Create a dispersion parameter object for use with other functions.
dispersion_params(family, dispersion)The generalized linear model family describing the distribution
of the response variable to be used. "poisson", "nbinomial", "binomial",
"beta", "Gamma", and "inverse.gaussian".
The value of the dispersion parameter.
A named numeric vector with class family containing the dispersion.
The variance function of an individual \(y\) (given \(\mu\)) for each generalized linear model family is given below:
family: \(Var(y)\)
poisson: \(\mu \phi\)
nbinomial: \(\mu + \mu^2 / \phi\)
binomial: \(n \mu (1 - \mu) \phi\)
beta: \(\mu (1 - \mu) / (1 + \phi)\)
Gamma: \(\mu^2 / \phi\)
inverse.gaussian: \(\mu^2 / \phi\)
The parameter \(\phi\) is a dispersion parameter that influences \(Var(y)\).
For the poisson and binomial families, \(\phi\) is always
one. Note that this inverse Gaussian parameterization is different than a
standard inverse Gaussian parameterization, which has variance \(\mu^3 / \lambda\).
Setting \(\phi = \lambda / \mu\) yields our parameterization, which is
preferred for computational stability. Also note that the dispersion parameter
is often defined in the literature as \(V(\mu) \phi\), where \(V(\mu)\) is the variance
function of the mean. We do not use this parameterization, which is important
to recognize while interpreting dispersion parameter estimates using spglm() or spgautor().
For more on generalized linear model constructions, see McCullagh and
Nelder (1989).
McCullagh P. and Nelder, J. A. (1989) Generalized Linear Models. London: Chapman and Hall.
dispersion_params("beta", dispersion = 1)
#> dispersion
#> 1
#> attr(,"class")
#> [1] "beta"