Package 'BKT'

Bayesian Knowledge Tracing

Description

Create a BKT (Bayesian Knowledge Tracing) model object with initial parameters. This function constructs a BKT model by taking in various parameters such as parallelization options, number of fits, random seed, and other model-specific settings. These parameters can later be modified during the fitting or cross-validation process.

Usage

bkt(
  parallel = TRUE,
  num_fits = 5,
  folds = 5,
  seed = sample(1:1e+08, 1),
  model_type = rep(FALSE, 4),
  forgets = FALSE,
  fixed = NULL,
  defaults = NULL,
  ...
)

Arguments

parallel	Logical. Indicates whether to use parallel computation. If set to TRUE, multithreading will be used to speed up model training.
num_fits	Integer. Number of fit iterations. The best model is selected from the total iterations.
folds	Integer. Number of folds used for cross-validation. This parameter is used during cross-validation to divide the data into parts.
seed	Numeric. Seed for the random number generator, which ensures reproducibility of results.
model_type	Logical vector. Specifies model variants to use. There are four possible variants: 'multilearn', 'multiprior', 'multipair', and 'multigs'. Each corresponds to a different modeling strategy.
forgets	Logical. Whether to include a forgetting factor in the model. If set to TRUE, the model will account for the possibility that learners may forget knowledge.
fixed	List. A nested list specifying which parameters to fix for specific skills during model fitting. Each skill can have certain parameters, such as "guesses" and "slips", set to TRUE (to fix) or FALSE (to let them vary). For example: list("skill_name" = list("guesses" = TRUE, "slips" = TRUE)).
defaults	List. The defaults parameter is a list that functions as a query dictionary. It is used to map column names in the data to the expected variables in the model. This helps ensure that the model can work with different datasets that may have varying column names.
...	Other parameters.

Value

A BKT model object, which can be used by other functions such as fitting the model, cross-validation, or making predictions.

Examples

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

---

Cross Validation

Description

Perform cross-validation on a BKT (Bayesian Knowledge Tracing) model. This function trains and evaluates the BKT model using cross-validation. It splits the dataset into training and validation sets, trains the model on the training data, and evaluates it on the validation data according to a specified metric.

Usage

crossvalidate(
  object,
  data = NULL,
  data_path = NULL,
  metric = rmse,
  parallel = FALSE,
  seed = NULL,
  num_fits = 1,
  folds = 5,
  forgets = FALSE,
  fixed = NULL,
  model_type = NULL,
  ...
)

Arguments

object	A BKT model object. The model to be cross-validated.
data	Data frame. The dataset to be used for cross-validation. If data is not provided, data_path should be used to load the dataset from a file.
data_path	Character. The file path to the dataset. This will be used if data is not provided.
metric	Function. The metric function used to evaluate model performance.
parallel	Logical. Indicates whether to use parallel computation. If set to TRUE, multithreading will be used to speed up model training.
seed	Numeric. Seed for the random number generator, which ensures reproducibility of results.
num_fits	Integer. Number of fit iterations. The best model is selected from the total iterations.
folds	Integer. Number of folds used for cross-validation. This parameter is used during cross-validation to divide the data into parts.
forgets	Logical. Whether to include a forgetting factor in the model. If set to TRUE, the model will account for the possibility that learners may forget knowledge.
fixed	List. A nested list specifying which parameters to fix for specific skills during model fitting. Each skill can have certain parameters, such as "guesses" and "slips", set to TRUE (to fix) or FALSE (to let them vary). For example: list("skill_name" = list("guesses" = TRUE, "slips" = TRUE)).
model_type	Logical vector. Specifies model variants to use. There are four possible variants: 'multilearn', 'multiprior', 'multipair', and 'multigs'. Each corresponds to a different modeling strategy.
...	Other parameters.

Value

A list containing the cross-validation results, including the average performance metric and any other relevant details from the validation process.

