mod_norm: Specify a Normal Model
View source: R/bage_mod-constructors.R
| mod_norm | 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 |
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
-
y_iis a scaled value for an, such of the log of income, for some combinationiof classifying variables, such as age, sex, and region; -
\mu_iis a mean; -
\xiis a standard deviation parameter; and -
w_iis a weight.
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
-
\beta^{0}is an intercept; -
\beta^{(m)},m = 1, \dots, M, is a main effect or interaction; and -
j_i^mis the element of\beta^{(m)}associated with celli.
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:
the name of a variable in
data, with or without quote marks, eg"wt"orwt;the number
1, in which no weights are used; ora formula, which is evaluated with
dataas its environment (see below for example).
See Also
-
mod_pois()Specify Poisson model -
mod_binom()Specify binomial model -
set_prior()Specify non-default prior for term -
set_disp()Specify non-default prior for standard deviation -
fit()Fit a model -
forecast()Forecast a model -
report_sim()Do a simulation study on a model
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))
