R: Extract residual standard deviation or dispersion parameter

sigma.glmmTMB {glmmTMB} | R Documentation

## 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 class '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 α as in Hardin and Hilbe (2007)): such that the variance equals μ(1+α).

nbinom2

  returns an overdispersion parameter (usually denoted θ or k); in contrast to most other families, larger θ corresponds to a lower variance which is μ(1+μ/θ).

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 φ, where the conditional variance is μ(1-μ)/(1+φ) (i.e., increasing φ 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 φ, where the variance is μφ

compois

  returns the value of 1/ν, When ν=1, compois is equivalent to the Poisson distribution. There is no closed form equation for the variance, but it is approximately undersidpersed when 1/ν <1 and approximately oversidpersed when 1/ν >1. In this implementation, μ 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

[Package glmmTMB version 0.2.2.0 Index]