Examples

data("simulation_data_50", package = "BKT")
model <- bkt(seed = 42, parallel = FALSE, num_fits = 1)
cv_results <- crossvalidate(model, data = simulation_data_50, folds = 2)
print(cv_results)

---

Evaluate

Description

Evaluate a BKT (Bayesian Knowledge Tracing) model using a specified metric. This function evaluates a fitted BKT model on a given dataset using a chosen performance metric. It takes either a data frame or a file path to the data and returns the evaluation result based on the specified metric (e.g., RMSE or accuracy).

Usage

evaluate(object, data = NULL, data_path = NULL, metric = rmse)

Arguments

object	A fitted BKT model object. This is the model to be evaluated.
data	Data frame. The dataset on which the model will be evaluated. If data is not provided, the function will attempt to load the dataset from the file specified by data_path.
data_path	Character. The file path to the dataset for evaluation. This will be used if data is not provided.
metric	Function or Function List. The evaluation metric used to assess the model performance. (Root Mean Square Error), but other metrics can also be specified.

Value

Numeric or List. The result of the evaluation based on the specified metric(s). For example, if rmse is used, the function will return the root mean square error for the model on the dataset.

Examples

data("simulation_data_50", package = "BKT")
model <- bkt(seed = 42, parallel = FALSE, num_fits = 1)
result <- fit(model, data = simulation_data_50)
eval_result <- evaluate(result, data = simulation_data_50)
print(eval_result)

---

Fetch a dataset

Description

Fetch a dataset from an online source. This function downloads a dataset from a provided URL and saves it to a specified location on the local system. The dataset must be publicly accessible, without requiring any password or authentication. It can then be used for further analysis or modeling.

Usage

fetch_dataset(object, link, loc)

Arguments

object	A BKT model object. The model can use the fetched dataset for fitting or other tasks.
link	Character. The URL where the dataset is located. This must be a publicly accessible URL.
loc	Character. The local file path where the dataset will be saved. The dataset will be stored at this location after download.

Value

None. The function downloads the data file to the specified location.

Examples

## Not run: 
model <- bkt()
fetch_dataset(model, "https://example.com/dataset.csv", tempdir())

## End(Not run)

---

fit bkt model

Description

Fit a BKT (Bayesian Knowledge Tracing) model. This function fits the BKT model using the provided data and various options, such as skill filtering, forget model, and parallelization. The function uses the model object created by bkt() and fits the data according to the specified parameters.

Usage

fit(
  object,
  data_path = NULL,
  data = NULL,
  parallel = FALSE,
  seed = NULL,
  num_fits = 1,
  forgets = FALSE,
  fixed = NULL,
  model_type = NULL,
  ...
)

Arguments

object	A BKT model object. The model to be cross-validated.
data_path	Character. The file path to the dataset. This will be used if data is not provided.
data	Data frame. The dataset to be used for cross-validation. If data is not provided, data_path should be used to load the dataset from a file.
parallel	Logical. Indicates whether to use parallel computation. If set to TRUE, multithreading will be used to speed up model training.
seed	Numeric. Seed for the random number generator, which ensures reproducibility of results.
num_fits	Integer. Number of fit iterations. The best model is selected from the total iterations.
forgets	Logical. Whether to include a forgetting factor in the model. If set to TRUE, the model will account for the possibility that learners may forget knowledge.
fixed	List. A nested list specifying which parameters to fix for specific skills during model fitting. Each skill can have certain parameters, such as "guesses" and "slips", set to TRUE (to fix) or FALSE (to let them vary). For example: list("skill_name" = list("guesses" = TRUE, "slips" = TRUE)).
model_type	Logical vector. Specifies model variants to use. There are four possible variants: 'multilearn', 'multiprior', 'multipair', and 'multigs'. Each corresponds to a different modeling strategy.
...	Other parameters.

Value

A fitted BKT model object, which can be used for predictions, cross-validation, or parameter analysis.

