Make a table of Bayesian model comparisons using the loo package.
Usage
# S3 method for class 'compare.loo'
model_parameters(model, include_IC = TRUE, include_ENP = FALSE, ...)Arguments
- model
An object of class brms::loo_compare.
- include_IC
Whether to include the information criteria (IC).
- include_ENP
Whether to include the effective number of parameters (ENP).
- ...
Additional arguments (not used for now).
Details
The rule of thumb is that the models are "very similar" if |elpd_diff| (the
absolute value of elpd_diff) is less than 4 (Sivula, Magnusson and Vehtari, 2020).
If superior to 4, then one can use the SE to obtain a standardized difference
(Z-diff) and interpret it as such, assuming that the difference is normally
distributed. The corresponding p-value is then calculated as 2 * pnorm(-abs(Z-diff)).
However, note that if the raw ELPD difference is small (less than 4), it doesn't
make much sense to rely on its standardized value: it is not very useful to
conclude that a model is much better than another if both models make very
similar predictions.
Examples
# \donttest{
library(brms)
#> Loading 'brms' package (version 2.22.0). Useful instructions
#> can be found by typing help('brms'). A more detailed introduction
#> to the package is available through vignette('brms_overview').
#>
#> Attaching package: ‘brms’
#> The following objects are masked from ‘package:mgcv’:
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#> s, t2
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#> me
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#> lognormal
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#> ar
m1 <- brms::brm(mpg ~ qsec, data = mtcars)
#> Compiling Stan program...
#> Start sampling
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#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
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m2 <- brms::brm(mpg ~ qsec + drat, data = mtcars)
#> Compiling Stan program...
#> Start sampling
#>
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
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m3 <- brms::brm(mpg ~ qsec + drat + wt, data = mtcars)
#> Compiling Stan program...
#> Start sampling
#>
#> SAMPLING FOR MODEL 'anon_model' NOW (CHAIN 1).
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#> Chain 1: Gradient evaluation took 1e-05 seconds
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x <- suppressWarnings(brms::loo_compare(
brms::add_criterion(m1, "loo"),
brms::add_criterion(m2, "loo"),
brms::add_criterion(m3, "loo"),
model_names = c("m1", "m2", "m3")
))
model_parameters(x)
#> # Fixed Effects
#>
#> Name | LOOIC | ELPD | Difference | Difference_SE | p
#> -------------------------------------------------------------
#> m3 | 158.31 | -79.15 | 0.00 | 0.00 |
#> m2 | 184.75 | -92.38 | -13.22 | 4.32 | 0.002
#> m1 | 204.62 | -102.31 | -23.16 | 4.39 | < .001
model_parameters(x, include_IC = FALSE, include_ENP = TRUE)
#> # Fixed Effects
#>
#> Name | ENP | ELPD | Difference | Difference_SE | p
#> -----------------------------------------------------------
#> m3 | 5.06 | -79.15 | 0.00 | 0.00 |
#> m2 | 3.88 | -92.38 | -13.22 | 4.32 | 0.002
#> m1 | 2.59 | -102.31 | -23.16 | 4.39 | < .001
# }