Family objects provide a convenient way to specify the details of the models
used by many model fitting functions. The family functions presented here are
for use with brms only and will **not** work with other model
fitting functions such as glm or glmer.
However, the standard family functions as described in
family will work with brms.
You can also specify custom families for use in brms with
the custom_family function.
brmsfamily(
family,
link = NULL,
link_sigma = "log",
link_shape = "log",
link_nu = "logm1",
link_phi = "log",
link_kappa = "log",
link_beta = "log",
link_zi = "logit",
link_hu = "logit",
link_zoi = "logit",
link_coi = "logit",
link_disc = "log",
link_bs = "log",
link_ndt = "log",
link_bias = "logit",
link_xi = "log1p",
link_alpha = "identity",
link_quantile = "logit",
threshold = "flexible",
refcat = NULL
)student(link = "identity", link_sigma = "log", link_nu = "logm1")
bernoulli(link = "logit")
beta_binomial(link = "logit", link_phi = "log")
negbinomial(link = "log", link_shape = "log")
geometric(link = "log")
lognormal(link = "identity", link_sigma = "log")
shifted_lognormal(link = "identity", link_sigma = "log", link_ndt = "log")
skew_normal(link = "identity", link_sigma = "log", link_alpha = "identity")
exponential(link = "log")
weibull(link = "log", link_shape = "log")
frechet(link = "log", link_nu = "logm1")
gen_extreme_value(link = "identity", link_sigma = "log", link_xi = "log1p")
exgaussian(link = "identity", link_sigma = "log", link_beta = "log")
wiener(
link = "identity",
link_bs = "log",
link_ndt = "log",
link_bias = "logit"
)
Beta(link = "logit", link_phi = "log")
dirichlet(link = "logit", link_phi = "log", refcat = NULL)
logistic_normal(link = "identity", link_sigma = "log", refcat = NULL)
von_mises(link = "tan_half", link_kappa = "log")
asym_laplace(link = "identity", link_sigma = "log", link_quantile = "logit")
cox(link = "log")
hurdle_poisson(link = "log", link_hu = "logit")
hurdle_negbinomial(link = "log", link_shape = "log", link_hu = "logit")
hurdle_gamma(link = "log", link_shape = "log", link_hu = "logit")
hurdle_lognormal(link = "identity", link_sigma = "log", link_hu = "logit")
hurdle_cumulative(
link = "logit",
link_hu = "logit",
link_disc = "log",
threshold = "flexible"
)
zero_inflated_beta(link = "logit", link_phi = "log", link_zi = "logit")
zero_one_inflated_beta(
link = "logit",
link_phi = "log",
link_zoi = "logit",
link_coi = "logit"
)
zero_inflated_poisson(link = "log", link_zi = "logit")
zero_inflated_negbinomial(link = "log", link_shape = "log", link_zi = "logit")
zero_inflated_binomial(link = "logit", link_zi = "logit")
zero_inflated_beta_binomial(
link = "logit",
link_phi = "log",
link_zi = "logit"
)
categorical(link = "logit", refcat = NULL)
multinomial(link = "logit", refcat = NULL)
cumulative(link = "logit", link_disc = "log", threshold = "flexible")
sratio(link = "logit", link_disc = "log", threshold = "flexible")
cratio(link = "logit", link_disc = "log", threshold = "flexible")
acat(link = "logit", link_disc = "log", threshold = "flexible")
A character string naming the distribution family of the response
variable to be used in the model. Currently, the following families are
supported: gaussian, student, binomial,
bernoulli, beta-binomial, poisson, negbinomial,
geometric, Gamma, skew_normal, lognormal,
shifted_lognormal, exgaussian, wiener,
inverse.gaussian, exponential, weibull,
frechet, Beta, dirichlet, von_mises,
asym_laplace, gen_extreme_value, categorical,
multinomial, cumulative, cratio, sratio,
acat, hurdle_poisson, hurdle_negbinomial,
hurdle_gamma, hurdle_lognormal, hurdle_cumulative,
zero_inflated_binomial, zero_inflated_beta_binomial,
zero_inflated_beta, zero_inflated_negbinomial,
zero_inflated_poisson, and zero_one_inflated_beta.
A specification for the model link function. This can be a name/expression or character string. See the 'Details' section for more information on link functions supported by each family.
Link of auxiliary parameter sigma if being predicted.
Link of auxiliary parameter shape if being predicted.
Link of auxiliary parameter nu if being predicted.
Link of auxiliary parameter phi if being predicted.
Link of auxiliary parameter kappa if being predicted.
Link of auxiliary parameter beta if being predicted.
Link of auxiliary parameter zi if being predicted.
Link of auxiliary parameter hu if being predicted.
Link of auxiliary parameter zoi if being predicted.
Link of auxiliary parameter coi if being predicted.
