ztpreg: Zero-truncated Poisson and Negative Binomial Regression...
In ipeglim: Imprecise Inferential Framework on Statistical Reasoning

Description Usage Arguments Value TODO Author(s) References See Also Examples

Zero-truncated Poisson and Negative Bionomial regression models are used for estimating the unknown population size using a single registration file in the stuides of Heijden (2003) and Cruffy (2008). Zero-truncated Negative Binomial is an alternative of zero-truncated Poisson model when an overdispersion is suspected.

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  ztpreg(formula, data, dist = c("poisson", "nbinom"),
    method = c("BFGS", "L-BFGS-B"), hessian = TRUE,
    ztrunc = TRUE, ...)

`formula`	a symbolic description of the model to be fit.
`data`	a data frame containg the variables in the model.
`dist`	a description of sampling model to be used in the model.
`method`	the method to be used in fitting model. The default method uses `BFGS` in the `optim` function.
`hessian`	logical, Should a numerically differentiated Hessian matrix about regression parameters be returned?
`ztrunc`	logical, Is the sampling model used in the model assumed that zeros are truncated?
`...`	other arguments

An object of class ztpr with components including

`formula`	formula used to be fitted,
`converged`	integer code which indicates a successful completion of optimization process,
`niters`	integer that indicates a number of iterations until convergence to estimates,
`cfs`	estimated regression coefficients,
`vcv`	estimated variance-covariance matrix of regression coefficients which is obtained by the inverse of Hessian matrix
`llk`	value of log-likelihood function at `cfs`.

Currently, predict, extractAIC, residuals, fitted, residual plot, deviance are not supported.
Support another method of 'L-BFGS-B'.

Chel Hee Lee <gnustats@gmail.com>

Peter GM van der Heijden, Rami Bustami, Maarten JLF Cruyff, Godfried Engbersen and Hans C van Houwelingen (2003), Point and interval estimation of the population size using the truncated Poisson regression model, Statistical Modelling, 3, pp. 305-322.

Cruyff MJ and van der Heijden (2008) Point and interval estimation of the population size using a zero-truncated negative binomial regression model, Biometrical Journal, 50(6), pp. 1035-1050.

Dankmar Boehning and Peter G. M. van der Heijden (2009), A Covarite adjustment for zero-truncated approaches to estimating the size of hidden and elusive populations, The Annals of Applied Statistics, 3(2), pp. 595-610.

optim, glm.fit

#
# dat <- simulateYX(N=1e3, Xreg=FALSE, param=2, ztrunc=TRUE)
# y <- dat$y

# m <- ztpr(formula=y~1, ztrunc=TRUE, dist="poisson")
# fit <- summary(m, HT.est=TRUE, LM.test=TRUE)
# mhat <- exp(fit$cfs)
# print(fit$LM.chisq)
# print(c(fit$N, fit$cil, fit$ciu))