families

Reference: https://paulbuerkner.com/brms/reference/brmsfamily.html

family()

Classes

Functions

brmsfamily(family, link=None, 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=None, **kwargs)

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.

Parameters:

Name	Type	Description	Default
family		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.	required
link	Optional[str]	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.	None
link_sigma	str	Link of auxiliary parameter sigma if being predicted.	'log'
link_shape	str	Link of auxiliary parameter shape if being predicted.	'log'
link_nu	str	Link of auxiliary parameter nu if being predicted.	'logm1'
link_phi	str	Link of auxiliary parameter phi if being predicted.	'log'
link_kappa	str	Link of auxiliary parameter kappa if being predicted.	'log'
link_beta	str	Link of auxiliary parameter beta if being predicted.	'log'
link_zi	str	Link of auxiliary parameter zi if being predicted.	'logit'
link_hu	str	Link of auxiliary parameter hu if being predicted.	'logit'
link_zoi	str	Link of auxiliary parameter zoi if being predicted.	'logit'
link_coi	str	Link of auxiliary parameter coi if being predicted.	'logit'
link_disc	str	Link of auxiliary parameter disc if being predicted.	'log'
link_bs	str	Link of auxiliary parameter bs if being predicted.	'log'
link_ndt	str	Link of auxiliary parameter ndt if being predicted.	'log'
link_bias	str	Link of auxiliary parameter bias if being predicted.	'logit'
link_xi	str	Link of auxiliary parameter xi if being predicted.	'log1p'
link_alpha	str	Link of auxiliary parameter alpha if being predicted.	'identity'
link_quantile	str	Link of auxiliary parameter quantile if being predicted.	'logit'
threshold	str	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.	'flexible'
refcat	Optional[str]	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.	None
bhaz		Currently for experimental purposes only.	required

family(fit, **kwargs)

Extract family object from a fitted model.

Parameters:

Name	Type	Description	Default
fit	FitResult or ListVector	Fitted brms model	required

student(link='identity', link_sigma='log', link_nu='logm1', **kwargs)

Student's t distribution for robust regression.

Parameters:

Name	Type	Description	Default
link	str	Link function for the mean	'identity'
link_sigma	str	Link function for sigma parameter	'log'
link_nu	str	Link function for degrees of freedom parameter	'logm1'

bernoulli(link='logit', **kwargs)

Bernoulli distribution for binary 0/1 outcomes.

Parameters:

Name	Type	Description	Default
link	str	Link function for the probability parameter	'logit'

beta_binomial(link='logit', link_phi='log', **kwargs)

Beta-binomial distribution for overdispersed binomial data.

Parameters:

Name	Type	Description	Default
link	str	Link function for the probability parameter	'logit'
link_phi	str	Link function for the precision parameter	'log'

negbinomial(link='log', link_shape='log', **kwargs)

Negative binomial distribution for overdispersed count data.

Parameters:

Name	Type	Description	Default
link	str	Link function for the mean	'log'
link_shape	str	Link function for the shape parameter	'log'

geometric(link='log', **kwargs)

Geometric distribution for count data (negative binomial with shape=1).

Parameters:

Name	Type	Description	Default
link	str	Link function for the mean	'log'

lognormal(link='identity', link_sigma='log', **kwargs)

Lognormal distribution for positive continuous data.

Parameters:

Name	Type	Description	Default
link	str	Link function for the mean on log scale	'identity'
link_sigma	str	Link function for sigma parameter	'log'

shifted_lognormal(link='identity', link_sigma='log', link_ndt='log', **kwargs)

Shifted lognormal distribution with non-decision time parameter.

Parameters:

Name	Type	Description	Default
link	str	Link function for the mean	'identity'
link_sigma	str	Link function for sigma parameter	'log'
link_ndt	str	Link function for non-decision time parameter	'log'

skew_normal(link='identity', link_sigma='log', link_alpha='identity', **kwargs)

Skew normal distribution for asymmetric continuous data.

Parameters:

Name	Type	Description	Default
link	str	Link function for the mean	'identity'
link_sigma	str	Link function for sigma parameter	'log'
link_alpha	str	Link function for skewness parameter	'identity'

exponential(link='log', **kwargs)

Exponential distribution for time-to-event data.

Parameters:

Name	Type	Description	Default
link	str	Link function for the rate parameter	'log'

weibull(link='log', link_shape='log', **kwargs)

Weibull distribution for survival and reliability analysis.

Parameters:

Name	Type	Description	Default
link	str	Link function for the scale parameter	'log'
link_shape	str	Link function for the shape parameter	'log'

frechet(link='log', link_nu='logm1', **kwargs)

Frechet distribution for extreme value analysis.

Parameters:

Name	Type	Description	Default
link	str	Link function for the scale parameter	'log'
link_nu	str	Link function for the shape parameter	'logm1'

gen_extreme_value(link='identity', link_sigma='log', link_xi='log1p', **kwargs)

Generalized extreme value distribution for extreme events.

