mod_binom: Specify a Binomial Model

In bage: Bayesian Estimation and Forecasting of Age-Specific Rates

Specify a Binomial Model

Description

Specify a model where the outcome is drawn from a binomial distribution.

Usage

mod_binom(formula, data, size)

Arguments

formula	An R formula, specifying the outcome and predictors.
data	A data frame containing the outcome and predictor variables, and the number of trials.
size	Name of the variable giving the number of trials, or a formula.

Details

The model is hierarchical. The probabilities in the binomial distribution are described by a prior model formed from dimensions such as age, sex, and time. The terms for these dimension themselves have models, as described in priors. These priors all have defaults, which depend on the type of term (eg an intercept, an age main effect, or an age-time interaction.)

Value

An object of class bage_mod.

Specifying size

The size argument can take two forms:

• the name of a variable in data, with or without quote marks, eg "population" or population; or

• a formula, which is evaluated with data as its environment (see below for example).

Mathematical details

The likelihood is

y_i \sim \text{binomial}(\gamma_i; w_i)

where

• subscript i identifies some combination of the the classifying variables, such as age, sex, and time;

• y_i is a count, such of number of births, such as age, sex, and region;

• \gamma_i is a probability of 'success'; and

• w_i is the number of trials.

The probabilities \gamma_i are assumed to be drawn a beta distribution

y_i \sim \text{Beta}(\xi^{-1} \mu_i, \xi^{-1} (1 - \mu_i))

where

• \mu_i is the expected value for \gamma_i; and

• \xi governs dispersion (ie variance.)

Expected value \mu_i equals, on a logit scale, the sum of terms formed from classifying variables,

\text{logit} \mu_i = \sum_{m=0}^{M} \beta_{j_i^m}^{(m)}

where

• \beta^{0} is an intercept;

• \beta^{(m)}, m = 1, \dots, M, is a main effect or interaction; and

• j_i^m is the element of \beta^{(m)} associated with cell i.

The \beta^{(m)} are given priors, as described in priors.

\xi has an exponential prior with mean 1. Non-default values for the mean can be specified with set_disp().

The model for \mu_i can also include covariates, as described in set_covariates().

See Also

• mod_pois() Specify Poisson model

• mod_norm() Specify normal model

• set_prior() Specify non-default prior for term

• set_disp() Specify non-default prior for dispersion

• fit() Fit a model

• augment() Extract values for probabilities, together with original data

• components() Extract values for hyper-parameters

• forecast() Forecast parameters and outcomes

• report_sim() Check model using simulation study

• replicate_data() Check model using replicate data

• Mathematical Details Detailed descriptions of models

Examples

mod <- mod_binom(oneperson ~ age:region + age:year,
                 data = nzl_households,
                 size = total)

## use formula to specify size
mod <- mod_binom(ncases ~ agegp + tobgp + alcgp,
                 data = esoph,
                 size = ~ ncases + ncontrols)

bage documentation built on Aug. 8, 2025, 6:09 p.m.