# sigma.glmmTMB: Extract residual standard deviation or dispersion parameter In glmmTMB: Generalized Linear Mixed Models using Template Model Builder

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

nbinom2

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).

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

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

tweedie

returns the value of phi, where the variance is phi*mu^p. The value of p can be extracted using the internal function `glmmTMB:::.tweedie_power`.

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

### References

• 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. https://CRAN.R-project.org/package=COMPoissonReg

glmmTMB documentation built on July 12, 2022, 5:06 p.m.