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Fit Rasch model by JML with optional WLE

Source: R/jmle_estimation.r
jmle_estimation.Rd

Fits the Rasch (1PL) model using joint maximum likelihood via an efficient C++ Newton-Raphson implementation. Missing responses (NA) are allowed. Optional epsilon adjustment helps avoid biased estimates due to extreme-score degeneracy, and centering ensures identifiability. Optionally returns Warm's WLE person estimates computed with the estimated item difficulties.

Usage

jmle_estimation(
  X,
  max_iter = 1000,
  conv = 1e-06,
  eps = 0,
  bias_correction = c("none", "simple", "analytic"),
  center = "items",
  max_update = 1.5,
  verbose = FALSE,
  estimatewle = FALSE,
  wle_adj = 1e-08
)

Arguments

X

Numeric matrix of responses (0/1) with possible NA for missing.

max_iter

Maximum NR iterations in C++ (default 1000).

conv

Convergence threshold on maximum absolute parameter change.

eps

Small positive value used to adjust extreme person scores. When eps = 0 (default), persons with all 0 or all 1 responses are excluded from the iterative JMLE updates and assigned -Inf / +Inf afterward. When eps > 0, no deletion is performed and extreme scores are regularized internally.

bias_correction

Character, one of "none", "simple", or "analytic". "none": no bias correction; "simple": fast finite-sample scaling of item difficulties by factor (I - 1) / I; "analytic": post-hoc first-order analytical bias correction using biasCorrection().

center

either "items" or "persons"; enforce mean(beta)=0 or mean(theta)=0.

max_update

Step-size clip per update to stabilize NR (default 1.5).

verbose

Logical, periodic progress from C++ (every 10 iters).

estimatewle

Logical, compute Warm's WLE per person using estimated beta.

wle_adj

Small adjustment to avoid extreme raw scores in WLE (default 1e-8).

Value

A list with components: - theta: numeric vector of person parameters - beta: numeric vector of item difficulties (mean 0 if center = "items") - iterations: integer iterations used - converged: logical convergence indicator - bias_correction_mode: selected bias correction mode - center: centering used ("items" or "persons") - wle_estimate: numeric vector of WLE (if estimatewle = TRUE) or NA - se_theta, se_beta: approximate JMLE-based standard errors (if implemented) - theta_analytic, beta_analytic: analytically bias-corrected parameters if bias_correction = "analytic", otherwise NULL