We study flexible Bayesian methods that are amenable to a wide range of learning problems involving complex high dimensional data structures, with minimal tuning. We consider parametric and semiparametric Bayesian models, that are applicable to both static and dynamic data, arising from a multitude of areas such as economics, finance and…

Configural frequency analysis (CFA), a new method for identifying types, is illustrated numerically. Relations to latent class analysis and to factor analysis are discussed. It is suggested to use CFA as a type-defining method instead of factor analysis if the variables are linked not only by first but also by higher-order associations. (RC)

The mathematical derivation of the statistics used for inference in some linear models assumes that values of the independent variables are pre-selected such that these variables can be treated as fixed rather than random variables. This assumption is often disregarded when these models are utilized in research. This study is an investigation of…

A mastery test is frequently described as follows: an examinee responds to n dichotomously scored test items. Depending upon the examinee's observed (number correct) score, a mastery decision is made and the examinee is advanced to the next level of instruction. Otherwise, a nonmastery decision is made and the examinee is given remedial work. This…

A model permitting construction of algorithms for the polynomial conjoint analysis of similarities is presented. This model, which is based on concepts used in nonmetric scaling, permits one to obtain the best approximate solution. The concepts used to construct nonmetric scaling algorithms are reviewed. Finally, examples of algorithmic models for…

Three methods of factor analyzing dichotomously scored item performance data were compared using two raw score data sets of 20-item tests, one reflecting normally distributed latent traits and the other reflecting uniformly distributed latent traits. This comparison was accomplished by using phi and tetrachoric correlations among dichotomous data…

The purpose of this paper is to derive explicit estimates of the parameters of a latent structure model when the skills represented by the test items are hierarchically related. Two special cases are described, which may be used as an approximation to the Dayton and Macready model and also provide initial estimates in an iterative estimation…

Three topics in factor analysis are covered: a) a reliability coefficient for assessing the quality of a maximum likelihood factor analysis, b) an application of three-mode factor analysis to serial learning data, showing variations in learning curves over stages of learning and individuals, and c) the use of personal probability functions to…

Aitkin's generalized least squares (GLS) principle, with the inverse of the observed variance-covariance matrix as a weight matrix, is applied to estimate the factor analysis model in the exploratory (unrestricted) case. It is shown that the GLS estimates are scale free and asymptotically efficient. The estimates are computed by a rapidly…

The question of whether test factor structure is indicative of the test item hierarchy was examined. Data from 1,000 subjects on two sets of five bivalued Law School Admission Test items, which were analyzed with latent trait methods of Bock and Lieberman and of Christoffersson in Psychometrika, were analyzed with an ordering-theoretic method to…

A mathematical model is proposed to describe how group differences in distributions of abilities, which are distinct from the target ability, influence the probability of a correct item response. In the multidimensional approach, differential item functioning is considered a function of the educational histories of the examinees. (SLD)