In this paper, we present a study of a large corpus of student logic exercises in which we explore the relationship between two distinct measures of difficulty: the proportion of students whose initial attempt at a given natural language to first-order logic translation is incorrect, and the average number of attempts that are required in order to…

A fundamental goal of educational research is identifying students' current stage of skill mastery (complete/partial/none). In recent years a number of cognitive diagnosis models have become a popular means of estimating student skill knowledge. However, these models become difficult to estimate as the number of students, items, and skills grows.…

Model evaluation in covariance structure analysis is critical before the results can be trusted. Due to finite sample sizes and unknown distributions of real data, existing conclusions regarding a particular statistic may not be applicable in practice. The bootstrap procedure automatically takes care of the unknown distribution and, for a given…

Two generalizations of canonical correlational analysis are developed. The partial, part, and bipartial canonical correlation coefficients are shown to be special cases of the generalization. Illustrative examples are provided. (Author/JKS)

It is shown that a weaker generalized inverse (Rao's g-inverse; Graybill's c-inverse) can be used in place of the Moore-Penrose generalized inverse to obtain multiple and canonical correlations from singular covariance matrices. Mathematical derivations are provided. (Author/JKS)

Proposes a comprehensive approach, generalized constrained multiple correspondence analysis, for imposing both row and column constraints on multivariate discrete data. Each set of discrete data is decomposed into several submatrices and then multiple correspondence analysis is applied to explore relationships among the decomposed submatrices.…

Maximally reliable composites found in canonical reliability when expressed in the form of a canonical factor analysis solution are shown to have highly desirable data reduction properties. Theoretical relationships among canonical factor analysis, principal components analysis and canonical reliability analysis are emphasized. (Author/JKS)

Monotonically convergent algorithms are described for maximizing sums of quotients of quadratic forms. Six (constrained) functions are investigated. The general formulation of the functions and the algorithms allow for application of the algorithms in various situations in multivariate analysis. (SLD)

Univariate procedures proposed by M. Brown and A. Forsythe (1974) and the multivariate procedures from D. Nel and C. van der Merwe (1986) were generalized to form five new multivariate alternatives to one-way multivariate analysis of variance (MANOVA) for use when dispersion matrices are heteroscedastic. These alternatives are evaluated for Type I…

The originally proposed multivariate meta-analysis approach for correlation matrices--analyze Pearson correlations, with each study's observed correlations replacing their population counterparts in its conditional-covariance matrix--performs poorly. Two refinements are considered: Analyze Fisher Z-transformed correlations, and substitute better…

Problems of sampling error and accumulated rounding error in canonical variate analysis are discussed. A new technique is presented which appears to be superior to canonical variate analysis when the ratio of variables to sampling units is greater than one to ten. Examples are presented. (Author/JKS)

Canonical analysis is frequently used in studies of relationships between sets of variables which are difficult to measure accurately, partly because of the true nature of the data and partly because of errors associated with the measurement instruments. Meredith's solution to the fallible data problem is examined. (Author/BJG)

The triangular decomposition method is suggested as a general technique for obtaining the various measures of an ill-conditioned matrix. The advantages of using triangular decomposition are computing nicety, cost, and parsimony. (Author/PN)