poissonff: Poisson Regression

Description Usage Arguments Details Value Warning Note Author(s) References See Also Examples

View source: R/family.glmgam.R

Description

Family function for a generalized linear model fitted to Poisson responses.

Usage

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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.

Value

An object of class "vglmff" (see vglmff-class). The object is used by modelling functions such as vglm, vgam, rrvglm, cqo, and cao.

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.

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.

Author(s)

Thomas W. Yee

References

McCullagh, P. and Nelder, J. A. (1989). Generalized Linear Models, 2nd ed. London: Chapman & Hall.

See Also

Links, hdeff.vglm, negbinomial, genpoisson1, genpoisson2, genpoisson0, gaitpoisson, zipoisson, pospoisson, oipospoisson, otpospoisson, skellam, mix2poisson, cens.poisson, ordpoisson, amlpoisson, inv.binomial, simulate.vlm, loglink, polf, rrvglm, cqo, cao, binomialff, poisson, Poisson, poisson.points, ruge, V1, V2, residualsvglm.

Examples

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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) 

Example output

Loading required package: stats4
Loading required package: splines
Family:  poissonff 
Informal classes: poissonff, VGAMglm 

Poisson distribution

Link:     loge(lambda)
Variance: lambda

Call:
vglm(formula = cbind(y1, y2) ~ x2, family = poissonff, data = pdata)


Coefficients:
(Intercept):1 (Intercept):2          x2:1          x2:2 
    0.9175762     1.0204439     1.0471179     1.0084276 

Degrees of Freedom: 200 Total; 196 Residual
Residual deviance: 235.6729 
Log-likelihood: -387.3006 

Call:
vglm(formula = y1 ~ x2, family = poissonff(bred = TRUE), data = pdata)


Coefficients:
(Intercept)          x2 
  0.9203612   1.0466136 

Degrees of Freedom: 100 Total; 98 Residual
Residual deviance: 116.6895 
Log-likelihood: -191.1954 
            loge(E[y1]) loge(E[y2])
(Intercept)   0.9175762    1.020444
x2            1.0471179    1.008428
            loge(lambda)
(Intercept)    0.9203612
x2             1.0466136

VGAM documentation built on Jan. 16, 2021, 5:21 p.m.