An Application of Latent Class Models to Assessment Data

Abstract

Responses of 17-year-olds to selected 1977-78 Na tional Assessment of Educational Progress (NAEP) mathematics exercises were analyzed, using latent class models. A single model was fitted to data from five independent samples of examinees, each of which responded to a different set of six algebra or prealge bra exercises. Four categories of items were found, defining five levels of content mastery, ranging from examinees unable to solve any of the exercises (43%) through those able to solve all the exercises (19%). The methods demonstrated are broadly applicable to assessment data, including matrix-sampled data, and provide an aggregate description of examinee abilities independent of the specific characteristics of individual exercises administered.

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