The Candecomp/Parafac (CP) model decomposes a three-way array into a prespecified number R of rank-1 arrays and a residual array, in which the sum of squares of the residual array is minimized. The practical use of CP is sometimes complicated by the occurrence of so-called degenerate solutions, in which some components are highly correlated in all…

The underlying statistical models for multiple regression analysis are typically attributed to two types of modeling: fixed and random. The procedures for calculating power and sample size under the fixed regression models are well known. However, the literature on random regression models is limited and has been confined to the case of all…

A key feature of the analysis of three-way arrays by Candecomp/Parafac is the essential uniqueness of the trilinear decomposition. We examine the uniqueness of the Candecomp/Parafac and Indscal decompositions. In the latter, the array to be decomposed has symmetric slices. We consider the case where two component matrices are randomly sampled…

Taxicab correspondence analysis is based on the taxicab singular value decomposition of a contingency table, and it shares some similar properties with correspondence analysis. It is more robust than the ordinary correspondence analysis, because it gives uniform weights to all the points. The visual map constructed by taxicab correspondence…

The problem of selecting (from several bionomial populations) the one with the highest probability is discussed in this brief article. Several approximate solutions are offered and the solution is extended to bivariate correlation. (Author/JKS)

Offers a method to simplify J x J x 2 arrays and shows that the transformation that simplifies an I x J x K array can also be used to simplify the complementary arrays of three different orders. Discusses the maximal simplicity for arrays. (SLD)

Provides a method for generating the class of all solutions (or at least a subset of that class) given a CANDECOMP/PARAFAC (CP) solution that satisfies certain conditions. Shows mathematically that the condition defined by J. Kruskal is necessary and sufficient when the rank of the solution is three, and it may hold for higher ranks. (SLD)

The problem of rotating a matrix orthogonally to a best least squares fit with another matrix of the same order has a closed-form solution based on a singular value decomposition. The optimal rotation matrix is not necessarily rigid, but may also involve a reflection. In some applications, only rigid rotations are permitted. Gower (1976) has…

The assumptions of the model for factor analysis do not exclude a class of indeterminate covariances between factors and error variables (Grayson, 2003). The construction of all factors of the model for factor analysis is generalized to incorporate indeterminate factor-error covariances. A necessary and sufficient condition is given for…

Estimates of conditional uncertainty, contingent uncertainty, and normed modifications of contingent uncertainity have been proposed for the two-way contingency table. The asymptotic standard errors of the estimates are derived. (Author)

In this study of robust regression techniques, it was found that the Jackknife does particularly poor in estimating a correlation when there are sharp deviations from normality. A simple example is provided. (RC)

As the literature indicates, no method is presently available which takes explicitly into account that the parameters of Lazarsfeld's latent class analysis are defined as probabilities and are therefore restricted to the interval (0,1). An appropriate transform on the parameters is presented in order to satisfy this constraint. (Author/JKS)

This note extends and elaborates Hubert's attempt to provide an interpretation of Freeman's measure of association, theta. The theta measure is used in a contingency table when observations are ordered on one variable and unordered on the other. No attempt is made to explore the distribution of theta. (Author/RC)

This paper is concerned with the development of a measure of the precision of a multidimensional euclidean structure. The measure is a precision index for each point in the structure, assuming that all the other points are precisely located. The measure is defined and two numerical methods are presented. (Author/CTM)

Two algorithms based on a latent class model are presented for discovering hierarchical relations that exist among a set of dichotomous items. The algorithms presented, and three competing deterministic algorithms are compared using computer-generated data. (Author/JKS)