sigma.glmmTMB: Extract residual standard deviation or dispersion parameter

Description

For Gaussian models, sigma returns the value of the residual standard deviation; for other families, it returns the dispersion parameter, however it is defined for that particular family. See details for each family below.

Usage

# S3 method for glmmTMB
sigma(object, ...)

Arguments

object

a “glmmTMB” fitted object

…

(ignored; for method compatibility)

Details

The value returned varies by family:

gaussian: returns the maximum likelihood estimate of the standard deviation (i.e., smaller than the results of sigma(lm(...)) by a factor of (n-1)/n)
nbinom1: returns an overdispersion parameter (usually denoted \(\alpha\) as in Hardin and Hilbe (2007)): such that the variance equals \(\mu(1+\alpha)\).
nbinom2: returns an overdispersion parameter (usually denoted \(\theta\) or \(k\)); in contrast to most other families, larger \(\theta\) corresponds to a lower variance which is \(\mu(1+\mu/\theta)\).
Gamma: Internally, glmmTMB fits Gamma responses by fitting a mean and a shape parameter; sigma is estimated as (1/sqrt(shape)), which will typically be close (but not identical to) that estimated by stats:::sigma.default, which uses sqrt(deviance/df.residual)
beta: returns the value of \(\phi\), where the conditional variance is \(\mu(1-\mu)/(1+\phi)\) (i.e., increasing \(\phi\) decreases the variance.) This parameterization follows Ferrari and Cribari-Neto (2004) (and the betareg package):
betabinomial: This family uses the same parameterization (governing the Beta distribution that underlies the binomial probabilities) as beta.
genpois: returns the value of \(\phi\), where the variance is \(\mu\phi\)
compois: returns the value of \(1/\nu\), When \(\nu=1\), compois is equivalent to the Poisson distribution. There is no closed form equation for the variance, but it is approximately undersidpersed when \(1/\nu <1\) and approximately oversidpersed when \(1/\nu >1\). In this implementation, \(\mu\) is excatly the mean, which differs from the COMPoissonReg package (Sellers & Lotze 2015).

The most commonly used GLM families (binomial, poisson) have fixed dispersion parameters which are internally ignored.

References

Ferrari SLP, Cribari-Neto F (2004). "Beta Regression for Modelling Rates and Proportions." J. Appl. Stat. 31(7), 799-815.
Hardin JW & Hilbe JM (2007). "Generalized linear models and extensions." Stata press.
Sellers K & Lotze T (2015). "COMPoissonReg: Conway-Maxwell Poisson (COM-Poisson) Regression". R package version 0.3.5. https://CRAN.R-project.org/package=COMPoissonReg