LOO predictive checks

Leave-One-Out (LOO) predictive checks. See the Plot Descriptions section, below, and Gabry et al. (2019) for details.

ppc_loo_pit_overlay(
  y,
  yrep,
  lw,
  pit,
  samples = 100,
  ...,
  size = 0.25,
  alpha = 0.7,
  trim = FALSE,
  bw = "nrd0",
  adjust = 1,
  kernel = "gaussian",
  n_dens = 1024
)

ppc_loo_pit_qq(
  y,
  yrep,
  lw,
  pit,
  compare = c("uniform", "normal"),
  ...,
  size = 2,
  alpha = 1
)

ppc_loo_pit(
  y,
  yrep,
  lw,
  pit,
  compare = c("uniform", "normal"),
  ...,
  size = 2,
  alpha = 1
)

ppc_loo_intervals(
  y,
  yrep,
  psis_object,
  subset = NULL,
  intervals = NULL,
  ...,
  prob = 0.5,
  prob_outer = 0.9,
  size = 1,
  fatten = 3,
  order = c("index", "median")
)

ppc_loo_ribbon(
  y,
  yrep,
  lw,
  psis_object,
  subset = NULL,
  intervals = NULL,
  ...,
  prob = 0.5,
  prob_outer = 0.9,
  alpha = 0.33,
  size = 0.25
)

Arguments

y	A vector of observations. See Details.
yrep	An \(S\) by \(N\) matrix of draws from the posterior predictive distribution, where \(S\) is the size of the posterior sample (or subset of the posterior sample used to generate `yrep`) and \(N\) is the number of observations (the length of `y`). The columns of `yrep` should be in the same order as the data points in `y` for the plots to make sense. See Details for additional instructions.
lw	A matrix of (smoothed) log weights with the same dimensions as `yrep`. See `loo::psis()` and the associated `weights()` method as well as the Examples section, below.
pit	For `ppc_loo_pit_overlay()` and `ppc_loo_pit_qq()`, optionally a vector of precomputed PIT values that can be specified instead of `y`, `yrep`, and `lw` (these are all ignored if `pit` is specified). If not specified the PIT values are computed internally before plotting.
samples	For `ppc_loo_pit_overlay()`, the number of data sets (each the same size as `y`) to simulate from the standard uniform distribution. The default is 100. The density estimate of each dataset is plotted as a thin line in the plot, with the density estimate of the LOO PITs overlaid as a thicker dark line.
...	Currently unused.
alpha, size, fatten	Arguments passed to code geoms to control plot aesthetics. For `ppc_loo_pit_qq()` and `ppc_loo_pit_overlay()`, `size` and `alpha` are passed to `ggplot2::geom_point()` and `ggplot2::geom_density()`, respectively. For `ppc_loo_intervals()`, `size` and `fatten` are passed to `ggplot2::geom_pointrange()`. For `ppc_loo_ribbon()`, `alpha` and `size` are passed to `ggplot2::geom_ribbon()`.
trim	Passed to `ggplot2::stat_density()`.
bw, adjust, kernel, n_dens	Optional arguments passed to `stats::density()` to override default kernel density estimation parameters. `n_dens` defaults to `1024`.
compare	For `ppc_loo_pit_qq()`, a string that can be either `"uniform"` or `"normal"`. If `"uniform"` (the default) the Q-Q plot compares computed PIT values to the standard uniform distribution. If `compare="normal"`, the Q-Q plot compares standardized PIT values to the standard normal distribution.
psis_object	If using loo version `2.0.0` or greater, an object returned by the `psis()` function (or by the `loo()` function with argument `save_psis` set to `TRUE`).
subset	For `ppc_loo_intervals()` and `ppc_loo_ribbon()`, an optional integer vector indicating which observations in `y` (and `yrep`) to include. Dropping observations from `y` and `yrep` manually before passing them to the plotting function will not work because the dimensions will not match up with the dimensions of `psis_object`, but if all of `y` and `yrep` are passed along with `subset` then bayesplot can do the subsetting internally for `y`, `yrep` and `psis_object`. See the Examples section for a demonstration.
intervals	For `ppc_loo_intervals()` and `ppc_loo_ribbon()`, optionally a matrix of precomputed LOO predictive intervals that can be specified instead of `yrep` and `lw` (these are both ignored if `intervals` is specified). If not specified the intervals are computed internally before plotting. If specified, `intervals` must be a matrix with number of rows equal to the number of data points and five columns in the following order: lower outer interval, lower inner interval, median (50%), upper inner interval and upper outer interval (column names are ignored).
prob, prob_outer	Values between 0 and 1 indicating the desired probability mass to include in the inner and outer intervals. The defaults are `prob=0.5` and `prob_outer=0.9`.
order	For `ppc_loo_intervals()`, a string indicating how to arrange the plotted intervals. The default (`"index"`) is to plot them in the order of the observations. The alternative (`"median"`) arranges them by median value from smallest (left) to largest (right).

Value

A ggplot object that can be further customized using the ggplot2 package.

