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
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)
This family uses the same parameterization (governing
the Beta distribution that underlies the binomial probabilities) as
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 the internal
The most commonly used GLM families
poisson) have fixed dispersion parameters which are
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
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