Guttman scale analysis may be considered as two inseparable endeavors: (1) to ascertain if a set of stimu!'i are unidimensional in nature and if so, (2) to tank order respondents along the same continuum based on their reaction to toe stimuli. For example, suppose a set of four attitude statements (S1-54) are constructed such that similarity of content exists (e.g. all concern attitude toward i...

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A comparison is made among four different optimization strategies for the linear unidimensional scaling task in the L2-norm: (1) dynamic programming; (2) an iterative quadratic assignment improvement heuristic; (3) the Guttman update strategy as modified by Pliner’s technique of smoothing; (4) a nonlinear programming reformulation by Lau, Leung, and Tse. The methods are all implemented through ...

We consider the covariance matrix for dichotomous Guttman items under a set of uniformity conditions, and obtain closed-form expressions for the eigenvalues and eigenvectors of the matrix. In particular, we describe the eigenvalues and eigenvectors of the matrix in terms of trigonometric functions of the number of items. Our results parallel those of Zwick (1987) for the correlation matrix unde...

Louis (Eliyahu) Gut tman, Scientific Director of The Israel Institute of Applied Social Research (IIASR) and Professor of Social and Psychological Assessment at The Hebrew University of Jerusalem, was born in Brooklyn, New York, on February 10, 1916, and died in Minneapolis, Minnesota, on October 25, 1987, while on a visit to the United States to deliver lectures and to get medical treatment. H...

This paper describes a method of explorative data analysis which allows to detect logical implications between items of a dichotomous questionnaire or test. These logical dependencies are organized to form a hierarchical structure (quasi-order) on the items. Our analysis method, which is called Inductive Item Tree Analysis, can be seen as a method of Boolean analysis. We discuss the relation of...

We give a historical introduction to item response theory, which places the work of Thurstone, Lord, Guttman and Coombs in a present-day perspective. The general assumptions of modern item response theory, local independence and monotonicity of response functions, are discussed, followed by a general framework for estimating item response models. Six classes of well-known item response models a...