bayestestR: weighted_posteriors – R documentation

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weighted_posteriors

Generate posterior distributions weighted across models

Description

Extract posterior samples of parameters, weighted across models. Weighting is done by comparing posterior model probabilities, via bayesfactor_models.

Usage

weighted_posteriors(..., prior_odds = NULL, missing = 0, verbose = TRUE)

## S3 method for class 'data.frame'
weighted_posteriors(..., prior_odds = NULL, missing = 0, verbose = TRUE)

## S3 method for class 'stanreg'
weighted_posteriors(
  ...,
  prior_odds = NULL,
  missing = 0,
  verbose = TRUE,
  effects = c("fixed", "random", "all"),
  component = c("conditional", "zi", "zero_inflated", "all"),
  parameters = NULL
)

## S3 method for class 'brmsfit'
weighted_posteriors(
  ...,
  prior_odds = NULL,
  missing = 0,
  verbose = TRUE,
  effects = c("fixed", "random", "all"),
  component = c("conditional", "zi", "zero_inflated", "all"),
  parameters = NULL
)

## S3 method for class 'blavaan'
weighted_posteriors(
  ...,
  prior_odds = NULL,
  missing = 0,
  verbose = TRUE,
  effects = c("fixed", "random", "all"),
  component = c("conditional", "zi", "zero_inflated", "all"),
  parameters = NULL
)

## S3 method for class 'BFBayesFactor'
weighted_posteriors(
  ...,
  prior_odds = NULL,
  missing = 0,
  verbose = TRUE,
  iterations = 4000
)

Arguments

`...`	Fitted models (see details), all fit on the same data, or a single `BFBayesFactor` object.
`prior_odds`	Optional vector of prior odds for the models compared to the first model (or the denominator, for `BFBayesFactor` objects). For `data.frame`s, this will be used as the basis of weighting.
`missing`	An optional numeric value to use if a model does not contain a parameter that appears in other models. Defaults to 0.
`verbose`	Toggle off warnings.
`effects`	Should results for fixed effects, random effects or both be returned? Only applies to mixed models. May be abbreviated.
`component`	Should results for all parameters, parameters for the conditional model or the zero-inflated part of the model be returned? May be abbreviated. Only applies to brms-models.
`parameters`	Regular expression pattern that describes the parameters that should be returned. Meta-parameters (like `lp__` or `prior_`) are filtered by default, so only parameters that typically appear in the `summary()` are returned. Use `parameters` to select specific parameters for the output.
`iterations`	For `BayesFactor` models, how many posterior samples to draw.

Details

Note that across models some parameters might play different roles. For example, the parameter A plays a different role in the model Y ~ A + B (where it is a main effect) than it does in the model Y ~ A + B + A:B (where it is a simple effect). In many cases centering of predictors (mean subtracting for continuous variables, and effects coding via contr.sum or orthonormal coding via contr.orthonorm for factors) can reduce this issue. In any case you should be mindful of this issue.

See bayesfactor_models details for more info on passed models.

Note that for BayesFactor models, posterior samples cannot be generated from intercept only models.

This function is similar in function to brms::posterior_average.

Value

A data frame with posterior distributions (weighted across models) .

Note

For BayesFactor < 0.9.12-4.3, in some instances there might be some problems of duplicate columns of random effects in the resulting data frame.

References

Clyde, M., Desimone, H., & Parmigiani, G. (1996). Prediction via orthogonalized model mixing. Journal of the American Statistical Association, 91(435), 1197-1208.
Hinne, M., Gronau, Q. F., van den Bergh, D., and Wagenmakers, E. (2019, March 25). A conceptual introduction to Bayesian Model Averaging. doi: 10.31234/osf.io/wgb64
Rouder, J. N., Haaf, J. M., & Vandekerckhove, J. (2018). Bayesian inference for psychology, part IV: Parameter estimation and Bayes factors. Psychonomic bulletin & review, 25(1), 102-113.
van den Bergh, D., Haaf, J. M., Ly, A., Rouder, J. N., & Wagenmakers, E. J. (2019). A cautionary note on estimating effect size.

Examples

if (require("rstanarm") && require("see")) {
  stan_m0 <- stan_glm(extra ~ 1,
    data = sleep,
    family = gaussian(),
    refresh = 0,
    diagnostic_file = file.path(tempdir(), "df0.csv")
  )

  stan_m1 <- stan_glm(extra ~ group,
    data = sleep,
    family = gaussian(),
    refresh = 0,
    diagnostic_file = file.path(tempdir(), "df1.csv")
  )


  res <- weighted_posteriors(stan_m0, stan_m1)

  plot(eti(res))
}

## With BayesFactor
if (require("BayesFactor")) {
  extra_sleep <- ttestBF(formula = extra ~ group, data = sleep)

  wp <- weighted_posteriors(extra_sleep)

  describe_posterior(extra_sleep, test = NULL)
  describe_posterior(wp$delta, test = NULL) # also considers the null
}


## weighted prediction distributions via data.frames
if (require("rstanarm")) {
  m0 <- stan_glm(
    mpg ~ 1,
    data = mtcars,
    family = gaussian(),
    diagnostic_file = file.path(tempdir(), "df0.csv"),
    refresh = 0
  )

  m1 <- stan_glm(
    mpg ~ carb,
    data = mtcars,
    family = gaussian(),
    diagnostic_file = file.path(tempdir(), "df1.csv"),
    refresh = 0
  )

  # Predictions:
  pred_m0 <- data.frame(posterior_predict(m0))
  pred_m1 <- data.frame(posterior_predict(m1))

  BFmods <- bayesfactor_models(m0, m1)

  wp <- weighted_posteriors(pred_m0, pred_m1,
    prior_odds = BFmods$BF[2]
  )

  # look at first 5 prediction intervals
  hdi(pred_m0[1:5])
  hdi(pred_m1[1:5])
  hdi(wp[1:5]) # between, but closer to pred_m1
}

bayestestR

Understand and Describe Bayesian Models and Posterior Distributions

v0.10.0

GPL-3

Authors

Dominique Makowski [aut, cre] (<https://orcid.org/0000-0001-5375-9967>, @Dom_Makowski), Daniel Lüdecke [aut] (<https://orcid.org/0000-0002-8895-3206>, @strengejacke), Mattan S. Ben-Shachar [aut] (<https://orcid.org/0000-0002-4287-4801>, @mattansb), Indrajeet Patil [aut] (<https://orcid.org/0000-0003-1995-6531>, @patilindrajeets), Michael D. Wilson [aut] (<https://orcid.org/0000-0003-4143-7308>), Paul-Christian Bürkner [rev], Tristan Mahr [rev] (<https://orcid.org/0000-0002-8890-5116>), Henrik Singmann [ctb] (<https://orcid.org/0000-0002-4842-3657>), Quentin F. Gronau [ctb] (<https://orcid.org/0000-0001-5510-6943>), Sam Crawley [ctb] (<https://orcid.org/0000-0002-7847-0411>)

Initial release