Latent structure analysis of the Test of English as a Foreign Language

Equating studies support the use of IRT methods for TOEFL equating, but there remains a discrepancy between IRT assumptions and diversity of the population served. The model assumes that a single latent proficiency variable underlies item performance, but the TOEFL candidate population is diverse, perhaps containing many groups with separate latent variables. This study attempted to identify such groups.

The basic and very suprising outcome of this study was that a single factor accurately accounted for the proportions of joint item successes; proportions of joint item success were proportional to the products of item difficulties. These results indicate that latent group effects are small. The search for groups included assessing the relative importance of two factors in accounting for examinees' item successes, but the balance of importance of the two factors was rather smoothly distributed, with much overlap between different national origins, and between different language backgrounds. Neither of these variables accounted for more than 25% of the variation of importance of the factors.

The present study supports equating with item response theory and suggests the use of a restrictive assumption of proportionality of item response curves. This single parameter model (not Rasch) could lead to simplified statistical procedures.