Priors for Intercept, Main Effects, Interactions

The models created with mod_pois(), mod_binom(), and mod_norm() include terms such as age effects and region-time interactions. Each of these terms requires a prior distribution. Current options for these priors are summarised in the table below.

Details

Prior	Description	Uses	Forecast	Along/By
`N()`	Elements drawn from normal distribution	Term with no natural order	Yes	No
`NFix()`	`N()` with 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 with trends	Yes	Yes
`DRW()`	Damped random walk	Smoothing, forecasting	Yes	Yes
`DRW2()`	Damped second-order random walk	Like `DRW()`, but with trends	Yes	Yes
`RW2_Infant()`	`RW2()` with infant indicator	Mortality age profiles	No	Yes
`RW_Seas()`	`RW()`, with seasonal effect	Terms involving time	Yes	Yes
`RW2_Seas()`	`RW2()`, with seasonal effect	Term involving time	Yes	Yes
`AR()`	Auto-regressive prior of order k	Mean reversion, forecasting	Yes	Yes
`AR1()`	Special case of `AR()`	Mean reversion, forecasting	Yes	Yes
`Lin()`	Linear trend, with independent errors	Parsimonious model for time	Yes	Yes
`Lin_AR()`	Linear trend, with AR errors	Term involving time, forecasting	Yes	Yes
`Lin_AR1()`	Linear trend, with AR1 errors	Terms involving time, forecasting	Yes	Yes
`Sp()`	P-Spline (penalised spline)	Smoothing, eg over age	No	Yes
`SVD()`	Age-sex profile based on SVD	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_Lin()`	`SVD()`, but coefficients follow `Lin()`	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
`SVD_DRW()`	`SVD()`, but coefficients follow `DRW()`	Age or age-sex and time	Yes	Yes
`SVD_DRW2()`	`SVD()`, but coefficients follow `DRW2()`	Age or age-sex and time	Yes	Yes

'Along' and 'by' dimensions

Priors for interaction terms often consist of a time-series-style model along one dimension, with a separate series for each combination of the remaining dimensions. For instance, a prior for an age-sex-time interaction might consist of a separate random walk along time for each combination of age-group and sex. In bage the dimension with the time-series-type model is referred to as the 'along' dimension, and the remaining dimensions are referred to as the 'by' dimensions.

Default prior

If no prior is specified for a term, then bage assigns the term a default prior using the following algorithm:

if the term has one or two 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().

Forecasting

A model can only be used for forecasting if

the model includes a time dimension, and
the prior for the time dimension supports forecasting.

If necessary, the time dimension can be identified using set_var_time(). The table above lists the priors that support forecasting.