R: LOO predictive checks

PPC-loo {bayesplot}

R Documentation

LOO predictive checks

Description

Leave-One-Out (LOO) predictive checks. See the Plot Descriptions section below for details.

Usage

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, lw, psis_object, intervals = NULL, ...,
  prob = 0.9, size = 1, fatten = 3, order = c("index", "median"))

ppc_loo_ribbon(y, yrep, lw, psis_object, intervals = NULL, ..., prob = 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`. If using loo < 2.0.0 see the `psislw` function in the loo package, which returns smoothed weights that can be used to specify `lw`. If using loo >= 2.0.0 see the `psis` function and the associated `weights` method.
`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 `geom_point` and `geom_density`, respectively. For `ppc_loo_intervals`, `size` and `fatten` are passed to `geom_pointrange`. For `ppc_loo_ribbon`, `alpha` and `size` are passed to `geom_ribbon`.
`trim`	Passed to `stat_density`.
`bw, adjust, kernel, n_dens`	Optional arguments passed to `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`).
`intervals`	For `ppc_loo_intervals` and `ppc_loo_ribbon`, optionally a matrix of precomputed LOO predictive intervals intervals with 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 three columns in the following order: the first for the lower bound of the interval, the second for median (50%), and the third for the interval upper bound (column names are ignored).
`prob`	A value between 0 and 1 indicating the desired probability mass to include in the intervals. The default is 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_qq,ppc_loo_pit_overlay

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. (2018) 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. (2018) 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. (2018). Visualization in Bayesian workflow. Journal of the Royal Statistical Society Series A, accepted for publication. arXiv preprint: http://arxiv.org/abs/1709.01449.

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/

Examples


## Not run: 
library(rstanarm)
library(loo)

head(radon)
fit <- stan_lmer(
  log_radon ~ floor + log_uranium + floor:log_uranium
               + (1 + floor | county),
  data = radon,
  iter = 1000,
  chains = 2  # ,cores = 2
 )
y <- radon$log_radon
yrep <- posterior_predict(fit)

if (packageVersion("loo") < "2.0.0") {
  psis1 <- psislw(-log_lik(fit), cores = 2)
  lw <- psis1$lw_smooth
} else {
  psis1 <- psis(-log_lik(fit), cores = 2)
  lw <- weights(psis1)
}

# marginal predictive check using LOO probability integral transform
color_scheme_set("orange")
ppc_loo_pit_overlay(y, yrep, lw = lw, adjust = 0.9)

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


# loo predictive intervals vs observations
sel <- 800:900
ppc_loo_intervals(y[sel], yrep[, sel], psis1$lw_smooth[, sel],
                  prob = 0.9, size = 0.5)

color_scheme_set("gray")
ppc_loo_intervals(y[sel], yrep[, sel], psis1$lw_smooth[, sel],
                  order = "median", prob = 0.8, size = 0.5)

## End(Not run)

[Package bayesplot version 1.5.0 Index]