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
Structural Latent Class Models
Anton K. Formann,Thomas Kohlmann +1 more
TL;DR: The linear logistic latent class analysis (LCA) model as mentioned in this paper relates the item latent probabilities of LCA to basic parameters representing the effects of explanatory variables, such as cognitive operations needed to solve the items.
Journal ArticleDOI
Algebraic Representations of Beliefs and Attitudes Ii: Microbelief Models For Dichotomous Belief Data
John Levi Martin,James Wiley +1 more
TL;DR: This paper demonstrates that an algebraic inversion of a data matrix, first used in test theory by Haertel and Wiley (1993), can be seen as a unique and interpretable decomposition that can recover information regarding the compositional formulas of the measured beliefs as well as the logical relations between the unobserved components.
Book ChapterDOI
A Latent Class Covariate Model with Applications to Criterion-Referenced Testing
TL;DR: For example, this article developed a more general model in which latent class membership is functionally related to one or more categorical and/or continuous concomitant variables (see Dayton & Macready, 1980b for a restricted model of this type).
Journal ArticleDOI
Identifiability in probabilistic knowledge structures
TL;DR: In this article, the authors characterised local identifiability of the Basic Local Independence Model (BLIM) through the rank of its Jacobian matrix and derived theoretical results, providing a full account of the trade-offs between parameters that occur in these situations, hold for arbitrary BLIMs, and are not limited to domains of particular cardinality.
Journal ArticleDOI
Bridges between deterministic and probabilistic models for binary data
TL;DR: It is claimed that corresponding to any deterministic model is an implicit stochastic model in which the Deterministic model fits imperfectly, with errors occurring at random.
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.