View source: R/bage_mod-constructors.R
mod_binom | R Documentation |
Specify a model where the outcome is drawn from a binomial distribution.
mod_binom(formula, data, size)
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. |
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.)
An object of class bage_mod
.
The size
argument can take two forms:
the name of a variable in data
, with or without
quote marks, eg "population"
or population
; or
a formula, which is evaluated with data
as its
environment (see below for example).
The likelihood is
y_i \sim \text{binomial}(\gamma_i; w_i)
where
subscript i
identifies some combination of the the
classifying variables, such as age, sex, and time;
y_i
is a count, such of number of births,
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
cell i
.
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()
.
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
augment()
Extract values for probabilities,
together with original data
components()
Extract values for hyper-parameters
forecast()
Forecast parameters and outcomes
report_sim()
Check model using simulation study
replicate_data()
Check model using replicate data
Mathematical Details Detailed descriptions of models
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)
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