Family function for GLMs and mixed models with Poisson and zero-truncated Poisson response.
Poisson (with a capital P) is a family that specifies the information required to fit a Poisson generalized linear model. Differs from the base version stats::poisson only in that it handles the zero-truncated variant, which can be specified either as Tpoisson(<link>) or as Poisson(<link>, trunc = 0L). The truncated poisson with mean μ_T is defined from the un-truncated poisson with mean μ_U, by restricting its response strictly positive value. μ_T=μ_U/(1-p0), where p0:=\exp(-μ_U) is the probability that the response is 0.
Poisson(link = "log", trunc = -1L) Tpoisson(link="log") # <Poisson object>$linkfun(mu, mu_truncated = FALSE) # <Poisson object>$linkinv(eta, mu_truncated = FALSE)
link |
log, sqrt or identity link, specified by any of the available ways for GLM links (name, character string, one-element character vector, or object of class |
trunc |
Either |
eta,mu |
Numeric (scalar or array). The linear predictor; and the expectation of response, truncated or not depending on |
mu_truncated |
Boolean. For |
The mu.eta member function is that of the base poisson family, hence ignores truncation.
predict, when applied on an object with a truncated-response family, by default returns μ_T. The simplest way to predict μ_U is to get the linear predictor value by predict(.,type="link"), and deduce μ_U using linkinv(.) (with default argument mu_truncated=FALSE), since getting μ_U from μ_T is comparatively less straightforward.
A family object.
McCullagh, P. and Nelder, J.A. (1989) Generalized Linear Models, 2nd edition. London: Chapman & Hall.
data("scotlip")
logLik(glm(I(1+cases)~1,family=Tpoisson(),data=scotlip))
logLik(fitme(I(1+cases)~1+(1|id),family=Tpoisson(),fixed=list(lambda=1e-8),data=scotlip))Please choose more modern alternatives, such as Google Chrome or Mozilla Firefox.