bayestestR (version 0.5.3)

bayesfactor_models: Bayes Factors (BF) for model comparison

Description

This function computes or extracts Bayes factors from fitted models.

The bf_* function is an alias of the main function.

Usage

bayesfactor_models(..., denominator = 1, verbose = TRUE)
bf_models(..., denominator = 1, verbose = TRUE)

Arguments

...

Fitted models (see details), all fit on the same data, or a single BFBayesFactor object (see 'Details').

denominator

Either an integer indicating which of the models to use as the denominator, or a model to be used as a denominator. Ignored for BFBayesFactor.

verbose

Toggle off warnings.

Value

A data frame containing the models' formulas (reconstructed fixed and random effects) and their BFs, that prints nicely.

Details

If the passed models are supported by insight the DV of all models will be tested for equality (else this is assumed to be true), and the models' terms will be extracted (allowing for follow-up analysis with bayesfactor_inclusion).

• For brmsfit or stanreg models, Bayes factors are computed using the bridgesampling package.

  • brmsfit models must have been fitted with save_all_pars = TRUE.

  • stanreg models must have been fitted with a defined diagnostic_file.

• For BFBayesFactor, bayesfactor_models() is mostly a wraparoud BayesFactor::extractBF().

• For all other model types (supported by insight), BIC approximations are used to compute Bayes factors.

In order to correctly and precisely estimate Bayes factors, a rule of thumb are the 4 P's: Proper Priors and Plentiful Posterior (i.e. probably at leat 40,000 samples instead of the default of 4,000).

A Bayes factor greater than 1 can be interpereted as evidence against the compared-to model (the denominator). One convention is that a Bayes factor greater than 3 can be considered as "substantial" evidence against the denominator model (and vice versa, a Bayes factor smaller than 1/3 indicates substantial evidence in favor of the denominator model) (Wetzels et al. 2011).

See also the Bayes factors vignette.

References

• Gronau, Q. F., Wagenmakers, E. J., Heck, D. W., and Matzke, D. (2019). A simple method for comparing complex models: Bayesian model comparison for hierarchical multinomial processing tree models using Warp-III bridge sampling. Psychometrika, 84(1), 261-284.

• Kass, R. E., and Raftery, A. E. (1995). Bayes Factors. Journal of the American Statistical Association, 90(430), 773-795.

• Robert, C. P. (2016). The expected demise of the Bayes factor. Journal of Mathematical Psychology, 72, 33<U+2013>37.

• Wagenmakers, E. J. (2007). A practical solution to the pervasive problems of p values. Psychonomic bulletin & review, 14(5), 779-804.

• Wetzels, R., Matzke, D., Lee, M. D., Rouder, J. N., Iverson, G. J., and Wagenmakers, E.-J. (2011). Statistical Evidence in Experimental Psychology: An Empirical Comparison Using 855 t Tests. Perspectives on Psychological Science, 6(3), 291<U+2013>298. 10.1177/1745691611406923

Examples

# NOT RUN {
# With lm objects:
# ----------------
lm1 <- lm(Sepal.Length ~ 1, data = iris)
lm2 <- lm(Sepal.Length ~ Species, data = iris)
lm3 <- lm(Sepal.Length ~ Species + Petal.Length, data = iris)
lm4 <- lm(Sepal.Length ~ Species * Petal.Length, data = iris)
bayesfactor_models(lm1, lm2, lm3, lm4, denominator = 1)
bayesfactor_models(lm2, lm3, lm4, denominator = lm1) # same result
bayesfactor_models(lm1, lm2, lm3, lm4, denominator = lm1) # same result

# }
# NOT RUN {
# With lmerMod objects:
# ---------------------
if (require("lme4")) {
  lmer1 <- lmer(Sepal.Length ~ Petal.Length + (1 | Species), data = iris)
  lmer2 <- lmer(Sepal.Length ~ Petal.Length + (Petal.Length | Species), data = iris)
  lmer3 <- lmer(
    Sepal.Length ~ Petal.Length + (Petal.Length | Species) + (1 | Petal.Width),
    data = iris
  )
  bayesfactor_models(lmer1, lmer2, lmer3, denominator = 1)
  bayesfactor_models(lmer1, lmer2, lmer3, denominator = lmer1)
}

# rstanarm models
# ---------------------
# (note that a unique diagnostic_file MUST be specified in order to work)
if (require("rstanarm")) {
  stan_m0 <- stan_glm(Sepal.Length ~ 1,
    data = iris,
    family = gaussian(),
    diagnostic_file = file.path(tempdir(), "df0.csv")
  )
  stan_m1 <- stan_glm(Sepal.Length ~ Species,
    data = iris,
    family = gaussian(),
    diagnostic_file = file.path(tempdir(), "df1.csv")
  )
  stan_m2 <- stan_glm(Sepal.Length ~ Species + Petal.Length,
    data = iris,
    family = gaussian(),
    diagnostic_file = file.path(tempdir(), "df2.csv")
  )
  bayesfactor_models(stan_m1, stan_m2, denominator = stan_m0)
}


# brms models
# --------------------
# (note the save_all_pars MUST be set to TRUE in order to work)
if (require("brms")) {
  brm1 <- brm(Sepal.Length ~ 1, data = iris, save_all_pars = TRUE)
  brm2 <- brm(Sepal.Length ~ Species, data = iris, save_all_pars = TRUE)
  brm3 <- brm(
    Sepal.Length ~ Species + Petal.Length,
    data = iris,
    save_all_pars = TRUE
  )

  bayesfactor_models(brm1, brm2, brm3, denominator = 1)
}


# BayesFactor
# ---------------------------
if (require("BayesFactor")) {
  data(puzzles)
  BF <- anovaBF(RT ~ shape * color + ID,
    data = puzzles,
    whichRandom = "ID", progress = FALSE
  )
  BF
  bayesfactor_models(BF) # basically the same
}
# }