RW1 temporal structure (First-order Random Walk)

Specify a first-order random walk temporal random effect. RW1 penalizes first differences, so adjacent time points are smoothed toward each other: phi[t] - phi[t-1] ~ N(0, sigma^2).

Usage

temporal_rw1(time_var, group_var = NULL, cyclic = FALSE, shared = NULL)

Arguments

time_var: A formula (~ time) or single character string naming the time variable in the data.
group_var: Optional formula (~ g) or character string naming a grouping variable. When supplied, a separate random walk is fit per group; NULL (default) fits a single walk shared across all observations.
cyclic: Logical. If TRUE, the random walk wraps around so the last time point is a neighbour of the first (cyclic boundary, e.g. month of year). Default FALSE.
shared: Whether the temporal effect is shared across processes in a multi-process model. NULL (default) shares the effect; FALSE fits process-specific effects and emits a warning about unshared confounding.

Value

A tulpa_temporal object.

Details

The precision matrix is rank T - 1 (one constraint needed). RW1 is the least smooth of the random-walk priors; for smoother trends see temporal_rw2(), and for a stationary alternative see temporal_ar1().

Examples

# Create temporal RW1 specification
temporal_rw1("year")
temporal_rw1("month", cyclic = TRUE)