families: Additional families

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

Additional families

Description

Additional families compatible with sdmTMB(). In addition to gaussian(), Gamma(), binomial(), and poisson(), sdmTMB provides:

• Continuous: student(), lognormal(), gengamma()

• Proportions: Beta(), ordbeta()

• Non-negative with exact zeros: tweedie()

• Counts: nbinom2(), nbinom1(), truncated_nbinom2(), truncated_nbinom1(), betabinomial()

• Censored counts: censored_poisson(), censored_nbinom2(), censored_nbinom1(), censored_binomial(), censored_betabinomial()

• Two-component mixtures: gamma_mix(), lognormal_mix(), nbinom2_mix()

• Delta/hurdle: delta_gamma(), delta_lognormal(), delta_gengamma(), delta_beta(), delta_truncated_nbinom2(), delta_truncated_nbinom1(), delta_gamma_mix(), delta_lognormal_mix()

See 'Binomial families', 'Censored families', and 'Delta/hurdle models' in the Details of sdmTMB().

Usage

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

lognormal(link = "log")

gengamma(link = "log")

Beta(link = "logit")

ordbeta(link = "logit")

tweedie(link = "log")

nbinom2(link = "log")

nbinom1(link = "log")

truncated_nbinom2(link = "log")

truncated_nbinom1(link = "log")

betabinomial(link = "logit")

censored_poisson(link = "log")

censored_nbinom2(link = "log")

censored_nbinom1(link = "log")

censored_binomial(link = "logit")

censored_betabinomial(link = "logit")

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

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

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

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

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

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

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

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

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

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

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

Arguments

link	Link.
df	Student-t degrees of freedom parameter. Can be NULL to estimate (default) or a numeric value > 1 to fix at a specific value.
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.
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

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).

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 ordbeta() family implements the ordered-beta regression of Kubinec (2023) for continuous responses on the closed unit interval ⁠[0, 1]⁠ with point masses at the endpoints. It is a parsimonious alternative to zero-one-inflated beta models because the three components (zeros, ones, and continuous (0, 1) values) share a single linear predictor. Two internal cutpoints are estimated and reported on the response scale (plogis()).

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).

The ⁠censored_*()⁠ families treat some counts as known only to lie within a range, e.g., to account for hook competition in longline surveys (Watson et al. 2023). Supply the bounds with sdmTMB(censored_upper = ...).

• censored_poisson(), censored_nbinom1(), and censored_nbinom2() have no upper limit on the count; use an offset of log hooks for effort.

• censored_binomial() and censored_betabinomial() take the number of trials (e.g., hooks) via weights, which caps the count.

All but censored_poisson() need the RTMB backend (the default). See censored_method in sdmTMBcontrol() for how censored_betabinomial() computes its likelihood, and the hook competition article.

The families ending in ⁠_mix()⁠ are 2-component mixtures where each distribution has its own mean but they share a 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 default first-component link (link1) for delta models of type = "standard" is "logit". For type = "poisson-link", the default link1 is "log".

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")}.

Ordered beta regression:

Kubinec, R. 2023. Ordered beta regression: a parsimonious, well-fitting model for continuous data with lower and upper bounds. Political Analysis 31(4): 519–536. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1017/pan.2022.20")}

Negative binomial families:

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

Censored families:

Watson, J., Edwards, A.M., and Auger-Méthé, M. 2023. A statistical censoring approach accounts for hook competition in abundance indices from longline surveys. Canadian Journal of Fisheries and Aquatic Sciences. 80(3): 468–486. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1139/cjfas-2022-0159")}

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")}.

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

student(link = "identity") # estimate df
student(link = "identity", df = 3) # fix df at 3
lognormal(link = "log")
gengamma(link = "log")
Beta(link = "logit")
ordbeta(link = "logit")
tweedie(link = "log")
nbinom2(link = "log")
nbinom1(link = "log")
truncated_nbinom2(link = "log")
truncated_nbinom1(link = "log")
betabinomial(link = "logit")
censored_poisson(link = "log")
censored_nbinom2(link = "log")
censored_nbinom1(link = "log")
censored_binomial(link = "cloglog")
censored_betabinomial(link = "cloglog")
gamma_mix(link = "log")
lognormal_mix(link = "log")
nbinom2_mix(link = "log")
delta_gamma()
delta_lognormal()
delta_gengamma()
delta_beta()
delta_truncated_nbinom2()
delta_truncated_nbinom1()
delta_gamma_mix()
delta_lognormal_mix()

sdmTMB documentation built on Oct. 17, 2026, 1:07 a.m.