Specify the membership weights of an mm() block

Defines the weights \(w_{ikt}\) — how much each member counts in the block's aggregation. w() defines a within-group measure over members; the aggregation function fn chooses which function of that measure (and of the vars attributes) to read off. Weights can be fixed, taken from observed data, or estimated from member characteristics:


w(~ 1/n)                          # equal weights
w(~ importance, scale = TRUE)     # observed, normalized
w(~ ilogit(b0 + b1 * q))          # estimated: b0, b1 are free parameters

One parameter rule (shared with fn): any symbol in the formula that is not a data column or reserved word (n, the group size) is a free parameter with a default prior. The build always messages the detected parameters (e.g. Estimating parameters: b0, b1 (w)), so a misspelled column name shows up immediately. Priors are set via prior(..., class = "w").

Who counts vs. how contributions combine: parameters that act on external member characteristics (importance, exposure time) belong in w(); parameters that act on the effect attribute (whatever is in vars()) belong in fn. Building weights from the same variable that is being aggregated (e.g. w(~ exp(om * x)) with vars(x)) is near-equivalent to a smooth-max in fn() and is flagged with a warning.

Usage

w(formula = ~1/n, scale = TRUE)

Arguments

formula: One-sided formula defining the raw weights. Group-level aggregation shortcuts (min(x), max(x), mean(x), sum(x), sd(x), var(x), median(x), mode(x), range(x), first(x), last(x), quantile(x, p)) are pre-computed in R. JAGS math functions (exp, log, ilogit, ...) pass through.
scale: Logical; if TRUE (default), weights are normalized to sum to 1 within each group, making them a probability measure over the group's members. Emergent fn() types require scale = TRUE.

Value

A bml_w object.

Details

Weight functions with estimated parameters must produce bounded, positive values across plausible parameter values; unbounded weight functions can crash the sampler. Use bounded forms such as w(~ ilogit(b0 + b1 * q), scale = TRUE) or the generalized logistic w(~ 1 / (1 + (n - 1) * exp(-(b0 + b1 * q))), scale = TRUE), keep scale = TRUE, standardize covariates, and use informative priors (prior(normal(0, 1), class = "w")). Weight parameters are initialized at 0 for stable starting values.

References

Rosche, B. (2026). A Multilevel Model for Coalition Governments: Uncovering Party-Level Dependencies Within and Between Governments. Political Analysis.

Examples

if (FALSE) { # \dontrun{
w(~ 1/n)                                # equal weights
w(~ importance, scale = TRUE)           # observed weights, normalized
w(~ ilogit(b0 + b1 * seniority))        # estimated weights
w(~ duration, scale = FALSE)            # unnormalized (aggregating sums)
} # }