priors: Priors for Intercept, Main Effects, Interactions
In bage: Bayesian Estimation and Forecasting of Age-Specific Rates

priors

R Documentation

Priors for Intercept, Main Effects, Interactions

Description

The models created with functions mod_pois(), mod_binom(), and mod_norm() always include an intercept, and typically include main effects and interactions formed from variables in input data. Most models, for instance include an age effect, and many include an interaction between age and sex/gender, or age and time.

The intercept, main effects, and interactions all have prior models that capture the expected behavior of the term. Current choices for priors summarised in the table below.

Priors where 'forecast' is yes can be used in forecasts for a time-varying terms such as an age-time interactions.

Priors where 'along' is yes distinguish between 'along' and 'by' dimensions.

Details

Prior	Description	Uses	Forecast	Along
`N()`	Elements drawn from normal distribution	Term with no natural order	Yes	No
`NFix()`	As for `N()`, but standard deviation fixed	Term with few elements	Yes	No
`Known()`	Values treated as known	Simulations, prior knowledge	No	No
`RW()`	Random walk	Smoothing	Yes	Yes
`RW2()`	Second-order random walk	Like `RW()`, but smoother	Yes	Yes
`RW_Seas()`	Random walk, with seasonal effect	Terms involving time	Yes	Yes
`RW2_Seas()`	Second-order random walk, with seasonal effect	Term involving time	Yes	Yes
`AR()`	Auto-regressive prior of order k	Mean reversion	Yes	Yes
`AR1()`	Auto-regressive prior of order 1 Special case of `AR()`	Mean reversion	Yes	Yes
`Lin()`	Linear trend, with independent normal	Parsimonious model for time	Yes	Yes
`Lin_AR()`	Linear trend, with autoregressive errors	Term involving time	Yes	Yes
`Lin_AR1()`	Linear trend, with AR1 errors	Terms involving time	Yes	Yes
`Sp()`	P-Spline (penalised spline)	Smoothing, eg over age	No	Yes
`SVD()`	Age or age-sex profile based on SVD of database	Age or age-sex	No	No
`SVD_AR()`	`SVD()`, but coefficients follow `AR()`	Age or age-sex and time	Yes	Yes
`SVD_AR1()`	`SVD()`, but coefficients follow `AR1()`	Age or age-sex and time	Yes	Yes
`SVD_RW()`	`SVD()`, but coefficients follow `RW()`	Age or age-sex and time	Yes	Yes
`SVD_RW2()`	`SVD()`, but coefficients follow `RW2()`	Age or age-sex and time	Yes	Yes

Default prior

The rule for selecting a default prior for a term is:

if term has less than 3 elements, use NFix();
otherwise, if the term involves time, use RW(), with time as the ‘along’ dimension;
otherwise, if the term involves age, use RW(), with age as the ‘along’ dimension;
otherwise, use N().