Effects from Fitted APC Model

Usage

# S3 method for class 'apc'
effects(
  object,
  mean = FALSE,
  quantiles = 0.5,
  update = FALSE,
  convention = c("age", "period", "cohort", "none"),
  combined = FALSE,
  ...
)

Arguments

object: an apc object
mean: logical. If TRUE, mean effects are computed
quantiles: Scalar or vector of quantiles to compute (only if mean=FALSE)
update: logical. If TRUE, the apc object including the effects is returned
convention: display-layer gauge convention for the linear trend (drift) in a full age-period-cohort model; one of "age" (default), "period", "cohort" or "none". See Details.
combined: logical. For heterogeneity models ("rw1+het" / "rw2+het"), if TRUE the returned effect is the full effect (smooth + iid heterogeneity component); if FALSE (default) only the smooth component is returned. Ignored for models without heterogeneity.
...: Additional arguments will be ignored

Value

List of age, period, cohort effects or apc object including effects (if update=TRUE)

Details

In a full age-period-cohort model the age, period and cohort effects are identifiable only up to one shared linear trend (drift), because a linear trend can be moved between the three effects without changing the fitted rates (Clayton and Schifflers, 1987). When the raw posterior samples are summarised directly, this non-identified trend makes the effect curves drift between MCMC iterations and between runs, so they are not reproducible.

convention fixes that single degree of freedom for display: "age" removes the linear slope of the age effect (age is shown as curvature about a zero trend, the drift is shown in the period and cohort effects); "period" and "cohort" pin the corresponding effect's slope to zero instead; "none" returns the raw, un-gauged effects (previous behaviour, curves may differ between runs). The gauge is applied per MCMC draw before the quantiles are computed, and only for full APC models – for models without all three effects there is no trend aliasing and the argument is ignored.

Fixing the gauge removes the run-to-run linear-trend (drift) component, which is typically the dominant source of non-reproducibility in the effect curves; the residual curvature and Monte-Carlo sampling noise are unaffected, so two independent runs are made much closer but need not agree exactly. The zero-slope property holds for every individual MCMC draw; because quantiles are non-linear, the summarised median/quantile curve has only approximately (not exactly) zero slope.

The gauge is display-only: it never modifies the stored samples (object$samples), and the fitted rates, the predictions from predict_apc and the DIC are invariant to it – only the way the common linear trend is split among the three curves changes. The convention actually used is recorded in attr(result, "gauge_convention").

Examples

if (FALSE) { # \dontrun{
data(apc)
model <- bamp(cases, population, age="rw1", period="rw1", cohort="rw1", periods_per_agegroup = 5)
effects(model)
} # }