sigma.glmmTMB: Extract residual standard deviation or dispersion parameter

View source: R/VarCorr.R

sigma.glmmTMBR Documentation

Extract residual standard deviation or dispersion parameter


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 class '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 a dispersion parameter (usually denoted \alpha as in Hardin and Hilbe (2007)): such that the variance equals \mu(1+\alpha).


returns a dispersion 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 index of dispersion \phi^2, where the variance is \mu\phi^2 (Consul & Famoye 1992)


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 exactly the mean (Huang 2017), which differs from the COMPoissonReg package (Sellers & Lotze 2015).


returns the value of \phi, where the variance is \phi\mu^p. The value of p can be extracted using family_params

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


  • Consul PC, and Famoye F (1992). "Generalized Poisson regression model. Communications in Statistics: Theory and Methods" 21:89–109.

  • 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.

  • Huang A (2017). "Mean-parametrized Conway–Maxwell–Poisson regression models for dispersed counts. " Statistical Modelling 17(6), 1-22.

  • Sellers K & Lotze T (2015). "COMPoissonReg: Conway-Maxwell Poisson (COM-Poisson) Regression". R package version 0.3.5.

glmmTMB documentation built on Oct. 7, 2023, 5:07 p.m.