 <- glm(satellites ~ width + color, data = cs, family = ztpoisson)
ztp2 <- zerotrunc(satellites ~ width + color, data = cs)
summary(ztp1, dispersion = 1) ## to get fixed dispersion as for poisson

Call:
glm(formula = satellites ~ width + color, family = ztpoisson, 
    data = cs)

Coefficients:
            Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.562699   0.645491   0.872    0.383
width       0.034238   0.022231   1.540    0.124
color       0.007166   0.066627   0.108    0.914

(Dispersion parameter for ztpoisson family taken to be 1)

    Null deviance: 220.54  on 110  degrees of freedom
Residual deviance: 218.16  on 108  degrees of freedom
AIC: 541.09

Number of Fisher Scoring iterations: 5

summary(ztp2)

Call:
zerotrunc(formula = satellites ~ width + color, data = cs)

Deviance residuals:
    Min      1Q  Median      3Q     Max 
-2.5409 -0.9350 -0.2051  0.6278  3.7722 

Coefficients (truncated poisson with log link):
            Estimate Std. Error z value Pr(>|z|)
(Intercept) 0.562699   0.645439   0.872    0.383
width       0.034238   0.022227   1.540    0.123
color       0.007166   0.066627   0.108    0.914

Number of iterations in BFGS optimization: 6 
Log-likelihood: -267.5 on 3 Df