# Poisson Regression Family function for a generalized linear model fitted to Poisson responses. ```r poissonff(link = "loglink", imu = NULL, imethod = 1, parallel = FALSE, zero = NULL, bred = FALSE, earg.link = FALSE, type.fitted = c("mean", "quantiles"), percentiles = c(25, 50, 75)) ``` ## Arguments - `link`: Link function applied to the mean or means. See `Links` for more choices and information. - `parallel`: A logical or formula. Used only if the response is a matrix. - `imu, imethod`: See `CommonVGAMffArguments` for more information. - `zero`: Can be an integer-valued vector specifying which linear/additive predictors are modelled as intercepts only. The values must be from the set {1,2, ,$M$}, where $M$ is the number of columns of the matrix response. See `CommonVGAMffArguments` for more information. - `bred, earg.link`: Details at `CommonVGAMffArguments`. Setting `bred = TRUE` should work for multiple responses and all `VGAM` link functions; it has been tested for `loglink`, `identity` but further testing is required. - `type.fitted, percentiles`: Details at `CommonVGAMffArguments`. ## Details $M$ defined above is the number of linear/additive predictors. With overdispersed data try `negbinomial`. ## Returns An object of class `"vglmff"` (see `vglmff-class`). The object is used by modelling functions such as `vglm`, `vgam`, `rrvglm`, `cqo`, and `cao`. ## References McCullagh, P. and Nelder, J. A. (1989). **Generalized Linear Models**, 2nd ed. London: Chapman & Hall. ## Author(s) Thomas W. Yee ## Note This function will handle a matrix response automatically. Regardless of whether the dispersion parameter is to be estimated or not, its value can be seen from the output from the `summary()` of the object. ## Warning With multiple responses, assigning a known dispersion parameter for **each** response is not handled well yet. Currently, only a single known dispersion parameter is handled well. ## See Also `Links`, `hdeff.vglm`, `negbinomial`, `genpoisson1`, `genpoisson2`, `genpoisson0`, `gaitdpoisson`, `zipoisson`, `N1poisson`, `pospoisson`, `skellam`, `mix2poisson`, `cens.poisson`, `ordpoisson`, `amlpoisson`, `inv.binomial`, `simulate.vlm`, `loglink`, `polf`, `rrvglm`, `cqo`, `cao`, `binomialff`, `poisson`, `Poisson`, `poisson.points`, `ruge`, `V1`, `V2`, `residualsvglm`, `margeff`. ## Examples ```r poissonff() set.seed(123) pdata <- data.frame(x2 = rnorm(nn <- 100)) pdata <- transform(pdata, y1 = rpois(nn, exp(1 + x2)), y2 = rpois(nn, exp(1 + x2))) (fit1 <- vglm(cbind(y1, y2) ~ x2, poissonff, data = pdata)) (fit2 <- vglm(y1 ~ x2, poissonff(bred = TRUE), data = pdata)) coef(fit1, matrix = TRUE) coef(fit2, matrix = TRUE) nn <- 200 cdata <- data.frame(x2 = rnorm(nn), x3 = rnorm(nn), x4 = rnorm(nn)) cdata <- transform(cdata, lv1 = 0 + x3 - 2*x4) cdata <- transform(cdata, lambda1 = exp(3 - 0.5 * (lv1-0)^2), lambda2 = exp(2 - 0.5 * (lv1-1)^2), lambda3 = exp(2 - 0.5 * ((lv1+4)/2)^2)) cdata <- transform(cdata, y1 = rpois(nn, lambda1), y2 = rpois(nn, lambda2), y3 = rpois(nn, lambda3)) ## Not run: lvplot(p1, y = TRUE, lcol = 2:4, pch = 2:4, pcol = 2:4, rug = FALSE) ```

poissonff function