Confidence/Credible/Compatibility Interval (CI)

Source: R/ci.R

Compute Confidence/Credible/Compatibility Intervals (CI) or Support Intervals (SI) for Bayesian and frequentist models. The Documentation is accessible for:

ci(x, ...)

# S3 method for class 'numeric'
ci(x, ci = 0.95, method = "ETI", verbose = TRUE, BF = 1, ...)

# S3 method for class 'data.frame'
ci(x, ci = 0.95, method = "ETI", BF = 1, rvar_col = NULL, verbose = TRUE, ...)

# S3 method for class 'brmsfit'
ci(
  x,
  ci = 0.95,
  method = "ETI",
  effects = "fixed",
  component = "conditional",
  parameters = NULL,
  verbose = TRUE,
  BF = 1,
  ...
)

Arguments

x

A stanreg or brmsfit model, or a vector representing a posterior distribution.

...

Currently not used.

ci

Value or vector of probability of the CI (between 0 and 1) to be estimated. Default to 0.95 (95%).

method

Can be "ETI" (default), "HDI", "BCI", "SPI" or "SI".

verbose

Toggle off warnings.

BF

The amount of support required to be included in the support interval.

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.

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.

Note

When it comes to interpretation, we recommend thinking of the CI in terms of an "uncertainty" or "compatibility" interval, the latter being defined as "Given any value in the interval and the background assumptions, the data should not seem very surprising" (Gelman & Greenland 2019).

There is also a plot()-method implemented in the see-package.

Model components

Possible values for the component argument depend on the model class. Following are valid options:

  • "all": returns all model components, applies to all models, but will only have an effect for models with more than just the conditional model component.

  • "conditional": only returns the conditional component, i.e. "fixed effects" terms from the model. Will only have an effect for models with more than just the conditional model component.

  • "smooth_terms": returns smooth terms, only applies to GAMs (or similar models that may contain smooth terms).

  • "zero_inflated" (or "zi"): returns the zero-inflation component.

  • "location": returns location parameters such as conditional, zero_inflated, or smooth_terms (everything that are fixed or random effects - depending on the effects argument - but no auxiliary parameters).

  • "distributional" (or "auxiliary"): components like sigma, dispersion, beta or precision (and other auxiliary parameters) are returned.

For models of class brmsfit (package brms), even more options are possible for the component argument, which are not all documented in detail here. See also ?insight::find_parameters.

References

Gelman A, Greenland S. Are confidence intervals better termed "uncertainty intervals"? BMJ 2019;l5381. 10.1136/bmj.l5381

See also

Other ci: bci(), eti(), hdi(), si(), spi()

Examples

library(bayestestR)

posterior <- rnorm(1000)
ci(posterior, method = "ETI")
#> 95% ETI: [-1.93, 1.97]
ci(posterior, method = "HDI")
#> 95% HDI: [-1.85, 2.04]

df <- data.frame(replicate(4, rnorm(100)))
ci(df, method = "ETI", ci = c(0.80, 0.89, 0.95))
#> Equal-Tailed Interval
#> 
#> Parameter |       80% ETI |       89% ETI |       95% ETI
#> ---------------------------------------------------------
#> X1        | [-1.46, 1.27] | [-1.60, 1.62] | [-1.96, 1.96]
#> X2        | [-1.19, 1.34] | [-1.42, 1.48] | [-2.02, 1.84]
#> X3        | [-1.26, 1.18] | [-1.72, 1.51] | [-2.20, 1.66]
#> X4        | [-1.01, 1.61] | [-1.33, 1.73] | [-1.85, 2.22]
ci(df, method = "HDI", ci = c(0.80, 0.89, 0.95))
#> Highest Density Interval
#> 
#> Parameter |       80% HDI |       89% HDI |       95% HDI
#> ---------------------------------------------------------
#> X1        | [-1.64, 1.02] | [-1.55, 1.73] | [-1.97, 1.80]
#> X2        | [-1.44, 0.99] | [-1.44, 1.49] | [-2.29, 1.72]
#> X3        | [-0.98, 1.35] | [-1.46, 1.56] | [-2.34, 1.52]
#> X4        | [-1.00, 1.62] | [-1.22, 1.89] | [-1.47, 2.39]

model <- suppressWarnings(rstanarm::stan_glm(
  mpg ~ wt,
  data = mtcars, chains = 2, iter = 200, refresh = 0
))
ci(model, method = "ETI", ci = c(0.80, 0.89))
#> Equal-Tailed Interval
#> 
#> Parameter   |        80% ETI |        89% ETI | Effects |   Component
#> ---------------------------------------------------------------------
#> (Intercept) | [34.88, 39.92] | [34.57, 40.72] |   fixed | conditional
#> wt          | [-6.12, -4.71] | [-6.44, -4.53] |   fixed | conditional
ci(model, method = "HDI", ci = c(0.80, 0.89))
#> Highest Density Interval
#> 
#> Parameter   |        80% HDI |        89% HDI
#> ---------------------------------------------
#> (Intercept) | [34.55, 39.51] | [34.47, 40.19]
#> wt          | [-6.15, -4.75] | [-6.14, -4.41]
bf <- BayesFactor::ttestBF(x = rnorm(100, 1, 1))
ci(bf, method = "ETI")
#> Equal-Tailed Interval
#> 
#> Parameter  |      95% ETI
#> -------------------------
#> Difference | [0.73, 1.08]
ci(bf, method = "HDI")
#> Highest Density Interval
#> 
#> Parameter  |      95% HDI
#> -------------------------
#> Difference | [0.74, 1.09]
model <- emmeans::emtrends(model, ~1, "wt", data = mtcars)
ci(model, method = "ETI")
#> Equal-Tailed Interval
#> 
#> X1      |        95% ETI
#> ------------------------
#> overall | [-6.69, -4.42]
ci(model, method = "HDI")
#> Highest Density Interval
#> 
#> X1      |        95% HDI
#> ------------------------
#> overall | [-6.53, -4.38]