Pieter M. Kroonenberg

Principal component analysis of three-mode data by means of alternating least squares algorithms

A new method to estimate the parameters of Tuckers three-mode principal component model is discussed, and the convergence properties of the alternating least squares algorithm to solve the estimation problem are considered. A special case of the general Tucker model, in which the principal component analysis is only performed over two of the three modes is briefly outlined as well. The Miller & Nicely data on the confusion of English consonants are used to illustrate the programs TUCKALS3 and TUCKALS2 which incorporate the algorithms for the two models described.

Cross-cultural patterns of attachment : A meta-analysis of the Strange Situation

VAN IJZENDOORN, MARINUS H , and KROONENBERG, PIETER M Cross-cultural Patterns of Attachment A Meta-Analysts of the Strange Situation CHILD DEVELOPMENT, 1988, 59, 147-156 Crosscultural research usmg Amsworths Strange Situation tends to rely on incomplete Information and to concentrate on individual rather than aggregated samples In this study, a widei perspective is taken by exammmg almost 2,000 Strange Situation classifications obtamed m 8 different countries Differences and similanties between distributions in classifications of samples are mvestigated usmg correspondence analysis Aggregation of samples per country and contment allowed for a firmer empirical basis foi cross-cultural analysis Substantial inhacultural diffeiences weie estabhshed, m a number of mstances, samples from l country resembled those in other countries more than they did each other The data also suggest a pattem of cross-cultuial differences, m which A classifications emerge äs relatively more prevalent m Western European counhies and C classificahons äs relatively more frequent m Israel and Japan Inbacultural vanaüon was nearly l 5 times the crosscultural Variation

The TUCKALS line: a suite of programs for three-way data analysis

Abstract This paper describes two programs (TUCKALS2 en TUCKALS3) with which three-way data can be analysed. Both are based on generalisations of standard (two-way) principal component analysis. The working of the programs, and the basic theory behind them, is explained, and is illustrated with data on the influence of alcohol on the behaviour of Australian twins.

Changes over time in the relationship between hand preference and writing hand among left-handers

In a cross-sectional Dutch sample the percentage of left-handers writing with their left hand increased from 0% for people of 40 yr and over, to 100% for 14 yr olds and younger. The implications of this result for the use of writing hand as an index for handedness are discussed, and causes for this phenomenon are briefly explored.

Cross-Cultural Consistency of Coding the Strange Situation

Abstract This study tested whether or not cross-cultural differences in attachment classification distributions result from systematic differences in coding practices. First, we investigated whether or not the interactive scales have been scored consistently in several different cross-cultural samples. Second, the Richters, Waters, and Vaughn (1988) functions were applied to address the question of whether or not attachment classifications were consistently based upon the same pattern of interactive behaviors. Third, cross-cultural coding differences were described from a multivariate perspective. Data sets from seven investigators in six countries were available for analysis. Analyses on this “multinational data set” revealed that except for distance interaction, the interactive scales in the two reunion episodes were scored in accordance with the original coding rules. Furthermore, a good to reasonable agreement appeared to exist between the original classifications and those computed by the functions, except for infants older than 20 months of age. The multivariate principal component analysis showed that classification groups across cultures were more alike than cultures across classification groups. Our data showed, therefore, that attachment classifications have been consistently coded across cultures.

Analysis of Variance of Multiply Imputed Data

As a procedure for handling missing data, Multiple imputation consists of estimating the missing data multiple times to create several complete versions of an incomplete data set. All these data sets are analyzed by the same statistical procedure, and the results are pooled for interpretation. So far, no explicit rules for pooling F tests of (repeated-measures) analysis of variance have been defined. In this article we outline the appropriate procedure for the results of analysis of variance (ANOVA) for multiply imputed data sets. It involves both reformulation of the ANOVA model as a regression model using effect coding of the predictors and applying already existing combination rules for regression models. The proposed procedure is illustrated using 3 example data sets. The pooled results of these 3 examples provide plausible F and p values.

Nonsymmetric Correspondence Analysis: A Tool for Analysing Contingency TablesWith a Dependence Structure

In this article a case is made for using nonsymmetric correspondence analysis to evaluate contingency tables with a dependence structure. A nontechnical overview of the method is presented in the article itself, while the relevant formulae are given in the Appendix. The technique is illustrated with three examples from such diverse areas as the intergenerational transfer of attachment, division of household tasks between recently married couples illustrating the handling of longitudinal data via supplementary variables, and attractiveness of products for shoplifting illustrating categorical multiple regression.

Some additional results on principal components analysis of three-mode data by means of alternating least squares algorithms

Kroonenberg and de Leeuw (1980) have developed an alternating least-squares method TUCKALS-3 as a solution for Tuckers three-way principal components model. The present paper offers some additional features of their method. Starting from a reanalysis of Tuckers problem in terms of a rank-constrained regression problem, it is shown that the fitted sum of squares in TUCKALS-3 can be partitioned according to elements of each mode of the three-way data matrix. An upper bound to the total fitted sum of squares is derived. Finally, a special case of TUCKALS-3 is related to the Carroll/Harshman CANDECOMP/PARAFAC model.

Genetic variability in cultivated common bean beyond the two major gene pools

It is generally accepted that two major gene pools exist in cultivatedcommon bean (Phaseolus vulgaris L.), a MiddleAmerican and an Andean one. Some evidence, based on unique phaseolin morphotypesand AFLP analysis, suggests that at least one more gene pool exists incultivated common bean. To investigate this hypothesis, 1072 accessions from acommon bean core collection from the primary centres of origin, held at CIAT,were investigated. Various agronomic and morphological attributes (14categorical and 11 quantitative) were measured. Multivariate analyses,consisting of homogeneity analysis and clustering for categorical data,clustering and ordination techniques for quantitative data and nonlinearprincipal component analysis for mixed data, were undertaken. The results ofmost analyses supported the existence of the two major gene pools. However, theanalysis of categorical data of protein types showed an additional minor genepool. The minor gene pool is designated North Andean and includes phaseolintypes CH, S and T; lectin types 312, Pr, B and K; and mostly A5, A6 and A4 typesα-amylase inhibitor. Analysis of the combined categorical data ofprotein types and some plant categorical data also suggested that some othergermplasm with C type phaseolin are distinguished from the major gene pools.

A survey of algorithms for exact distributions of test statistics in r × c contingency tables with fixed margins

Testing of independence in an r x c tables is generally carried out by using a continuous limiting distribution of the test statistic, rather than the discrete distribution itself. This paper surveys algorithms for the computation of the latter. The central idea is the efficient enumeration of all tables with the same margins, or of a suitable subset thereof. The simplest case is Fishers exact test for a 2 x 2 table and a one-side alternative hypothesis. Fishers method is easily extended to r x c tables and to arbitrary statistics.