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 |
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_i
is a scaled value for an, such of the log of income, for some combinationi
of classifying variables, such as age, sex, and region; -
\mu_i
is a mean; -
\xi
is a standard deviation parameter; and -
w_i
is 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^m
is 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
data
as 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))