Journal ArticleDOI
A probabilistic formulation and statistical analysis of guttman scaling
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TLDR
In this paper, the latent or true nature of subjects is identified with a limited number of response patterns (the Guttman scale patterns), and the probability of an observed response pattern can be written as the sum of products of the true type multiplied by the chance of sufficient response error to cause the observed pattern to appear.Abstract:
By proposing that the latent or true nature of subjects is identified with a limited number of response patterns (the Guttman scale patterns), the probability of an observed response pattern can be written as the sum of products of the probability of the true type multiplied by the chance of sufficient response error to cause the observed pattern to appear. This model contains the proportions of the true types as parameters plus some misclassification probabilities as parameters. Maximum likelihood methods are used to make estimates and test the fit for some examples.read more
Citations
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The Validation of Learning Hierarchies.
TL;DR: A review was made of the various procedures for sequencing instructional units in individualized instruction programs and recommendation were made concerning the direction future research should follow, with a focus on improving model-based procedures.
Journal ArticleDOI
Alam and Alas: Questioning Error Assignments in Unidimensional Guttman Scaling:
TL;DR: In this article, an alternative to the traditional minimizing error rule is suggested through ALAM and ALAS criteria which use ordinal information in scalable item marginals, which is used in the Guttman scalogram error assignment.
Journal ArticleDOI
On latent distance analysis and the mle algorithm
Nobuoki Eshima,Chooichiro Asano +1 more
TL;DR: An algorithm is proposed, which does not give any improper solution, after transforming the latent response parameters to the logistic form and applying the new MLE procedure, which depends on the EM algorithm.
Journal ArticleDOI
Measuring Mental Abilities with Latent State Models
TL;DR: This paper reviewed the latent state models which have been proposed for measuring aptitude and achievement, and outlined the measurement problems that can now be solved with latent state model, and discussed how latent state and latent trait models are related.
References
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Book
Linear statistical inference and its applications
TL;DR: Algebra of Vectors and Matrices, Probability Theory, Tools and Techniques, and Continuous Probability Models.
Journal ArticleDOI
Linear Statistical Inference and its Applications
P. G. Moore,C. Radhakrishna Rao +1 more
TL;DR: The theory of least squares and analysis of variance has been studied in the literature for a long time, see as mentioned in this paper for a review of some of the most relevant works. But the main focus of this paper is on the analysis of variance.
Journal ArticleDOI
The approximation of one matrix by another of lower rank
Carl Eckart,Gale Young +1 more
TL;DR: In this paper, the problem of approximating one matrix by another of lower rank is formulated as a least-squares problem, and the normal equations cannot be immediately written down, since the elements of the approximate matrix are not independent of one another.