Link of auxiliary parameter disc if being predicted.
Link of auxiliary parameter bs if being predicted.
Link of auxiliary parameter ndt if being predicted.
Link of auxiliary parameter bias if being predicted.
Link of auxiliary parameter xi if being predicted.
Link of auxiliary parameter alpha if being predicted.
Link of auxiliary parameter quantile if being predicted.
A character string indicating the type
of thresholds (i.e. intercepts) used in an ordinal model.
"flexible" provides the standard unstructured thresholds,
"equidistant" restricts the distance between
consecutive thresholds to the same value, and
"sum_to_zero" ensures the thresholds sum to zero.
Optional name of the reference response category used in
categorical, multinomial, dirichlet and
logistic_normal models. If NULL (the default), the first
category is used as the reference. If NA, all categories will be
predicted, which requires strong priors or carefully specified predictor
terms in order to lead to an identified model.
Below, we list common use cases for the different families. This list is not ment to be exhaustive.
Family gaussian can be used for linear regression.
Family student can be used for robust linear regression
that is less influenced by outliers.
Family skew_normal can handle skewed responses in linear
regression.
Families poisson, negbinomial, and geometric
can be used for regression of unbounded count data.
Families bernoulli, binomial, and beta_binomial
can be used for binary regression (i.e., most commonly logistic
regression).
Families categorical and multinomial can be used for
multi-logistic regression when there are more than two possible outcomes.
Families cumulative, cratio ('continuation ratio'),
sratio ('stopping ratio'), and acat ('adjacent category')
leads to ordinal regression.
Families Gamma, weibull, exponential,
lognormal, frechet, inverse.gaussian, and cox
(Cox proportional hazards model) can be used (among others) for
time-to-event regression also known as survival regression.
Families weibull, frechet, and gen_extreme_value
('generalized extreme value') allow for modeling extremes.
Families beta, dirichlet, and logistic_normal
can be used to model responses representing rates or probabilities.
Family asym_laplace allows for quantile regression when fixing
the auxiliary quantile parameter to the quantile of interest.
Family exgaussian ('exponentially modified Gaussian') and
shifted_lognormal are especially suited to model reaction times.
Family wiener provides an implementation of the Wiener
diffusion model. For this family, the main formula predicts the drift
parameter 'delta' and all other parameters are modeled as auxiliary parameters
(see brmsformula for details).
Families hurdle_poisson, hurdle_negbinomial,
hurdle_gamma, hurdle_lognormal, zero_inflated_poisson,
zero_inflated_negbinomial, zero_inflated_binomial,
zero_inflated_beta_binomial, zero_inflated_beta,
zero_one_inflated_beta, and hurdle_cumulative allow to estimate
zero-inflated and hurdle models. These models can be very helpful when there
are many zeros in the data (or ones in case of one-inflated models)
that cannot be explained by the primary distribution of the response.
Below, we list all possible links for each family. The first link mentioned for each family is the default.
Families gaussian, student, skew_normal,
exgaussian, asym_laplace, and gen_extreme_value
support the links (as names) identity, log, inverse,
and softplus.
Families poisson, negbinomial, geometric,
zero_inflated_poisson, zero_inflated_negbinomial,
hurdle_poisson, and hurdle_negbinomial support
log, identity, sqrt, and softplus.
Families binomial, bernoulli, beta_binomial,
zero_inflated_binomial, zero_inflated_beta_binomial,
Beta, zero_inflated_beta, and zero_one_inflated_beta
support logit, probit, probit_approx, cloglog,
cauchit, identity, and log.
Families cumulative, cratio, sratio,
acat, and hurdle_cumulative support logit,
probit, probit_approx, cloglog, and cauchit.
Families categorical, multinomial, and dirichlet
support logit.
Families Gamma, weibull, exponential,
frechet, and hurdle_gamma support
log, identity, inverse, and softplus.
Families lognormal and hurdle_lognormal
support identity and inverse.
Family logistic_normal supports identity.
Family inverse.gaussian supports 1/mu^2,
inverse, identity, log, and softplus.
Family von_mises supports tan_half and
identity.
Family cox supports log, identity,
and softplus for the proportional hazards parameter.
Family wiener supports identity, log,
and softplus for the main parameter which represents the
drift rate.
Please note that when calling the Gamma family
function of the stats package, the default link will be
inverse instead of log although the latter is the default in
brms. Also, when using the family functions gaussian,
binomial, poisson, and Gamma of the stats
package (see family), special link functions
such as softplus or cauchit won't work. In this case, you
have to use brmsfamily to specify the family with corresponding link
function.
brm,
family,
customfamily
# create a family object
(fam1 <- student("log"))
# alternatively use the brmsfamily function
(fam2 <- brmsfamily("student", "log"))
# both leads to the same object
identical(fam1, fam2)
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