K-fold cross-validation

The kfold method performs exact \(K\)-fold cross-validation. First the data are randomly partitioned into \(K\) subsets of equal size (or as close to equal as possible), or the user can specify the folds argument to determine the partitioning. Then the model is refit \(K\) times, each time leaving out one of the \(K\) subsets. If \(K\) is equal to the total number of observations in the data then \(K\)-fold cross-validation is equivalent to exact leave-one-out cross-validation (to which loo is an efficient approximation).

# S3 method for stanreg
kfold(
  x,
  K = 10,
  ...,
  folds = NULL,
  save_fits = FALSE,
  cores = getOption("mc.cores", 1)
)

Arguments

x	A fitted model object returned by one of the rstanarm modeling functions. See stanreg-objects.
K	For kfold, the number of subsets (folds) into which the data will be partitioned for performing \(K\)-fold cross-validation. The model is refit K times, each time leaving out one of the K folds. If the folds argument is specified then K will automatically be set to length(unique(folds)), otherwise the specified value of K is passed to loo::kfold_split_random to randomly partition the data into K subsets of equal (or as close to equal as possible) size.
...	Currently ignored.
folds	For kfold, an optional integer vector with one element per observation in the data used to fit the model. Each element of the vector is an integer in 1:K indicating to which of the K folds the corresponding observation belongs. There are some convenience functions available in the loo package that create integer vectors to use for this purpose (see the Examples section below and also the kfold-helpers page).
save_fits	For kfold, if TRUE, a component 'fits' is added to the returned object to store the cross-validated stanreg objects and the indices of the omitted observations for each fold. Defaults to FALSE.
cores	The number of cores to use for parallelization. Instead fitting separate Markov chains for the same model on different cores, by default kfold will distribute the K models to be fit across the cores (using parLapply on Windows and mclapply otherwise). The Markov chains for each model will be run sequentially. This will often be the most efficient option, especially if many cores are available, but in some cases it may be preferable to fit the K models sequentially and instead use the cores for the Markov chains. This can be accomplished by setting options(mc.cores) to be the desired number of cores to use for the Markov chains and also manually specifying cores=1 when calling the kfold function. See the end of the Examples section for a demonstration.

Value

An object with classes 'kfold' and 'loo' that has a similar structure as the objects returned by the loo and waic methods and is compatible with the loo_compare function for comparing models.

References

Vehtari, A., Gelman, A., and Gabry, J. (2017). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and Computing. 27(5), 1413--1432. doi:10.1007/s11222-016-9696-4. arXiv preprint: http://arxiv.org/abs/1507.04544/

Yao, Y., Vehtari, A., Simpson, D., and Gelman, A. (2018) Using stacking to average Bayesian predictive distributions. Bayesian Analysis, advance publication, doi:10.1214/17-BA1091. (online).

Examples

# \donttest{
fit1 <- stan_glm(mpg ~ wt, data = mtcars, refresh = 0)
fit2 <- stan_glm(mpg ~ wt + cyl, data = mtcars, refresh = 0)
fit3 <- stan_glm(mpg ~ disp * as.factor(cyl), data = mtcars, refresh = 0)

# 10-fold cross-validation
# (if possible also specify the 'cores' argument to use multiple cores)
(kfold1 <- kfold(fit1, K = 10))
#> Fitting model 1 out of 10
#> Fitting model 2 out of 10
#> Fitting model 3 out of 10
#> Fitting model 4 out of 10
#> Fitting model 5 out of 10
#> Fitting model 6 out of 10
#> Fitting model 7 out of 10
#> Fitting model 8 out of 10
#> Fitting model 9 out of 10
#> Fitting model 10 out of 10
#> 
#> Based on 10-fold cross-validation
#> 
#>            Estimate  SE
#> elpd_kfold    -83.6 4.2
#> p_kfold          NA  NA
#> kfoldic       167.2 8.5
kfold2 <- kfold(fit2, K = 10)
#> Fitting model 1 out of 10
#> Fitting model 2 out of 10
#> Fitting model 3 out of 10
#> Fitting model 4 out of 10
#> Fitting model 5 out of 10
#> Fitting model 6 out of 10
#> Fitting model 7 out of 10
#> Fitting model 8 out of 10
#> Fitting model 9 out of 10
#> Fitting model 10 out of 10
kfold3 <- kfold(fit3, K = 10)
#> Fitting model 1 out of 10
#> Fitting model 2 out of 10
#> Fitting model 3 out of 10
#> Fitting model 4 out of 10
#> Fitting model 5 out of 10
#> Fitting model 6 out of 10
#> Fitting model 7 out of 10
#> Fitting model 8 out of 10
#> Fitting model 9 out of 10
#> Fitting model 10 out of 10
loo_compare(kfold1, kfold2, kfold3)
#>      elpd_diff se_diff
#> fit3  0.0       0.0   
#> fit2 -4.6       6.1   
#> fit1 -6.0       5.0   

# stratifying by a grouping variable
# (note: might get some divergences warnings with this model but 
# this is just intended as a quick example of how to code this)
fit4 <- stan_lmer(mpg ~ disp + (1|cyl), data = mtcars, refresh = 0)
#> Warning: There were 5 divergent transitions after warmup. Increasing adapt_delta above 0.95 may help. See
#> http://mc-stan.org/misc/warnings.html#divergent-transitions-after-warmup
#> Warning: Examine the pairs() plot to diagnose sampling problems
table(mtcars$cyl)
#> 
#>  4  6  8 
#> 11  7 14 
folds_cyl <- loo::kfold_split_stratified(K = 3, x = mtcars$cyl)
table(cyl = mtcars$cyl, fold = folds_cyl)
#>    fold
#> cyl 1 2 3
#>   4 4 4 3
#>   6 2 2 3
#>   8 5 5 4
kfold4 <- kfold(fit4, folds = folds_cyl, cores = 2)
#> Fitting K = 3 models distributed over 2 cores
print(kfold4)
#> 
#> Based on 3-fold cross-validation
#> 
#>            Estimate  SE
#> elpd_kfold    -86.4 4.2
#> p_kfold          NA  NA
#> kfoldic       172.7 8.5
# }

# Example code demonstrating the different ways to specify the number 
# of cores and how the cores are used
# 
# options(mc.cores = NULL)
# 
# # spread the K models over N_CORES cores (method 1)
# kfold(fit, K, cores = N_CORES)
# 
# # spread the K models over N_CORES cores (method 2)
# options(mc.cores = N_CORES)
# kfold(fit, K)
#  
# # fit K models sequentially using N_CORES cores for the Markov chains each time
# options(mc.cores = N_CORES)
# kfold(fit, K, cores = 1)