Plot Descriptions

ppc_loo_pit_overlay(), ppc_loo_pit_qq()

The calibration of marginal predictions can be assessed using probability integral transformation (PIT) checks. LOO improves the check by avoiding the double use of data. See the section on marginal predictive checks in Gelman et al. (2013, p. 152--153) and section 5 of Gabry et al. (2019) for an example of using bayesplot for these checks.The LOO PIT values are asymptotically uniform (for continuous data) if the model is calibrated. The ppc_loo_pit_overlay() function creates a plot comparing the density of the LOO PITs (thick line) to the density estimates of many simulated data sets from the standard uniform distribution (thin lines). See Gabry et al. (2019) for an example of interpreting the shape of the miscalibration that can be observed in these plots.The ppc_loo_pit_qq() function provides an alternative visualization of the miscalibration with a quantile-quantile (Q-Q) plot comparing the LOO PITs to the standard uniform distribution. Comparing to the uniform is not good for extreme probabilities close to 0 and 1, so it can sometimes be useful to set the compare argument to "normal", which will produce a Q-Q plot comparing standardized PIT values to the standard normal distribution that can help see the (mis)calibration better for the extreme values. However, in most cases we have found that the overlaid density plot (ppc_loo_pit_overlay()) function will provided a clearer picture of calibration problems that the Q-Q plot.

ppc_loo_intervals(), ppc_loo_ribbon()

Similar to ppc_intervals() and ppc_ribbon() but the intervals are for the LOO predictive distribution.

References

Gelman, A., Carlin, J. B., Stern, H. S., Dunson, D. B., Vehtari, A., and Rubin, D. B. (2013). Bayesian Data Analysis. Chapman & Hall/CRC Press, London, third edition. (p. 152--153)

Gabry, J. , Simpson, D. , Vehtari, A. , Betancourt, M. and Gelman, A. (2019), Visualization in Bayesian workflow. J. R. Stat. Soc. A, 182: 389-402. doi:10.1111/rssa.12378. (journal version, arXiv preprint, code on GitHub)

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: https://arxiv.org/abs/1507.04544/

Examples


# \dontrun{
suppressPackageStartupMessages(library(rstanarm))
suppressPackageStartupMessages(library(loo))

head(radon)
#>   floor county  log_radon log_uranium
#> 1     1 AITKIN 0.83290912  -0.6890476
#> 2     0 AITKIN 0.83290912  -0.6890476
#> 3     0 AITKIN 1.09861229  -0.6890476
#> 4     0 AITKIN 0.09531018  -0.6890476
#> 5     0  ANOKA 1.16315081  -0.8473129
#> 6     0  ANOKA 0.95551145  -0.8473129
fit <- stan_lmer(
  log_radon ~ floor + log_uranium + floor:log_uranium
               + (1 + floor | county),
  data = radon,
  iter = 1000,
  chains = 2,  # cores = 2
  refresh = 500
 )
#> 
#> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 1).
#> Chain 1: 
#> Chain 1: Gradient evaluation took 0.000408 seconds
#> Chain 1: 1000 transitions using 10 leapfrog steps per transition would take 4.08 seconds.
#> Chain 1: Adjust your expectations accordingly!
#> Chain 1: 
#> Chain 1: 
#> Chain 1: Iteration:   1 / 1000 [  0%]  (Warmup)
#> Chain 1: Iteration: 500 / 1000 [ 50%]  (Warmup)
#> Chain 1: Iteration: 501 / 1000 [ 50%]  (Sampling)
#> Chain 1: Iteration: 1000 / 1000 [100%]  (Sampling)
#> Chain 1: 
#> Chain 1:  Elapsed Time: 12.721 seconds (Warm-up)
#> Chain 1:                3.25757 seconds (Sampling)
#> Chain 1:                15.9786 seconds (Total)
#> Chain 1: 
#> 
#> SAMPLING FOR MODEL 'continuous' NOW (CHAIN 2).
#> Chain 2: 
#> Chain 2: Gradient evaluation took 0.000195 seconds
#> Chain 2: 1000 transitions using 10 leapfrog steps per transition would take 1.95 seconds.
#> Chain 2: Adjust your expectations accordingly!
#> Chain 2: 
#> Chain 2: 
#> Chain 2: Iteration:   1 / 1000 [  0%]  (Warmup)
#> Chain 2: Iteration: 500 / 1000 [ 50%]  (Warmup)
#> Chain 2: Iteration: 501 / 1000 [ 50%]  (Sampling)
#> Chain 2: Iteration: 1000 / 1000 [100%]  (Sampling)
#> Chain 2: 
#> Chain 2:  Elapsed Time: 12.5864 seconds (Warm-up)
#> Chain 2:                3.23027 seconds (Sampling)
#> Chain 2:                15.8167 seconds (Total)
#> Chain 2: 
y <- radon$log_radon
yrep <- posterior_predict(fit)

loo1 <- loo(fit, save_psis = TRUE, cores = 2)
#> Warning: Found 1 observation(s) with a pareto_k > 0.7. We recommend calling 'loo' again with argument 'k_threshold = 0.7' in order to calculate the ELPD without the assumption that these observations are negligible. This will refit the model 1 times to compute the ELPDs for the problematic observations directly.
psis1 <- loo1$psis_object
lw <- weights(psis1)

# marginal predictive check using LOO probability integral transform
color_scheme_set("orange")
ppc_loo_pit_overlay(y, yrep, lw = lw)

ppc_loo_pit_qq(y, yrep, lw = lw)
ppc_loo_pit_qq(y, yrep, lw = lw, compare = "normal")


# loo predictive intervals vs observations
keep_obs <- 1:50
ppc_loo_intervals(y, yrep, psis_object = psis1, subset = keep_obs)

color_scheme_set("gray")
ppc_loo_intervals(y, yrep, psis_object = psis1, subset = keep_obs,
                  order = "median")
# }

Arguments

Value

Plot Descriptions

References

See also

Examples