Two-Level Nonparametric Scaling for Dichotomous Data
This chapter considers a two-level design where the objects to be scaled are the higher-level units. Nested within each object are lowerlevel units, called subjects, and a set of dichotomous items is administered to each subject. The subjects are regarded as strictly parallel tests for the objects. Examples are the scaling of teachers on the basis of their pupils’ responses, or of neighborhoods on the basis of responses by inhabitants. A two-level version of the nonparametric scaling method first proposed by (1971) is elaborated upon. The probabilities of positive responses to the items are assumed to be increasing functions of the value on a latent trait. The latent trait value for each subject is composed of an objectdependent value and a subject-dependent deviation from this value. The consistency of responses within, but also between objects is expressed by two-level versions of Loevinger’s H -coefficients. The availability of parallel tests is used to calculate a reliability coefficient.
KeywordsCovariance Stein Heroin Meijer
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