Compute Modified Item Response Probabilities

Description

Compute Modified Item Response Probabilities

Usage

compute_Modified_probabilities(results, theta_all)

Arguments

Value

A numeric matrix of predicted probabilities with dimensions length(theta_all) rows by nrow(results) columns. Each cell contains the probability of a correct response for a given ability level and item, calculated using the logistic function: exp(\theta - \beta) / (1 + exp(\theta - \beta)), where \beta is the item threshold. Columns are named after the items.

Examples

set.seed(123)
sample_data <- matrix(sample(c(0, 1), 100, replace = TRUE), ncol = 10)
prepared <- prepare_data(sample_data)
irt_results <- fit_binary_irt(prepared$matrix, prepared$total_score)

abilities <- seq(0, 10, length.out = 5)

probs <- compute_Modified_probabilities(irt_results, abilities)

print(head(probs))

Extract Rasch Item Difficulties in Original Order

Description

Extract Rasch Item Difficulties in Original Order

Usage

extract_rasch_difficulties_ordered(final_logit_matrix)

Arguments

Value

A data frame containing the calculated difficulty parameters for each item, with the following columns:

• Item_Number: The sequential index of the item.

• Item_Name: The name or label of the item.

• Difficulty_Logit: The item difficulty parameter (beta) expressed on the logit scale, rounded to four decimal places. Higher values indicate more difficult items.

Examples

set.seed(123)
sample_data <- matrix(sample(c(0, 1), 100, replace = TRUE), ncol = 10)
colnames(sample_data) <- paste0("Q", 1:10)
prepared <- prepare_data(sample_data)
irt_results <- fit_binary_irt(prepared$matrix, prepared$total_score)
probs <- compute_Modified_probabilities(irt_results, prepared$total_score)
logits <- rasch_logit(probs)

difficulty_table <- extract_rasch_difficulties_ordered(logits)

print(difficulty_table)

Fit Binary IRT Model using GLM

Description

Fit Binary IRT Model using GLM

Usage

fit_binary_irt(data_mat, total_score)

Arguments

Value

A data frame with one row per item and the following columns:

• Item: The name of the item.

• Intercept: The estimated intercept parameter from the GLM logit model.

• Slope: The estimated slope parameter (discrimination) from the GLM logit model.

• threshold: The calculated item difficulty (also known as the beta parameter), computed as -Intercept / Slope. This represents the point on the ability scale where the probability of a correct response is 0.5.

Examples

set.seed(42)
sample_data <- matrix(sample(c(0, 1), 50, replace = TRUE), ncol = 5)
colnames(sample_data) <- paste0("Item", 1:5)

prepared <- prepare_data(sample_data)

irt_results <- fit_binary_irt(prepared$matrix, prepared$total_score)

print(irt_results)

Plot Item Characteristic Curves (ICC)

Description

Plot Item Characteristic Curves (ICC)

Usage

plot_item_curves(theta_all, Modified_prob_matrix, results)

Arguments

Value

No return value, called for side effects. It generates a series of plots showing the Item Characteristic Curves (ICC) for each item in the model.

Examples

set.seed(123)
sample_data <- matrix(sample(c(0, 1), 100, replace = TRUE), ncol = 10)
prepared <- prepare_data(sample_data)
irt_results <- fit_binary_irt(prepared$matrix, prepared$total_score)

theta_range <- seq(0, 10, length.out = 100)
probs <- compute_Modified_probabilities(irt_results, theta_range)

# Plot the curves
plot_item_curves(theta_range, probs, irt_results)

Plot Rasch Item Curves

Description

Plot Rasch Item Curves

Usage

plot_rasch_curves(prob_matrix, final_logit_matrix)

Arguments

Value

No return value, called for side effects. It generates a series of plots showing the Rasch Item Characteristic Curves (ICC) with difficulty indicators.

Examples

set.seed(123)
sample_data <- matrix(sample(c(0, 1), 100, replace = TRUE), ncol = 10)
prepared <- prepare_data(sample_data)
irt_results <- fit_binary_irt(prepared$matrix, prepared$total_score)
probs <- compute_Modified_probabilities(irt_results, prepared$total_score)
logits <- rasch_logit(probs)

# Plot the Rasch curves
plot_rasch_curves(probs, logits)

Prepare Data for IRT Analysis

Description

Prepare Data for IRT Analysis

Usage

prepare_data(data)

Arguments

Value

A list containing the following two components:

• matrix: A numeric matrix of the original data, converted to numeric format and potentially reordered by total score.

• total_score: A numeric vector representing the sum of correct responses (row sums) for each person, sorted in descending order if the original data was unsorted.

Examples

set.seed(123)
raw_data <- data.frame(
  item1 = c(1, 0, 1, 1),
  item2 = c(0, 0, 1, 1),
  item3 = c(1, 1, 1, 0)
)

prepared <- prepare_data(raw_data)

print(prepared$matrix)
print(prepared$total_score)

Compute Logit and Row Means

Description

Compute Logit and Row Means

Usage

rasch_logit(prob_matrix)

Arguments

Value

A numeric matrix of logit transformations (log-odds) with dimensions nrow(prob_matrix) rows by ncol(prob_matrix) + 1 columns. The first columns contain the logit values for each item, and the final column, named Row_Mean_Logit, contains the mean logit across all items for each person, which serves as an estimate of Student Ability.

Examples

set.seed(123)
sample_data <- matrix(sample(c(0, 1), 100, replace = TRUE), ncol = 10)
prepared <- prepare_data(sample_data)
irt_results <- fit_binary_irt(prepared$matrix, prepared$total_score)
probs <- compute_Modified_probabilities(irt_results, prepared$total_score)

logit_results <- rasch_logit(probs)

print(head(logit_results))

Run the GLM-Based Rasch Analysis Suite

Description

This function launches the interactive Shiny application for Rasch analysis using the GLM framework.

Usage

runGLMRaschSuite()

Value

This function launches the Shiny app and does not return a value.