Bayesian Knowledge Tracing Model

Fitting, cross-validating, and predicting with Bayesian Knowledge Tracing (BKT) models. It is designed for analyzing educational datasets to trace student knowledge over time. The package includes functions for fitting BKT models, evaluating their performance using various metrics, and making predictions on new data. It provides functionality similar to the 'Python' package 'pyBKT' authored by Zachary A. Pardos ([email protected]) at < https://github.com/CAHLR/pyBKT>.

BKT: Bayesian Knowledge Tracing in R

BKT fits Bayesian Knowledge Tracing models to student response sequences. It supports model fitting, parameter inspection, prediction, evaluation, cross-validation, parameter fixing, and several BKT variants.

The package is based on the ideas implemented by pyBKT.

Installation

Install the development version from GitHub:

# install.packages("remotes")
remotes::install_github("Feng-Ji-Lab/bkt")

Then load the package:

library(BKT)

Included example data

The package includes simulation_data_50, a small simulated dataset containing 50 students and 494 response records:

data("simulation_data_50", package = "BKT")
head(simulation_data_50)

The required columns are:

• order_id: response order within a student sequence
• correct: 1 for a correct response and 0 for an incorrect response
• student_id: student identifier
• skill_name: skill identifier

BKT recognizes student_id automatically, so no column mapping is needed for the included simulation data.

Fit a model

Create and fit a model directly from the included data frame:

library(BKT)
data("simulation_data_50", package = "BKT")

model <- bkt(seed = 42, num_fits = 1, parallel = FALSE)
fitted_model <- fit(model, data = simulation_data_50)

params(fitted_model)

The returned parameter table contains the estimated learning, guessing, slipping, and prior probabilities for the mathematic skill.

Prediction and evaluation

Use a fitted model to generate response and knowledge-state probabilities:

predictions <- predict_bkt(fitted_model, data = simulation_data_50)
head(predictions)

The result contains the original data plus:

• correct_predictions: predicted probability of a correct response
• state_predictions: predicted probability associated with the latent knowledge state

The default evaluation metric is root mean squared error:

evaluate(fitted_model, data = simulation_data_50)

A custom metric can also be supplied:

mae <- function(true_vals, pred_vals) {
  mean(abs(true_vals - pred_vals))
}

evaluate(fitted_model, data = simulation_data_50, metric = mae)

Cross-validation

Run cross-validation without downloading an external dataset:

model <- bkt(seed = 42, num_fits = 1, parallel = FALSE)

cv_results <- crossvalidate(
  model,
  data = simulation_data_50,
  folds = 2,
  parallel = FALSE
)

cv_results

Forgetting model

Set forgets = TRUE when fitting to estimate a forgetting probability:

model <- bkt(seed = 42, num_fits = 1, parallel = FALSE)
fitted_with_forgetting <- fit(
  model,
  data = simulation_data_50,
  forgets = TRUE
)

params(fitted_with_forgetting)

Fix model parameters

Use set_coef() to initialize a parameter and fixed to keep it unchanged during fitting:

model <- bkt(seed = 42, num_fits = 1, parallel = FALSE)
model <- set_coef(
  model,
  list(mathematic = list(prior = 0.5))
)

fitted_fixed <- fit(
  model,
  data = simulation_data_50,
  skills = "mathematic",
  fixed = list(mathematic = list(prior = TRUE))
)

params(fitted_fixed)

Custom column names

For a data frame with different column names, provide a defaults mapping. This example renames the included simulation data in memory:

custom_data <- simulation_data_50
names(custom_data) <- c("sequence", "answer", "learner", "skill")

model <- bkt(
  seed = 42,
  num_fits = 1,
  parallel = FALSE,
  defaults = list(
    order_id = "sequence",
    correct = "answer",
    user_id = "learner",
    skill_name = "skill"
  )
)

fitted_custom <- fit(model, data = custom_data)
params(fitted_custom)

Alternatively, a CSV file can be supplied with data_path. In-memory data frames are preferable for reproducible examples because they do not require downloads or temporary files.

Model variants

The supported variants are enabled through fit():

• multilearn = TRUE: separate learning rates by learning resource
• multiprior = TRUE: separate prior probabilities by group
• multipair = TRUE: learning rates based on consecutive resource pairs
• multigs = TRUE: separate guess and slip rates by item

Variant data must contain the corresponding class column, supplied through defaults when its name differs from the variant argument. For example:

variant_data <- simulation_data_50
variant_data$item <- paste0("item_", variant_data$order_id %% 2 + 1)

model <- bkt(
  seed = 42,
  num_fits = 1,
  parallel = FALSE,
  defaults = list(multigs = "item")
)

fitted_multigs <- fit(
  model,
  data = variant_data,
  multigs = TRUE
)

params(fitted_multigs)

Simulate data

New BKT response sequences can be generated locally:

set.seed(42)

simulated_data <- simulate_bkt_data(
  prior = 0.2,
  guess = 0.1,
  slip = 0.1,
  learn = 0.3,
  num_students = 5,
  min_questions = 5,
  max_questions = 10
)

head(simulated_data)

The function returns a data frame by default. Use output_file only when a CSV file is explicitly needed.

License

BKT is licensed under the MIT License.