Shortest Probability Interval (SPI)

Compute the Shortest Probability Interval (SPI) of posterior distributions. The SPI is a more computationally stable HDI. The implementation is based on the algorithm from the SPIn package.

spi(x, ...)

# S3 method for class 'numeric'
spi(x, ci = 0.95, verbose = TRUE, ...)

# S3 method for class 'data.frame'
spi(x, ci = 0.95, rvar_col = NULL, verbose = TRUE, ...)

# S3 method for class 'brmsfit'
spi(
  x,
  ci = 0.95,
  effects = "fixed",
  component = "conditional",
  parameters = NULL,
  verbose = TRUE,
  ...
)

# S3 method for class 'get_predicted'
spi(x, ci = 0.95, use_iterations = FALSE, verbose = TRUE, ...)

Arguments

x

Vector representing a posterior distribution, or a data frame of such vectors. Can also be a Bayesian model. bayestestR supports a wide range of models (see, for example, methods("hdi")) and not all of those are documented in the 'Usage' section, because methods for other classes mostly resemble the arguments of the .numeric or .data.framemethods.

...

Currently not used.

ci

Value or vector of probability of the (credible) interval - CI (between 0 and 1) to be estimated. Default to .95 (95%).

verbose

Toggle off warnings.

rvar_col

A single character - the name of an rvar column in the data frame to be processed. See example in p_direction().

effects

Should variables for fixed effects ("fixed"), random effects ("random") or both ("all") be returned? Only applies to mixed models. May be abbreviated.

For models of from packages brms or rstanarm there are additional options:

"fixed" returns fixed effects.
"random_variance" return random effects parameters (variance and correlation components, e.g. those parameters that start with sd_ or cor_).
"grouplevel" returns random effects group level estimates, i.e. those parameters that start with r_.
"random" returns both "random_variance" and "grouplevel".
"all" returns fixed effects and random effects variances.
"full" returns all parameters.

component

Which type of parameters to return, such as parameters for the conditional model, the zero-inflated part of the model, the dispersion term, etc. See details in section Model Components. May be abbreviated. Note that the conditional component also refers to the count or mean component - names may differ, depending on the modeling package. There are three convenient shortcuts (not applicable to all model classes):

component = "all" returns all possible parameters.
If component = "location", location parameters such as conditional, zero_inflated, smooth_terms, or instruments are returned (everything that are fixed or random effects - depending on the effects argument - but no auxiliary parameters).
For component = "distributional" (or "auxiliary"), components like sigma, dispersion, beta or precision (and other auxiliary parameters) are returned.

parameters

Regular expression pattern that describes the parameters that should be returned. Meta-parameters (like lp__ or prior_) are filtered by default, so only parameters that typically appear in the summary() are returned. Use parameters to select specific parameters for the output.

use_iterations

Logical, if TRUE and x is a get_predicted object, (returned by insight::get_predicted()), the function is applied to the iterations instead of the predictions. This only applies to models that return iterations for predicted values (e.g., brmsfit models).

Value

A data frame with following columns:

Parameter The model parameter(s), if x is a model-object. If x is a vector, this column is missing.
CI The probability of the credible interval.
CI_low, CI_high The lower and upper credible interval limits for the parameters.

Details

The SPI is an alternative method to the HDI (hdi()) to quantify uncertainty of (posterior) distributions. The SPI is said to be more stable than the HDI, because, the "HDI can be noisy (that is, have a high Monte Carlo error)" (Liu et al. 2015). Furthermore, the HDI is sensitive to additional assumptions, in particular assumptions related to the different estimation methods, which can make the HDI less accurate or reliable.

Note

The code to compute the SPI was adapted from the SPIn package, and slightly modified to be more robust for Stan models. Thus, credits go to Ying Liu for the original SPI algorithm and R implementation.

References

Liu, Y., Gelman, A., & Zheng, T. (2015). Simulation-efficient shortest probability intervals. Statistics and Computing, 25(4), 809–819. https://doi.org/10.1007/s11222-015-9563-8

Examples

library(bayestestR)

posterior <- rnorm(1000)
spi(posterior)
#> 95% SPI: [-1.96, 1.96]
spi(posterior, ci = c(0.80, 0.89, 0.95))
#> Shortest Probability Interval
#> 
#> 80% SPI       |       89% SPI |       95% SPI
#> ---------------------------------------------
#> [-1.17, 1.34] | [-1.50, 1.70] | [-1.96, 1.96]

df <- data.frame(replicate(4, rnorm(100)))
spi(df)
#> Shortest Probability Interval
#> 
#> Parameter |       95% SPI
#> -------------------------
#> X1        | [-2.04, 1.89]
#> X2        | [-1.64, 1.96]
#> X3        | [-2.10, 1.73]
#> X4        | [-1.89, 2.38]
spi(df, ci = c(0.80, 0.89, 0.95))
#> Shortest Probability Interval
#> 
#> Parameter |       80% SPI |       89% SPI |       95% SPI
#> ---------------------------------------------------------
#> X1        | [-1.05, 1.44] | [-1.43, 1.76] | [-2.04, 1.89]
#> X2        | [-0.90, 1.17] | [-1.37, 1.41] | [-1.64, 1.96]
#> X3        | [-1.41, 1.42] | [-1.98, 1.42] | [-2.10, 1.73]
#> X4        | [-1.27, 1.37] | [-2.00, 1.37] | [-1.89, 2.38]
# \donttest{
library(rstanarm)
model <- suppressWarnings(
  stan_glm(mpg ~ wt + gear, data = mtcars, chains = 2, iter = 200, refresh = 0)
)
spi(model)
#> Shortest Probability Interval
#> 
#> Parameter   |        95% SPI
#> ----------------------------
#> (Intercept) | [28.02, 47.24]
#> wt          | [-6.77, -4.16]
#> gear        | [-2.30,  1.58]
# }