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 = FALSE,
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
Epsilon adjustment for extreme person scores (default 0).
- bias_correction
Logical, simple post-hoc scaling of item betas.
- 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 = TRUE) - iterations: integer iterations used - converged: logical convergence indicator - bias_correction, centered: echoes of inputs - wle_estimate: numeric vector of WLE (if estimatewle = TRUE) or NA