Parameters:

Name	Type	Description	Default
link	str	Link function for the location parameter	'identity'
link_sigma	str	Link function for the scale parameter	'log'
link_xi	str	Link function for the shape parameter	'log1p'

exgaussian(link='identity', link_sigma='log', link_beta='log', **kwargs)

Ex-Gaussian distribution for reaction time data.

Parameters:

Name	Type	Description	Default
link	str	Link function for the mean	'identity'
link_sigma	str	Link function for Gaussian SD parameter	'log'
link_beta	str	Link function for exponential rate parameter	'log'

wiener(link='identity', link_bs='log', link_ndt='log', link_bias='logit', **kwargs)

Wiener diffusion model for two-choice reaction time data.

Parameters:

Name	Type	Description	Default
link	str	Link function for drift rate	'identity'
link_bs	str	Link function for boundary separation	'log'
link_ndt	str	Link function for non-decision time	'log'
link_bias	str	Link function for initial bias	'logit'

Beta(link='logit', link_phi='log', **kwargs)

Beta distribution for data between 0 and 1.

Parameters:

Name	Type	Description	Default
link	str	Link function for the mean	'logit'
link_phi	str	Link function for the precision parameter	'log'

xbeta(link='logit', link_phi='log', link_kappa='log', **kwargs)

Extended beta distribution with additional shape parameter.

Parameters:

Name	Type	Description	Default
link	str	Link function for the mean	'logit'
link_phi	str	Link function for precision parameter	'log'
link_kappa	str	Link function for kappa shape parameter	'log'

dirichlet(link='logit', link_phi='log', refcat=None, **kwargs)

Dirichlet distribution for compositional data.

Parameters:

Name	Type	Description	Default
link	str	Link function for the mean	'logit'
link_phi	str	Link function for the precision parameter	'log'
refcat	str	Reference category	None

logistic_normal(link='identity', link_sigma='log', refcat=None, **kwargs)

Logistic-normal distribution for compositional data.

Parameters:

Name	Type	Description	Default
link	str	Link function for the mean	'identity'
link_sigma	str	Link function for sigma parameter	'log'
refcat	str	Reference category	None

von_mises(link='tan_half', link_kappa='log', **kwargs)

Von Mises distribution for circular/directional data.

Parameters:

Name	Type	Description	Default
link	str	Link function for the mean direction	'tan_half'
link_kappa	str	Link function for concentration parameter	'log'

asym_laplace(link='identity', link_sigma='log', link_quantile='logit', **kwargs)

Asymmetric Laplace distribution for quantile regression.

Parameters:

Name	Type	Description	Default
link	str	Link function for the location	'identity'
link_sigma	str	Link function for sigma parameter	'log'
link_quantile	str	Link function for the quantile parameter	'logit'

cox(link='log', **kwargs)

Cox proportional hazards model for survival data.

Parameters:

Name	Type	Description	Default
link	str	Link function for the hazard rate	'log'

hurdle_poisson(link='log', link_hu='logit', **kwargs)

Hurdle Poisson distribution for zero-inflated count data.

Parameters:

Name	Type	Description	Default
link	str	Link function for the mean	'log'
link_hu	str	Link function for hurdle parameter	'logit'

hurdle_negbinomial(link='log', link_shape='log', link_hu='logit', **kwargs)

Hurdle negative binomial for overdispersed zero-inflated count data.

Parameters:

Name	Type	Description	Default
link	str	Link function for the mean	'log'
link_shape	str	Link function for shape parameter	'log'
link_hu	str	Link function for hurdle parameter	'logit'

hurdle_gamma(link='log', link_shape='log', link_hu='logit', **kwargs)

Hurdle Gamma distribution for zero-inflated positive continuous data.

Parameters:

Name	Type	Description	Default
link	str	Link function for the mean	'log'
link_shape	str	Link function for shape parameter	'log'
link_hu	str	Link function for hurdle parameter	'logit'

hurdle_lognormal(link='identity', link_sigma='log', link_hu='logit', **kwargs)

Hurdle lognormal for zero-inflated positive continuous data.

Parameters:

Name	Type	Description	Default
link	str	Link function for the mean	'identity'
link_sigma	str	Link function for sigma parameter	'log'
link_hu	str	Link function for hurdle parameter	'logit'

hurdle_cumulative(link='logit', link_hu='logit', link_disc='log', threshold='flexible', **kwargs)

Hurdle cumulative for zero-inflated ordinal data.

Parameters:

Name	Type	Description	Default
link	str	Link function for the ordinal response	'logit'
link_hu	str	Link function for hurdle parameter	'logit'
link_disc	str	Link function for discrimination parameter	'log'
threshold	str	Type of threshold structure	'flexible'

zero_inflated_beta(link='logit', link_phi='log', link_zi='logit', **kwargs)

Zero-inflated beta for data between 0 and 1 with excess zeros.

Parameters:

Name	Type	Description	Default
link	str	Link function for the mean	'logit'
link_phi	str	Link function for precision parameter	'log'
link_zi	str	Link function for zero-inflation parameter	'logit'

zero_one_inflated_beta(link='logit', link_phi='log', link_zoi='logit', link_coi='logit', **kwargs)

Zero-one-inflated beta for data between 0 and 1 with excess zeros and ones.

