Additional families — Families • sdmTMB

Additional families compatible with sdmTMB().

Usage

Beta(link = "logit")

lognormal(link = "log")

gengamma(link = "log")

gamma_mix(link = "log")

lognormal_mix(link = "log")

nbinom2_mix(link = "log")

nbinom2(link = "log")

nbinom1(link = "log")

truncated_nbinom2(link = "log")

truncated_nbinom1(link = "log")

student(link = "identity", df = 3)

tweedie(link = "log")

censored_poisson(link = "log")

delta_gamma(link1, link2 = "log", type = c("standard", "poisson-link"))

delta_gamma_mix(link1 = "logit", link2 = "log")

delta_gengamma(link1, link2 = "log", type = c("standard", "poisson-link"))

delta_lognormal(link1, link2 = "log", type = c("standard", "poisson-link"))

delta_lognormal_mix(link1, link2 = "log", type = c("standard", "poisson-link"))

delta_truncated_nbinom2(link1 = "logit", link2 = "log")

delta_truncated_nbinom1(link1 = "logit", link2 = "log")

delta_poisson_link_gamma(link1 = "log", link2 = "log")

delta_poisson_link_lognormal(link1 = "log", link2 = "log")

delta_beta(link1 = "logit", link2 = "logit")

Arguments

link: Link.
df: Student-t degrees of freedom fixed value parameter.
link1: Link for first part of delta/hurdle model. Defaults to "logit" for type = "standard" and "log" for type = "poisson-link".
link2: Link for second part of delta/hurdle model.
type: Delta/hurdle family type. "standard" for a classic hurdle model. "poisson-link" for a Poisson-link delta model (Thorson 2018).

Value

A list with elements common to standard R family objects including family, link, linkfun, and linkinv. Delta/hurdle model families also have elements delta (logical) and type (standard vs. Poisson-link).

Details

delta_poisson_link_gamma() and delta_poisson_link_lognormal() have been deprecated in favour of delta_gamma(type = "poisson-link") and delta_lognormal(type = "poisson-link").

The gengamma() family was implemented by J.T. Thorson and uses the Prentice (1974) parameterization such that the lognormal occurs as the internal parameter gengamma_Q (reported in print() or summary() as "Generalized gamma Q") approaches 0. If Q matches phi the distribution should be the gamma.

The families ending in _mix() are 2-component mixtures where each distribution has its own mean but a shared scale parameter. (Thorson et al. 2011). See the model-description vignette for details. The parameter plogis(log_p_mix) is the probability of the extreme (larger) mean and exp(log_ratio_mix) + 1 is the ratio of the larger extreme mean to the "regular" mean. You can see these parameters in model$sd_report.

The nbinom2 negative binomial parameterization is the NB2 where the variance grows quadratically with the mean (Hilbe 2011).

The nbinom1 negative binomial parameterization lets the variance grow linearly with the mean (Hilbe 2011).

For student(), the degrees of freedom parameter is currently not estimated and is fixed at df.

References

Generalized gamma family:

Prentice, R.L. 1974. A log gamma model and its maximum likelihood estimation. Biometrika 61(3): 539–544. doi:10.1093/biomet/61.3.539

Stacy, E.W. 1962. A Generalization of the Gamma Distribution. The Annals of Mathematical Statistics 33(3): 1187–1192. Institute of Mathematical Statistics.

Families ending in _mix():

Thorson, J.T., Stewart, I.J., and Punt, A.E. 2011. Accounting for fish shoals in single- and multi-species survey data using mixture distribution models. Can. J. Fish. Aquat. Sci. 68(9): 1681–1693. doi:10.1139/f2011-086 .

Negative binomial families:

Hilbe, J. M. 2011. Negative binomial regression. Cambridge University Press.

Poisson-link delta families:

Thorson, J.T. 2018. Three problems with the conventional delta-model for biomass sampling data, and a computationally efficient alternative. Canadian Journal of Fisheries and Aquatic Sciences, 75(9), 1369-1382. doi:10.1139/cjfas-2017-0266

Examples

Beta(link = "logit")
#> 
#> Family: Beta 
#> Link function: logit 
#> 
lognormal(link = "log")
#> 
#> Family: lognormal 
#> Link function: log 
#> 
gengamma(link = "log")
#> 
#> Family: gengamma 
#> Link function: log 
#> 
gamma_mix(link = "log")
#> 
#> Family: gamma_mix 
#> Link function: log 
#> 
lognormal_mix(link = "log")
#> 
#> Family: lognormal_mix 
#> Link function: log 
#> 
nbinom2_mix(link = "log")
#> 
#> Family: nbinom2_mix 
#> Link function: log 
#> 
nbinom2(link = "log")
#> 
#> Family: nbinom2 
#> Link function: log 
#> 
nbinom1(link = "log")
#> 
#> Family: nbinom1 
#> Link function: log 
#> 
truncated_nbinom2(link = "log")
#> 
#> Family: truncated_nbinom2 
#> Link function: log 
#> 
truncated_nbinom1(link = "log")
#> 
#> Family: truncated_nbinom1 
#> Link function: log 
#> 
student(link = "identity")
#> 
#> Family: student 
#> Link function: identity 
#> 
tweedie(link = "log")
#> 
#> Family: tweedie 
#> Link function: log 
#> 
censored_poisson(link = "log")
#> 
#> Family: censored_poisson 
#> Link function: log 
#> 
delta_gamma()
#> 
#> Family: binomial Gamma 
#> Link function: logit log 
#> 
delta_gamma_mix()
#> 
#> Family: binomial gamma_mix 
#> Link function: logit log 
#> 
delta_gengamma()
#> 
#> Family: binomial gengamma 
#> Link function: logit log 
#> 
delta_lognormal()
#> 
#> Family: binomial lognormal 
#> Link function: logit log 
#> 
delta_lognormal_mix()
#> 
#> Family: binomial lognormal_mix 
#> Link function: logit log 
#> 
delta_truncated_nbinom2()
#> 
#> Family: binomial truncated_nbinom2 
#> Link function: logit log 
#> 
delta_truncated_nbinom1()
#> 
#> Family: binomial truncated_nbinom1 
#> Link function: logit log 
#> 
delta_beta()
#> 
#> Family: binomial Beta 
#> Link function: logit logit 
#>