Unlike Classical Test Theory, IRT models the probability of a specific response as a function of the underlying latent trait ($\theta$). The 2PL model incorporates item difficulty ($b$) and item discrimination ($a$). The probability of a correct response is given by: $$P(X = 1 | \theta, b, a) = \frac{e^{a(\theta - b)}}{1 + e^{a(\theta - b)}}$$

Before comparing latent means across groups, one must establish measurement invariance. This typically proceeds in a hierarchical sequence: configural invariance (same factor structure), metric invariance (equal factor loadings), and scalar invariance (equal item intercepts).