mod_norm {bage}R Documentation

Specify a Normal Model

Description

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

Usage

mod_norm(formula, data, weights)

Arguments

formula

An R formula, specifying the outcome and predictors.

data

A data frame containing outcome, predictor, and, optionally, weights variables.

weights

Name of the weights variable, a 1, or a formula. See below for details.

Details

The model is hierarchical. The means in the normal 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.)

Internally, the outcome variable scaled to have mean 0 and sd 1.

Value

An object of class bage_mod_norm.

Mathematical details

The likelihood is

y_i \sim \text{N}(\mu_i, \xi^2 / w_i)

where

The scaling of the outcome variable is done internally. If y_i^* is the original, then y_i = (y_i^* - m)/s where m and s are the sample mean and standard deviation of y_i^*.

In some applications, w_i is set to 1 for all i.

The means \mu_i equal the sum of terms formed from classifying variables,

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

where

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

The prior for \xi is described in set_disp().

Specifying weights

The weights argument can take three forms:

See Also

Examples

mod <- mod_norm(value ~ diag:age + year,
                data = nld_expenditure,
                weights = 1)

## use formula to specify weights
mod <- mod_norm(value ~ diag:age + year,
                data = nld_expenditure,
                weights = ~sqrt(value))

[Package bage version 0.9.0 Index]