Building out a measurement model to incorporate complexities of testing in the language domain

This paper provides a summary of a novel and integrated way to think about the item response models (most often used in measurement applications in social science areas such as psychology, education, and especially testing of various kinds) from the viewpoint of the statistical theory of generalized linear and nonlinear mixed models. In addition, this new approach emphasizes how item response models can be coordinated and broadened to emphasize their explanatory uses beyond their standard descriptive uses. The basic explanatory principle is that item responses can be modeled as a function of qualities and features of various measurement contexts. These qualities and features can be: (a) characteristics of (i) items, (ii) persons, and (iii) combinations of items and persons; (b) observed or latent (of either items or persons); and (c) continuous or categorical. These ideas are exemplified in the context of a reading comprehension test. The paper starts with an introduction to the framework and then provides: (a) a description of the data that will be used to illustrate the new framework; (b) a discussion of data structure; (c) a brief description of the statistical approach we used; (d) a discussion of how the framework helps one to conceptualize existing item response models, linking the formal features of the models to substantive issues in the assessment of reading comprehension, as well as incorporating an example that goes beyond the usual range of item response models; and (e) a brief summary of further expansion.