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.)

Value

An object of class bage_mod_norm.

Scaling of outcome and weights

Internally, mod_norm() scales the outcome variable to have mean 0 and standard deviation 1, and scales the weights to have mean 1. This scaling allows mod_norm() to use the same menu of priors as mod_pois() and mod_binom().

augment() always returns values on the original scale, rather than the transformed scale.

components() by default returns values on the transformed scale. But if original_scale is TRUE, it returns some types of values on the original scale. See components() for details.

Specifying weights

The weights argument can take three forms:

Mathematical details

The likelihood is

y_i \sim \text{N}(\gamma_i, w_i^{-1} \sigma^2)

where

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

Internally, bage works with standardized versions of \gamma_i and \sigma^2:

\mu_i = (\gamma_i - \bar{y}) / s

\xi^2 = \sigma^2 / (\bar{w} s^2)

where

\bar{y} = \sum_{i=1}^n y_i / n

s = \sqrt{\sum_{i=1}^n (y_i - \bar{y})^2 / (n-1)}

\bar{w} = \sum_{i=1}^n w_i / n

Mean parameter \mu_i is modelled as the sum of terms formed from classifying variables and covariates,

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

where

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

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 0.9.4 Index]