A Discrete Latent State Approach to Diagnostic Testing

The overriding goal of this project has been to develop a general framework for representation of item responses which can be used to represent data in applications such as mastery tests and other kinds of achievement tests, where there is reason to believe that current foundations are deficient. The strategy which the author originally proposed for pursuing this goal involved building a model for signed-number addition test data gathered by Tatsuoka and Birenbaum (1979). They have shown that this data cannot be represented by a unidimensional model because of a number of systematic error patterns exhibited by different subgroups of students. The immediate subgoals of the project have been to: 1) validate a finite latent state model which I developed to account for this data; and 2) extend this model to deal with change over time; and 3) develop optimal procedures based on the model for testing mastery of the signed-number addition concept. Keywords: Parameter invariance; Componental analysis.