Chapter 13: Bayesian inference and decision making with bayestestR

1. Purpose

bayestestR implements a wide range indices for posterior description and decision-oriented summaries (probability of direction, ropes, equivalence tests, etc.). Here we treat the coefficients component of a glmb fit as stored i.i.d. draws and summarize them using bayestestR.

This complements Chapter 12 (optional bayesplot graphics, commented out in the vignette) with tabular summaries you can cite in applied reports.

2. Example: logistic regression posterior for coefficients

data(menarche, package = "MASS")

Age2 <- menarche$Age - 13
Menarche_Model_Data <- data.frame(
  Menarche  = menarche$Menarche,
  Total     = menarche$Total,
  Age2      = Age2
)

ps <- Prior_Setup(
  cbind(Menarche, Total - Menarche) ~ Age2,
  family = binomial(link = "logit"),
  data   = Menarche_Model_Data
)

fit_logit <- glmb(
  cbind(Menarche, Total - Menarche) ~ Age2,
  family  = binomial(link = "logit"),
  pfamily = dNormal(mu = ps$mu, Sigma = ps$Sigma),
  data    = Menarche_Model_Data,
  n             = 800,
  use_parallel  = FALSE
)

coef_draws <- as.data.frame(fit_logit$coefficients)

3. Point and interval summaries

bayestestR::describe_posterior(coef_draws)
#> Summary of Posterior Distribution
#> 
#> Parameter   |    Median |        95% CI |     pd |          ROPE | % in ROPE
#> ----------------------------------------------------------------------------
#> (Intercept) | -7.06e-03 | [-0.13, 0.11] | 54.62% | [-0.10, 0.10] |    95.00%
#> Age2        |      1.62 | [ 1.51, 1.73] |   100% | [-0.10, 0.10] |        0%
bayestestR::hdi(coef_draws, ci = 0.89)
#> Highest Density Interval
#> 
#> Parameter   |       89% HDI
#> ---------------------------
#> (Intercept) | [-0.10, 0.08]
#> Age2        | [ 1.54, 1.72]
bayestestR::rope(coef_draws, range = c(-0.02, 0.02))
#> # Proportion of samples inside the ROPE [-0.02, 0.02]:
#> 
#> Parameter   | Inside ROPE
#> -------------------------
#> (Intercept) |     24.74 %
#> Age2        |      0.00 %
bayestestR::p_direction(coef_draws)
#> Probability of Direction
#> 
#> Parameter   |     pd
#> --------------------
#> (Intercept) | 54.62%
#> Age2        |   100%

Tune rope(..., range = ...) to match substantive “practical equivalence” hypotheses on the logit scale (see also the binomial likelihood discussion in Chapter 09). For richer reporting pipelines (parameters, performance, …), see the easystats ecosystem linking out from ?bayestestR.

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Chapter 13: Bayesian inference and decision making with bayestestR

Kjell Nygren

1. Purpose

2. Example: logistic regression posterior for coefficients

3. Point and interval summaries

See also