get_family: Return causl_fam function from integer index

In rje42/causl: Methods for Specifying, Simulating from and Fitting Causal Models

Return causl_fam function from integer index

Description

Return causl_fam function from integer index

Usage

get_family(val)

gaussian_causl_fam(link)

t_causl_fam(link)

Gamma_causl_fam(link)

binomial_causl_fam(link)

beta_causl_fam(link)

categorical_causl_fam(link)

ordinal_causl_fam(link)

Arguments

val	integer corresponding to distributional family
link	link function

Details

The functions gaussian_causl_fam() etc. represent the functions that are returned by get_family().

A few function of this form can be defined by the user, and it should return the following:

• name: the name of the relevant family;

• ddist: a function returning the density of the distributions;

• qdist: a function returning the quantiles from probabilities;

• rdist: a function to sample values from the distribution;

• pdist: a cumulative distribution function;

• pars: a list of the names of the parameters used;

• default: a function that returns a list of the default values for an observation and each of the parameters;

• link: the specified link function.

The function should also give the output the class "causl_family", so that it is interpreted appropriately. Note that ddist should have a log argument, to allow the log-likelihood to be evaluated.

The only parameterization of the categorical family currently implemented is the multivariate logistic parameterization. For a random variable X with K states, dependence on a vector \boldsymbol{Z} uses:

\log \dfrac{P(X=k)}{P(X=1)} = \beta_{k}^T \boldsymbol{Z},

and the \beta_k vectors are stored as (\beta_2,\dots,\beta_K).

The ordinal family is parameterized using a variation of the ordinal logistic regression model. This takes the logits of entries in the cumulative distribution function and treats the covariates variables linearly on that scale. Suppose \boldsymbol{Z} is the vector of covariates and there are K levels, then

\log \dfrac{P(X \leq k)}{P(X > k)} = \beta_k^T \boldsymbol{Z}.

As in the categorical case, the vectors \beta_k are stored as (\beta_1,\ldots,\beta_{K-1}).

Functions

• gaussian_causl_fam(): Gaussian distribution family

• t_causl_fam(): Student's t distribution family

• Gamma_causl_fam(): Gamma distribution family

• binomial_causl_fam(): binomial distribution family

• beta_causl_fam(): beta distribution family

• categorical_causl_fam(): multinomial/categorical distribution family

• ordinal_causl_fam(): ordinal categorical distribution family

See Also

family_vals

rje42/causl documentation built on June 1, 2025, 2:50 p.m.