convert_d_to_b: Convert Mirt's d Parameter to IRT Difficulty b

In irtsim: Monte Carlo Simulation-Based Sample-Size Planning for Item Response Theory

Convert Mirt's d Parameter to IRT Difficulty b

Description

Applies the delta method to convert d (intercept) to b (difficulty) under the 2PL/GRM parameterization: b = -d / a. Propagates standard errors and confidence intervals correctly.

Usage

convert_d_to_b(a_info, d_info)

Arguments

a_info	A list with elements est, se, ci_lower, ci_upper for the discrimination parameter a. Typically from extract_one_param().
d_info	A list with elements est, se, ci_lower, ci_upper for the intercept parameter d. Typically from extract_one_param().

Details

The delta method variance for b = -d/a is:

\text{Var}(b) = \frac{\text{Var}(d)}{a^2} + \frac{d^2 \text{Var}(a)}{a^4}

CI bounds are transformed directly: b_ci = -d_ci / a.

Value

A list with elements est, se, ci_lower, ci_upper for the converted difficulty parameter b, using delta method variance propagation.

irtsim documentation built on April 24, 2026, 1:07 a.m.