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Post Info TOPIC: Multilevel Bayesian Models of Categorical Data Annotation
RobySul


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Multilevel Bayesian Models of Categorical Data Annotation
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  • Operating System: macOS Mojave 10.14.4
  • brms Version: 2.8.0

I have been reading the paper “Multilevel Bayesian Models of Categorical Data Annotation 20” by Bob Carpenter, and have been enjoying learning about Bayesian methods for modeling sets of categorizations by multiple raters.

In the paper, analysis of a dataset comprising of 5 rater’s classification of 3869 dental x-rays for the presence or absence of dental caries is provided. By googling around, I managed to source what I think is the dataset from the randomLCA package in R.

 
library(randomLCA)
#> Loading required package: lattice
data(dentistry)

 

In the paper, four modeling approaches are described:

  1. Binomial model fit (model 4.1), to estimate distributions for prevalence, sensitivity, and specificity
  2. Beta-Binomial by Annotator Fit (model 4.2), to estimate prevalence, sensitivity, and specificity by rater
  3. Beta-Binomial by Item Fit (model 4.3), to estimate prevalence, sensitivity, and specificity by item
  4. Logistic Fit (model 4.4), to estimate prevalence, sensitivity, and specificity by rater and item

I would be very grateful, for my learning, whether someone could demonstrate how models 4.1 to 4.4 might fit using brms.

 



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Anonymous

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Certainly, I'd be happy to help you with that!

To fit the four models described in the paper using brms, you can use the following code:

Model 4.1: Binomial model fit

library(brms)

# Define the formula for the model
formula_4.1 <- bf(y | trials(n) ~ 1)

# Fit the model using brms
fit_4.1 <- brm(
  formula_4.1, data = dentistry,
  family = binomial(),
  prior = c(set_prior("normal(0, 1)", class = "Intercept"))
)

Model 4.2: Beta-Binomial by Annotator Fit

# Define the formula for the model
formula_4.2 <- bf(y | trials(n) ~ 1 + (1 | annotator))

# Fit the model using brms
fit_4.2 <- brm(
  formula_4.2, data = dentistry,
  family = betabinomial(),
  prior = c(set_prior("normal(0, 1)", class = "Intercept")),
  control = list(adapt_delta = 0.99)
)

Model 4.3: Beta-Binomial by Item Fit

# Define the formula for the model
formula_4.3 <- bf(y | trials(n) ~ 1 + (1 | item))

# Fit the model using brms
fit_4.3 <- brm(
  formula_4.3, data = dentistry,
  family = betabinomial(),
  prior = c(set_prior("normal(0, 1)", class = "Intercept")),
  control = list(adapt_delta = 0.99)
)

Model 4.4: Logistic Fit

# Define the formula for the model
formula_4.4 <- bf(y | trials(n) ~ 1 + (1 | item) + (1 | annotator))

# Fit the model using brms
fit_4.4 <- brm(
  formula_4.4, data = dentistry,
  family = binomial(),
  prior = c(set_prior("normal(0, 1)", class = "Intercept")),
  control = list(adapt_delta = 0.99)
)

Note that for the Beta-Binomial models (4.2 and 4.3), we use the betabinomial() family function in brms. Also, we set adapt_delta = 0.99 in the control the argument to ensure good mixing of the MCMC algorithm and data annotation

I hope this helps you with your learning! Let me know if you have any further questions.

 

 

 

 

 



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