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.
# S3 method for glmmTMB
sigma(object, ...)a “glmmTMB” fitted object
(ignored; for method compatibility)
The value returned varies by family:
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)
returns an overdispersion parameter (usually denoted \(\alpha\) as in Hardin and Hilbe (2007)): such that the variance equals \(\mu(1+\alpha)\).
returns an overdispersion parameter (usually denoted \(\theta\) or \(k\)); in contrast to most other families, larger \(\theta\) corresponds to a lower variance which is \(\mu(1+\mu/\theta)\).
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)
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):
This family uses the same parameterization (governing
the Beta distribution that underlies the binomial probabilities) as beta.
returns the value of \(\phi\), where the variance is \(\mu\phi\)
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.
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