# nbinom2: Family functions for glmmTMB In glmmTMB: Generalized Linear Mixed Models using Template Model Builder

## Description

Family functions for glmmTMB

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25``` ```nbinom2(link = "log") nbinom1(link = "log") compois(link = "log") truncated_compois(link = "log") genpois(link = "log") truncated_genpois(link = "log") truncated_poisson(link = "log") truncated_nbinom2(link = "log") truncated_nbinom1(link = "log") beta_family(link = "logit") betabinomial(link = "logit") tweedie(link = "log") ziGamma(link = "inverse") ```

## Arguments

 `link` (character) link function for the conditional mean ("log", "logit", "probit", "inverse", "cloglog", "identity", or "sqrt")

## Details

If specified, the dispersion model uses a log link. Denoting the variance as V, the dispersion parameter as phi=exp(eta) (where eta is the linear predictor from the dispersion model), and the predicted mean as mu:

gaussian

(from base R): constant V=phi

Gamma

(from base R) phi is the shape parameter. V=mu*phi

ziGamma

a modified version of `Gamma` that skips checks for zero values, allowing it to be used to fit hurdle-Gamma models

nbinom2

Negative binomial distribution: quadratic parameterization (Hardin & Hilbe 2007). V=mu*(1+mu/phi) = mu+mu^2/phi.

nbinom1

Negative binomial distribution: linear parameterization (Hardin & Hilbe 2007). V=mu*(1+phi)

truncated_nbinom2

Zero-truncated version of nbinom2: variance expression from Shonkwiler 2016. Simulation code (for this and the other truncated count distributions) is taken from C. Geyer's functions in the `aster` package; the algorithms are described in this vignette.

compois

Conway-Maxwell Poisson distribution: parameterized with the exact mean (Huang 2017), which differs from the parameterization used in the COMPoissonReg package (Sellers & Shmueli 2010, Sellers & Lotze 2015). V=mu*phi.

genpois

Generalized Poisson distribution (Consul & Famoye 1992). V=mu*exp(eta). (Note that Consul & Famoye (1992) define phi differently.) Our implementation is taken from the `HMMpa` package, based on Joe and Zhu (2005) and implemented by Vitali Witowski.

beta

Beta distribution: parameterization of Ferrari and Cribari-Neto (2004) and the betareg package (Cribari-Neto and Zeileis 2010); V=mu*(1-mu)/(phi+1)

betabinomial

Beta-binomial distribution: parameterized according to Morris (1997). V=mu*(1-mu)*(n*(phi+n)/(phi+1))

tweedie

Tweedie distribution: V=phi*mu^p. The power parameter is restricted to the interval 1<p<2. Code taken from the `tweedie` package, written by Peter Dunn.

## Value

returns a list with (at least) components

 `family` length-1 character vector giving the family name `link` length-1 character vector specifying the link function `variance` a function of either 1 (mean) or 2 (mean and dispersion parameter) arguments giving a value proportional to the predicted variance (scaled by `sigma(.)`)

## References

• Consul PC & 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.

• Joe H, Zhu R (2005). "Generalized Poisson Distribution: The Property of Mixture of Poisson and Comparison with Negative Binomial Distribution." Biometrical Journal 47(2): 219–29. doi:10.1002/bimj.200410102.

• Morris W (1997). "Disentangling Effects of Induced Plant Defenses and Food Quantity on Herbivores by Fitting Nonlinear Models." American Naturalist 150:299-327.

• 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

• Sellers K & Shmueli G (2010) "A Flexible Regression Model for Count Data." Annals of Applied Statistics 4(2), 943–61. https://doi.org/10.1214/09-AOAS306.

• Shonkwiler, J. S. (2016). "Variance of the truncated negative binomial distribution." Journal of Econometrics 195(2), 209–210. doi:10.1016/j.jeconom.2016.09.002

glmmTMB documentation built on Sept. 20, 2021, 5:07 p.m.