mod_binom {bage} | R Documentation |
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
.
Mathematical details
The likelihood is
y_i \sim \text{binomial}(\gamma_i; w_i)
where
-
y_i
is a count, such of number of births, for some combinationi
of classifying variables, 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 celli
.
The \beta^{(m)}
are given priors, as described in priors.
The prior for \xi
is described in set_disp()
.
Specifying size
The size
argument can take two forms:
the name of a variable in
data
, with or without quote marks, eg"population"
orpopulation
; ora formula, which is evaluated with
data
as its environment (see below for example).
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 -
forecast()
Forecast a model -
report_sim()
Do a simulation study on a model
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)