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Bayesian Model Averaging on Small-Area Estimates

Source: R/model-compare.R
model_average.Rd

Averages the area-level predictions across multiple fitted HBMs. Weights may be supplied manually or computed automatically from leave-one-out cross-validation via loo_model_weights – the canonical Bayesian stacking / pseudo-BMA approach of Yao et al.\ (2018).

Usage

model_average(
  ...,
  weights = NULL,
  method = c("manual", "stacking", "pseudobma"),
  newdata = NULL
)

Arguments

...

Two or more hbmfit objects.

weights

Numeric weights of the same length as the number of models, or NULL. When NULL and method = "manual", equal weights are used.

method

Character. Weighting method: "manual" (default), "stacking" (Yao et al. 2018), or "pseudobma". When "stacking" or "pseudobma", weights must be NULL; an error is raised otherwise.

newdata

Optional new data.frame forwarded to sae_predict.

Value

An hbsae_results object of averaged predictions. The computed weights are attached as an attribute "weights".

Details

Three weighting modes are supported:

  • method = "manual" (default when weights is supplied): use the user-supplied weights vector directly. Internally normalised to sum to 1.

  • method = "stacking": weights are obtained from loo::loo_model_weights(loo_list, method = "stacking"), which optimises a log-score over a simplex. Recommended when models are well-specified but capture different features of the data (Yao et al.\ 2018).

  • method = "pseudobma": weights are obtained from loo::loo_model_weights(loo_list, method = "pseudobma"), a smoothed pseudo-BMA+ that resembles classical BMA but uses PSIS-LOO log scores. Use as a robust default when one model is much better than the others.

Internally calls sae_predict on each model and then sae_aggregate with method = "weighted".

References

Yao, Y., Vehtari, A., Simpson, D., & Gelman, A. (2018). Using stacking to average Bayesian predictive distributions (with discussion). Bayesian Analysis, 13(3), 917–1007. doi:10.1214/17-BA1091

Vehtari, A., Gelman, A., & Gabry, J. (2017). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and Computing, 27(5), 1413–1432.

Examples

# \donttest{
# See ?model_compare_all for the full example fitting m1 / m2.
# Manual:    avg <- model_average(m1, m2, weights = c(0.6, 0.4))
# Stacking:  avg <- model_average(m1, m2, method = "stacking")
# Pseudo-BMA: avg <- model_average(m1, m2, method = "pseudobma")
# }