Bayesian Linear Models

Bayesian Linear Models
04 - Binary outcomes
Stefano Coretta
University of Edinburgh
2023/07/07
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The MALD data: Accuracy

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Binary outcomes

rt_bm_5 <- brm(
  ACC ~ IsWord,
  data = mald,
  family = "bernoulli",
  backend = "cmdstanr",
  cores = 4,
  file = "./data/cache/rt_bm_5",
  seed = my_seed
)

Bernoulli is the family of probability distributions used for binary variables.

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Binary outcomes

## Population-Level Effects: 
##             Estimate Est.Error l-89% CI u-89% CI Rhat Bulk_ESS Tail_ESS
## Intercept      -2.24      0.09    -2.38    -2.11 1.00     2604     2534
## IsWordFALSE     0.43      0.11     0.25     0.61 1.00     3484     2713

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Binary outcomes

## Population-Level Effects: 
##             Estimate Est.Error l-89% CI u-89% CI Rhat Bulk_ESS Tail_ESS
## Intercept      -2.24      0.09    -2.38    -2.11 1.00     2604     2534
## IsWordFALSE     0.43      0.11     0.25     0.61 1.00     3484     2713

What are those numbers?!

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Binary outcomes

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Binary outcomes

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Binary outcomes

## Population-Level Effects: 
##             Estimate Est.Error l-89% CI u-89% CI Rhat Bulk_ESS Tail_ESS
## Intercept      -2.24      0.09    -2.38    -2.11 1.00     2604     2534
## IsWordFALSE     0.43      0.11     0.25     0.61 1.00     3484     2713

round(plogis(-2.24), 2)

## [1] 0.1

round(plogis(-2.24 + 0.43), 2)

## [1] 0.14

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