Examples

data("simulation_data_50", package = "BKT")
model <- bkt(seed = 42, parallel = FALSE, num_fits = 1)
result <- fit(
  model,
  data = simulation_data_50
)

---

Load

Description

Load a BKT model from a file. This function loads a previously saved BKT model from an RDS file. The model attributes are restored into the provided model object, allowing it to be used for further analysis or predictions.

Usage

load_model(model, loc)

Arguments

model	A BKT model object into which the saved model's attributes will be loaded.
loc	Character. The file path from which the model will be loaded, typically an .rds file.

Value

The updated BKT model object with the restored attributes from the saved model.

Examples

data("simulation_data_50", package = "BKT")
model <- bkt(seed = 42, parallel = FALSE, num_fits = 1)
fitted_model <- fit(model, data = simulation_data_50)
model_file <- tempfile(fileext = ".rds")
save_model(fitted_model, model_file)
loaded_model <- load_model(bkt(), model_file)
unlink(model_file)

---

Extract Parameters from BKT model

Description

Extract fitted parameters from a BKT model. This function retrieves the parameters from a fitted BKT model object. The parameters include model-specific values such as "learns", "guesses", "slips", and "forgets". These parameters are returned in a format that is easy to print or manipulate for further analysis.

Usage

params(object)

Arguments

object

A fitted BKT model object. The model should have been previously fitted using the fit() function, otherwise no parameters will be available.

Value

A data frame containing the fitted model parameters. The data frame will typically include columns such as 'learns', 'guesses', 'slips', and other model-specific values.

Examples

data("simulation_data_50", package = "BKT")
model <- bkt(seed = 42, parallel = FALSE, num_fits = 1)
result <- fit(model, data = simulation_data_50)
params_df <- params(result)
print(params_df)

---

Predict

Description

Predict outcomes using a fitted BKT model. This function uses a trained Bayesian Knowledge Tracing (BKT) model to make predictions on new data. The predictions include both the likelihood of a correct response (correct_predictions) and the estimated hidden state of the learner's knowledge (state_predictions).

Usage

predict_bkt(model, data_path = NULL, data = NULL)

Arguments

model	A trained BKT model object. The model must have been previously fitted using the fit() function. If the model is not fitted, an error will be raised.
data_path	Character. The file path to the dataset on which predictions will be made. If this is provided, the function will read data from the file.
data	Data frame. A pre-loaded dataset to be used for predictions. This can be used instead of specifying data_path.

Value

A data frame containing the original data with two additional columns: correct_predictions and state_predictions.

Examples

data("simulation_data_50", package = "BKT")
model <- bkt(seed = 42, parallel = FALSE, num_fits = 1)
fit_model <- fit(model, data = simulation_data_50)
predictions <- predict_bkt(fit_model, data = simulation_data_50)
head(predictions)

---

Save

Description

Save a BKT model to a file. This function saves a trained BKT model to a specified file location. The model is stored as an RDS file, which can be loaded back into R using the load_model() function.

Usage

save_model(model, loc)

Arguments

model	A trained BKT model object to be saved.
loc	Character. The file path where the model will be saved, typically with an .rds extension.

Value

None. The function saves the model to the specified location.

Examples

data("simulation_data_50", package = "BKT")
model <- bkt(seed = 42, parallel = FALSE, num_fits = 1)
fit_model <- fit(model, data = simulation_data_50)
model_file <- tempfile(fileext = ".rds")
save_model(fit_model, model_file)
unlink(model_file)

---

Set Coefficients for BKT Model

Description

This function sets or initializes the parameters of a Bayesian Knowledge Tracing (BKT) model. The user can manually specify the values for different parameters associated with specific skills.

Usage

set_coef(object, values)

Arguments

object	An object of the BKT model. This is the model for which the parameters will be set or initialized.
values	A list containing the skill names and their corresponding BKT parameters. Each skill should have its own list of parameters. The parameters can include 'prior', 'learns', 'forgets', 'guesses', and 'slips'. Example structure: list("skill_name" = list("learns" = ..., "guesses" = ...)).

