Family objects provide a convenient way to specify the details of the models
used by many model fitting functions. The familiy functions presented here are
currently 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 decribed in
family will work with brms.
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 = c("flexible", "equidistant"))student(link = "identity", link_sigma = "log", link_nu = "logm1")
bernoulli(link = "logit")
negbinomial(link = "log", link_shape = "log")
geometric(link = "log")
lognormal(link = "identity", link_sigma = "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")
von_mises(link = "tan_half", link_kappa = "log")
asym_laplace(link = "identity", link_sigma = "log",
link_quantile = "logit")
hurdle_poisson(link = "log")
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")
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")
categorical(link = "logit")
cumulative(link = "logit", link_disc = "log", threshold = c("flexible",
"equidistant"))
sratio(link = "logit", link_disc = "log", threshold = c("flexible",
"equidistant"))
cratio(link = "logit", link_disc = "log", threshold = c("flexible",
"equidistant"))
acat(link = "logit", link_disc = "log", threshold = c("flexible",
"equidistant"))
A character string naming the distribution
of the response variable be used in the model.
Currently, the following families are supported:
gaussian, student, binomial,
bernoulli, poisson, negbinomial,
geometric, Gamma, lognormal,
exgaussian, skew_normal, wiener,
inverse.gaussian, exponential, weibull,
frechet, Beta, von_mises, asym_laplace,
gen_extreme_value, categorical, cumulative,
cratio, sratio, acat, hurdle_poisson,
hurdle_negbinomial, hurdle_gamma, hurdle_lognormal,
zero_inflated_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 and
"equidistant" restricts the distance between
consecutive thresholds to the same value.
Family gaussian with identity link leads to linear regression.
Family student with identity link leads to
robust linear regression that is less influenced by outliers.
Family skew_normal can handle skewed responses in linear regression.
Families poisson, negbinomial, and geometric
with log link lead to regression models for count data.
Families binomial and bernoulli with logit link leads to
logistic regression and family categorical to 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, and
inverse.gaussian can be used (among others) for survival regression.
Families weibull, frechet, and gen_extreme_value
('generalized extreme value') allow for modeling extremes.
Family asym_laplace allows for quantile regression when fixing
the auxiliary quantile parameter to the quantile of interest.
Family exgaussian ('exponentially modified Gaussian') is especially
suited to model reaction times and the wiener family 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, and zero_one_inflated_beta
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.
Families hurdle_lognormal and hurdle_gamma are
especially useful, as traditional lognormal or Gamma
models cannot be reasonably fitted for data containing zeros in the response.
In the following, we list all possible links for each family.
The families gaussian, student, skew_normal,
exgaussian, asym_laplace, and gen_extreme_value
accept the links (as names) identity, log, and inverse;
families poisson, negbinomial, geometric,
zero_inflated_poisson, zero_inflated_negbinomial,
hurdle_poisson, and hurdle_negbinomial the links
log, identity, and sqrt;
families binomial, bernoulli, Beta,
zero_inflated_binomial, zero_inflated_beta,
and zero_one_inflated_beta the links logit,
probit, probit_approx, cloglog,
cauchit, and identity;
families cumulative, cratio, sratio,
and acat the links logit, probit,
probit_approx, cloglog, and cauchit;
family categorical the link logit;
families Gamma, weibull, exponential,
frechet, and hurdle_gamma the links
log, identity, and inverse;
families lognormal and hurdle_lognormal
the links identity and inverse;
family inverse.gaussian the links 1/mu^2,
inverse, identity and log;
family von_mises the link tan_half;
family wiener the link identity.
The first link mentioned for each family is the default.
Please note that when calling the Gamma
family function, the default link will be inverse not log.
Also, the probit_approx link cannot be used when calling the
binomial family function.
The current implementation of inverse.gaussian models has some
convergence problems and requires carefully chosen prior distributions
to work efficiently. For this reason, we currently do not recommend
to use the inverse.gaussian family, unless you really feel
that your data requires exactly this type of model.
# NOT RUN {
# 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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