Journal ArticleDOI
A probabilistic formulation and statistical analysis of guttman scaling
Reads0
Chats0
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
More filters
Journal ArticleDOI
Psychometric Considerations in the Analysis of Reading Skill Hierarchies.
Larry H. Ludlow,George Hillocks +1 more
TL;DR: In this article, the psychometric models of Rasch and Guttman are used to illustrate contrasting yet complementary approaches to investigating hierarchical structures of reading skills, and specific results from the Rasch model underscore its greater potential as a reading skills diagnostic techique.
Journal ArticleDOI
Clifford collier clogg, 1949-1995: a tribute to his life and work
TL;DR: Clifford Collier Clogg as mentioned in this paper reviewed his scholarly contributions to the social sciences and statistics and extended some of his work on model comparisons, focusing on issues of standardization and population undercount.
Journal ArticleDOI
Empirical Examination of a Learning Hierarchy Using an Item Response Theory Model
TL;DR: In this paper, the use of several measurement models for the analysis of data arising from learning hierarchies is discussed, and the results of an empirical investigation of the application of an item response theory (IRT) model to a learning hierarchy in subtraction are examined.
Journal ArticleDOI
Latent Class Analysis of Respondent Scalability
TL;DR: In this paper, the authors examined seven latent class models for a cumulative scale and performed a simulation study to study the efficacy of different models for data that follow the scale model perfectly.
Journal ArticleDOI
A comparison of model selection indices for nested latent class models
TL;DR: In this article, the authors compared the performance of chi-squared statistics with three information criteria, Akaike's AIC, Schwarz's BIC and Bozdogan's CAIC.
References
More filters
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.