Details

This function allows users to manually specify or update the parameters of a BKT model for different skills. The values should be provided as a named list, with each skill having its own sublist of BKT parameters. The function performs checks to ensure that the provided parameters are valid in terms of type, length, and existence.

Value

The updated BKT model object with the newly set coefficients.

Examples

data("simulation_data_50", package = "BKT")
# Initialize a BKT model
model <- bkt(seed = 42, parallel = FALSE, num_fits = 1)

# Set custom parameters for a specific skill
model <- set_coef(model, list(
  "mathematic" = list("prior" = 0.5, "learns" = 0.2)
))

# Fit the model with fixed parameters
result <- fit(model,
  forgets = TRUE,
  data = simulation_data_50,
  skills = "mathematic",
  fixed = list("mathematic" = list("prior" = TRUE))
)

---

Simulate Data from a Bayesian Knowledge Tracing (BKT) Model

Description

This function generates simulated student response data based on the BKT model. Each student is modeled as having a latent skill mastery state that can evolve over a sequence of activities according to specified learning, guessing, and slipping probabilities. The generated dataset can be used for testing, model evaluation, or demonstration purposes.

Usage

simulate_bkt_data(
  prior,
  guess,
  slip,
  learn,
  num_students,
  min_questions,
  max_questions,
  output_file = NULL
)

Arguments

prior	Numeric. Initial probability that a student has mastered the skill before any questions. Corresponds to the BKT parameter \(P_p\).
guess	Numeric. Probability that a student answers correctly despite not mastering the skill. Corresponds to the BKT parameter \(P_g\).
slip	Numeric. Probability that a student answers incorrectly despite mastering the skill. Corresponds to the BKT parameter \(P_s\).
learn	Numeric. Probability that a student transitions from the unmastered to mastered state after each activity. Corresponds to the BKT parameter \(P_l\).
num_students	Integer. Number of students to simulate.
min_questions	Integer. Minimum number of questions (activities) per student.
max_questions	Integer. Maximum number of questions (activities) per student. Each student's actual sequence length is randomly drawn from 1 to max_questions.
output_file	Character. Optional file path. If provided, the generated dataset will be written to a CSV file.

Details

The simulated responses follow the standard BKT transition logic:

$P(K_{t+1} = 1) = P(K_t = 1) + (1 - P(K_t = 1)) \times P_l$

and the observed correctness is drawn as:

$P(C_t = 1) = P(K_t = 1)(1 - P_s) + (1 - P(K_t = 1))P_g.$

Value

A data frame with the following columns:

• order_id: Integer, the order of the question within a student's sequence.

• correct: Binary (0/1), indicating whether the student answered correctly.

• student_id: Integer, the unique identifier for each student.

• skill_name: Character, the skill associated with the responses (currently fixed as "mathematic").

Examples

prior <- 0.2
guess <- 0.1
slip <- 0.1
learn <- 0.3
num_students <- 5
min_questions <- 5
max_questions <- 10

simulated_data <- simulate_bkt_data(
    prior = prior,
    guess = guess,
    slip = slip,
    learn = learn,
    num_students = num_students,
    min_questions = min_questions,
    max_questions = max_questions
)
head(simulated_data)

---

Simulated dataset with 2000 students

Description

Simulated dataset with 2000 students

Usage

simulation_data_2000

Format

An object of class data.frame with 19987 rows and 4 columns.

---

Simulated dataset

Description

A simulated BKT dataset containing 50 students with maximum sequence length of 10.

Usage

simulation_data_50

Format

A data frame with 50 students:

student_id

Student ID

skill_name

Skill name

order_id

response ID

correct

Binary outcome (0/1)

Source

Simulated using RBKT simulation functions.

---

Simulated dataset with 500 students

Description

Simulated dataset with 500 students

Usage

simulation_data_500

Format

An object of class data.frame with 5020 rows and 4 columns.

---