Random Walk Prior

Use a random walk to model a main effect, or use multiple random walks to model an interaction. Typically used with age or time effects or with interactions that involve age or time.

Usage

RW(s = 1, along = NULL)

Arguments

s

Scale for the prior for the innovations. Default is 1.

along

Name of the variable to be used as the "along" variable. Only used with interactions.

Value

An object of class "bage_prior_rw".

Details

If RW() is used with an interaction, separate random walks are constructed along the "along" variable, within each combination of the "by" variables.

Argument s controls the size of innovations. Smaller values for s tend to give smoother series.

Mathematical details

When RW() is used with a main effect,

$$\beta_j = \beta_{j-1} + \epsilon_j$$ $$\epsilon_j \sim \text{N}(0, \tau^2),$$

and when it is used with an interaction,

$$\beta_{u,v} = \beta_{u,v-1} + \epsilon_{u,v}$$ $$\epsilon_{u,v} \sim \text{N}(0, \tau^2),$$

where

• \(\pmb{\beta}\) is the main effect or interaction;

• \(j\) denotes position within the main effect;

• \(v\) denotes position within the "along" variable of the interaction; and

• \(u\) denotes position within the "by" variable(s) of the interaction.

Parameter \(\tau\) has a half-normal prior $$\tau \sim \text{N}^+(0, \text{s}^2),$$ where s is provided by the user.

See also

• RW2() Second-order random walk

• AR() Autoregressive with order k

• AR1() Autoregressive with order 1

• Sp() Smoothing via splines

• SVD() Smoothing of age via singular value decomposition

• priors Overview of priors implemented in bage

• set_prior() Specify prior for intercept, main effect, or interaction

Examples

RW()
#>   RW() 
#>        s: 1
#>    along: NULL
RW(s = 0.5)
#>   RW(s=0.5) 
#>        s: 0.5
#>    along: NULL
RW(along = "cohort")
#>   RW(along="cohort") 
#>        s: 1
#>    along: cohort