Evidence of external validity based on individual score estimates is still relevant in many psychometric applications. From a model-based perspective, however, the topic appears to have been rather neglected in recent decades. Thus, in structural equation modelling (SEM), this evidence is sought to be obtained structurally, bypassing the scoring stage. And, in item response theory (IRT), the score interest mostly focuses on internal properties. Taking this state of affairs into account, this paper develops and proposes a model-based approach, intended for noncognitive measures, that combines SEM and IRT developments, and which allows a detailed assessment of the external validity of a class of score estimates to be carried out. The starting point is a general extended model that also includes the relevant external variables. From this general model, four well-known extended IRT models can be derived and fitted at the structural level. Next, on the basis of the structural results, a series of unconditional (population-dependent) and conditional (population-independent) indices that describe the model-implied relation between the score estimates and each external variable are developed and proposed. The practical relevance of the proposal is discussed mainly around three applications: assessing model appropriateness, obtaining point and interval prediction estimates at the individual level, and shortening a test while optimizing the external validity of the resulting version. The functioning of the proposal is illustrated using a real-data example.
Ferrando et al. (2026) studied this question.