skellam (version 0.2.3)

skellam.reg: Regression assuming a Skellam distribution

Description

Regression assuming a Skellam distribution.

Usage

skellam.reg(y, x)

Value

A list including:

loglik

The maximised log-likelihood value.

param1

The estimated regression coefficients of \(\lambda_1\). This is matrix, with the first column being the estimated regression coefficients. The second column is their relevant standard error. The third column is the t value (coef/se(coef)) and the final column is the p-value of the Wald test.

param2

The estimated regression coefficients of \(\lambda_2\). This is matrix, with the first column being the estimated regression coefficients. The second column is their relevant standard error. The third column is the t value (coef/se(coef)) and the final column is the p-value of the Wald test.

Arguments

y

A vector of integers, positive or negative.

x

A matrix, a vector or a data.frame with the covariates.

Author

Michail Tsagris

Details

We use the exponential link function to ensure that the both \(\lambda_s\) are positive. The command nlm does the main job.

References

Skellam, J. G. (1946) The frequency distribution of the difference between two Poisson variates belonging to different populations. Journal of the Royal Statistical Society, series A 109/3, 26.

Strackee, J.; van der Gon, J. J. D. (1962) The frequency distribution of the difference between two Poisson variates. Statistica Neerlandica 16/1, 17-23.

Karlis and Ntzoufras IMA 2009 presentation http://www2.stat-athens.aueb.gr/~jbn/papers/files/20_Karlis_Ntzoufras_2009_IMA_presentation_handouts_v01.pdf

Examples

require('skellam')

set.seed(0)

x <- rnorm(1000)
y1 <- rpois(1000, exp(1 + 1 * x) )
y2 <- rpois(1000 , exp(-1 + 1 * x) )
y <- y2 - y1
skellam.reg(y, x)