# Binary (Dichotomous) Item Response Theory Estimation Estimates item and person parameters for binary item response models using either Marginal Maximum Likelihood or Joint Maximum Likelihood. ```r binary_irt(data, model = "2PL", method = "EM", control = list()) ``` ## Arguments - `data`: A N x J data.frame of dichotomous responses (0/1). - `model`: String. "Rasch", "2PL" (2-Parameter Logistic), or "3PL" (3-Parameter Logistic). - `method`: String. "EM" (Marginal Maximum Likelihood via Expectation-Maximization) or "MLE" (Joint Maximum Likelihood). - `control`: A `list` of control parameters for the estimation algorithm: * `max_iter`: Maximum number of EM iterations (default = 100). * `converge_tol`: Convergence criterion for parameter change (default = 1e-4). * `theta_range`: Numeric vector of length 2 specifying the integration grid bounds (default = c(-4, 4)). * `quad_points`: Number of quadrature points (default = 21). * `verbose`: Logical; if `TRUE`, prints progress to console. ## Returns A list containing: * `item_params`: A data frame of estimated item parameters (discrimination, difficulty, guessing) and their standard errors. * `person_params`: A data frame of estimated person abilities (theta) and standard errors. * `model_fit`: A data frame containing fit statistics such as Akaike’s Information Criterion (AIC), the Bayesian Information Criterion (BIC), and Log-Likelihood. * `settings`: A list of control parameters used in the estimation. ## Examples ```r # # Simulate data set.seed(123) N <- 500; J <- 10 true_theta <- rnorm(N) true_b <- seq(-2, 2, length.out=J) true_a <- runif(J, 0.8, 1.2) data_mat <- matrix(NA, N, J) for(i in 1:N) { p <- 1 / (1 + exp(-true_a * (true_theta[i] - true_b))) data_mat[i,] <- rbinom(J, 1, p) } df <- as.data.frame(data_mat) names(df) <- paste0("Q", 1:J) # # Run Function res <- binary_irt(df, model="2PL", method="EM") # View Results head(res$item_params) head(res$person_params) print(res$model_fit) # --- Example 2: With Package Data --- data("ela1", package = "tirt") # Subset the first 30 columns (must use the object name 'data_binary') df <- ela1[, 1:30] # Run Function on package data real_res <- binary_irt(df, model="2PL", method="EM") head(real_res$item_params) ```

binary_irt function