Journal ArticleDOI
A probabilistic formulation and statistical analysis of guttman scaling
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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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Journal ArticleDOI
Model Selection Information Criteria for Non-Nested Latent Class Models
TL;DR: This article investigated the use of three model selection information criteria—Akaike AIC, Schwarz SIC, and Bozdogan CAIC—for non-nested models and found that SIC and CAIC were superior to AIC for relatively simple models, whereas AIC was superior for more complex models, although accuracy was often quite low for such models.
Journal ArticleDOI
A New Model for Scaling Response Patterns: An Application of the Quasi-Independence Concept
TL;DR: This model, using methods already developed for the study of quasi-independence in contingency tables, is shown how to test whether the model fits the observed data, estimate the proportion of intrinsically scalable (and unscalable) individuals, and estimate the distribution of the intrinsically scalable individuals among the d different scale types.
Journal ArticleDOI
Self-help interventions for smoking cessation.
TL;DR: Self-help interventions for smoking cessation are an important bridge between the clinical and public health approaches to smoking cessation, with lower quit rates for self-help programs that are likely due to differences in program adherence.
Journal ArticleDOI
Latent class analysis in medical research.
Anton K. Formann,Thomas Kohlmann +1 more
TL;DR: Different variants of latent class analysis (LCA) for dichotomous data are described in the following: the basic (unconstrained) model, models with parameters fixed to given values and with equality constraints on parameters, multigroup LCA including mixed-group vali dation, and linear logistic LCAincluding its relationship to the Rasch model and to the measurement of change in latent subgroups.
An Ordering-Theoretic Method to Determine Hierarchies Among Items. Research Report #23.
William M. Bart,David J. Krus +1 more
TL;DR: Ordering theory shares with classical models the item response matrix, but does not use summation across subject rows to express in the form of the correct responses of a subject his standing on the trait measured.
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.