Parameters:

Name	Type	Description	Default
link	str	Link function for the mean	'logit'
link_phi	str	Link function for precision parameter	'log'
link_zoi	str	Link function for zero-or-one inflation parameter	'logit'
link_coi	str	Link function for conditional one inflation parameter	'logit'

zero_inflated_poisson(link='log', link_zi='logit', **kwargs)

Zero-inflated Poisson for count data with excess zeros.

Parameters:

Name	Type	Description	Default
link	str	Link function for the mean	'log'
link_zi	str	Link function for zero-inflation parameter	'logit'

zero_inflated_negbinomial(link='log', link_shape='log', link_zi='logit', **kwargs)

Zero-inflated negative binomial for overdispersed count data with excess zeros.

Parameters:

Name	Type	Description	Default
link	str	Link function for the mean	'log'
link_shape	str	Link function for shape parameter	'log'
link_zi	str	Link function for zero-inflation parameter	'logit'

zero_inflated_binomial(link='logit', link_zi='logit', **kwargs)

Zero-inflated binomial for binary count data with excess zeros.

Parameters:

Name	Type	Description	Default
link	str	Link function for probability parameter	'logit'
link_zi	str	Link function for zero-inflation parameter	'logit'

zero_inflated_beta_binomial(link='logit', link_phi='log', link_zi='logit', **kwargs)

Zero-inflated beta-binomial for overdispersed binomial data with excess zeros.

Parameters:

Name	Type	Description	Default
link	str	Link function for probability parameter	'logit'
link_phi	str	Link function for precision parameter	'log'
link_zi	str	Link function for zero-inflation parameter	'logit'

categorical(link='logit', refcat=None, **kwargs)

Categorical distribution for unordered multi-category outcomes.

Parameters:

Name	Type	Description	Default
link	str	Link function for category probabilities	'logit'
refcat	str	Reference category	None

multinomial(link='logit', refcat=None, **kwargs)

Multinomial distribution for count data across multiple categories.

Parameters:

Name	Type	Description	Default
link	str	Link function for category probabilities	'logit'
refcat	str	Reference category	None

dirichlet_multinomial(link='logit', link_phi='log', refcat=None, **kwargs)

Dirichlet-multinomial for overdispersed categorical count data.

Parameters:

Name	Type	Description	Default
link	str	Link function for category probabilities	'logit'
link_phi	str	Link function for precision parameter	'log'
refcat	str	Reference category	None

cumulative(link='logit', link_disc='log', threshold='flexible', **kwargs)

Cumulative (proportional odds) model for ordinal outcomes.

Parameters:

Name	Type	Description	Default
link	str	Link function for cumulative probabilities	'logit'
link_disc	str	Link function for discrimination parameter	'log'
threshold	str	Type of threshold structure	'flexible'

sratio(link='logit', link_disc='log', threshold='flexible', **kwargs)

Sequential (stopping) ratio model for ordinal outcomes.

Parameters:

Name	Type	Description	Default
link	str	Link function for sequential ratios	'logit'
link_disc	str	Link function for discrimination parameter	'log'
threshold	str	Type of threshold structure	'flexible'

cratio(link='logit', link_disc='log', threshold='flexible', **kwargs)

Continuation ratio model for ordinal outcomes.

Parameters:

Name	Type	Description	Default
link	str	Link function for continuation ratios	'logit'
link_disc	str	Link function for discrimination parameter	'log'
threshold	str	Type of threshold structure	'flexible'

acat(link='logit', link_disc='log', threshold='flexible', **kwargs)

Adjacent category model for ordinal outcomes.

Parameters:

Name	Type	Description	Default
link	str	Link function for adjacent category ratios	'logit'
link_disc	str	Link function for discrimination parameter	'log'
threshold	str	Type of threshold structure	'flexible'

gaussian(link='identity', link_sigma='log', **kwargs)

Gaussian (normal) distribution for continuous data.

Parameters:

Name	Type	Description	Default
link	str	Link function for the mean	'identity'
link_sigma	str	Link function for the standard deviation	'log'

poisson(link='log', **kwargs)

Poisson distribution for count data.

Parameters:

Name	Type	Description	Default
link	str	Link function for the rate parameter	'log'

binomial(link='logit', **kwargs)

Binomial distribution for binary count data.

Parameters:

Name	Type	Description	Default
link	str	Link function for the probability parameter	'logit'

Gamma(link='log', link_shape='log', **kwargs)

Gamma distribution for positive continuous data.

Parameters:

Name	Type	Description	Default
link	str	Link function for the mean	'log'
link_shape	str	Link function for the shape parameter	'log'

inverse_gaussian(link='1/mu^2', link_shape='log', **kwargs)

Inverse Gaussian distribution for positive continuous data.

Parameters:

Name	Type	Description	Default
link	str	Link function for the mean	'1/mu^2'
link_shape	str	Link function for the shape parameter	'log'