families: Additional families

In sdmTMB: Spatial and Spatiotemporal SPDE-Based GLMMs with 'TMB'

Additional families

Description

Additional families compatible with sdmTMB().

Usage

Beta(link = "logit")

lognormal(link = "log")

gengamma(link = "log")

gamma_mix(link = "log", p_extreme = NULL)

lognormal_mix(link = "log", p_extreme = NULL)

nbinom2_mix(link = "log", p_extreme = NULL)

nbinom2(link = "log")

nbinom1(link = "log")

truncated_nbinom2(link = "log")

truncated_nbinom1(link = "log")

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

tweedie(link = "log")

censored_poisson(link = "log")

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

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

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"),
  p_extreme = NULL
)

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")

betabinomial(link = "logit")

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

Arguments

link	Link.
p_extreme	Optional fixed probability for the extreme component. If NULL (default), this is estimated. If specified, must be a proportion between 0 and 1.
df	Student-t degrees of freedom parameter. Can be NULL to estimate (default) or a numeric value > 1 to fix at a specific value.
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).

Details

The default link1 for delta models of type = "standard" is "logit". The default link1 for delta models of type = "poisson-link" is "log".

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 p_extreme = plogis(logit_p_extreme) 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 parameter p_extreme can be fixed a priori and passed in as a proportion for these families.

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 estimated by default (df = NULL). You can fix it at a specific value by providing a number > 1 (e.g., df = 3).

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).

References

Generalized gamma family:

Prentice, R.L. 1974. A log gamma model and its maximum likelihood estimation. Biometrika 61(3): 539–544. \Sexpr[results=rd]{tools:::Rd_expr_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.

Dunic, J.C., Conner, J., Anderson, S.C., and Thorson, J.T. 2025. The generalized gamma is a flexible distribution that outperforms alternatives when modelling catch rate data. ICES Journal of Marine Science 82(4): fsaf040. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1093/icesjms/fsaf040")}.

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. \Sexpr[results=rd]{tools:::Rd_expr_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. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1139/cjfas-2017-0266")}

Examples

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") # estimate df
student(link = "identity", df = 3) # fix df at 3
tweedie(link = "log")
censored_poisson(link = "log")
delta_gamma()
delta_gamma_mix()
delta_gengamma()
delta_lognormal()
delta_lognormal_mix()
delta_truncated_nbinom2()
delta_truncated_nbinom1()
betabinomial(link = "logit")
delta_beta()

sdmTMB documentation built on Nov. 26, 2025, 9:06 a.m.