Education and Child Studies

Kroonenberg and de Leeuw (1980) have developed an alternating least-squares method TUCKALS-3 as a solution for Tucker's three-way principal components model. The present paper offers some additional features of their method. Starting from a reanalysis of Tucker's 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.

A new method to estimate the parameters of Tucker's 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.

In this paper we present a four-step procedure for performing a Tucker2 analysis on three-way data in the case a number of observations are missing. The procedure consists of (1) creating multiple complete data sets via multiple imputation of the missing data, (2) analysing these data sets with the Tucker2 model, (3) combining both the row and the column component matrices of these analyses to create centroid solutions using Generalised Procrustes analyses, and (4) using these centroid solutions to find the associated core slices appertaining to the centroid solutions. This procedure will produce both the basic parameters of the Tucker2 model and estimates of their variability due to the missing data. Chromatographic data are used as an illustration.

Long-term plant breeding programs generate large quantities of genealogical, geno-typic, phenotypic and environment characterization data. Marker-trait association studies are starting to be used to integrate and represent such data, but the results are context 2 V. N. Arief et al. dependent, as trait associated markers depend on the germplasm investigated, the environments in which they are studied, and the interaction of genotype and environment. The concept of a trait-associated marker block, defined as markers in a linkage disequi-librium block that show significant association with a trait, addresses non-independency of markers in association analysis. A Phenome Atlas is a collection of diagrammatic representations of chromosome regions that affect trait inheritance (phenome maps) to document the patterns of trait inheritance across the genome. This methodology is illustrated using the Wheat Phenome Atlas constructed from a genome wide association study of 20 economically important traits from the first 25 years of an international wheat breeding program. Three-way principal component analysis then provides information about which genotypes carry favourable trait-associated marker block combinations , which marker blocks discriminate among genotypes and which marker block combinations are available for any given combination of genotypes and traits. Context dependency is illustrated through different patterns of marker trait association profiles being observed when analysing the same genotypes for different marker blocks and trait combinations, and through data obtained from different combinations of environments.

Ten trials evaluated the performance of several late tropical maize populations (La Posta Sequía, Pool 26 Sequía and Tuxpeño Sequía) selected for tolerance to drought during flowering and grain filling and also for yield potential. Families (S 1 or full-sib) had been selected recurrently for six to eight years on an index of traits. Pattern (clustering and ordination) analysis was used to analyse the relative performance of entries that included cycles of selection for drought tolerance in the populations and non-drought tolerant checks. Mean environment (E) yields ranged from 1.0 to 10.4 t ha 1 . Analysis of variance showed that 97.9% of the total sums of squares was accounted for by E, and that, of the remaining sums of squares the G E (genotype by environment interaction) was almost 3 times that of the contribution of G alone. Cluster analysis separated the checks, the earlier maturing drought tolerant entries and the later maturing drought tolerant entries. This was verified by principal component (PC) analysis of the G E matrix. Grouping of the environments (i.e. based on entry performance), resulted in the separation of different types of droughts, and of medium and high yielding well-watered environments. The patterns of discrimination observed indicated that the yield gains under drought would have been unlikely to occur if selection had been done only in well-watered environments. Within each population, selection improved broad adaptation (higher mean yield) to both drought and well-watered environments and cycles of selection 'jumped' from non-drought-tolerant to drought-tolerant groups as their specific adaptation to drought environments increased.

The Handbooks of Attachment represent authoritative collections of state-of-the-art reviews of the whole spectrum of attachment research. In this paper these handbooks are used to present a detailed quantitative view of the major research areas and the leading researchers in the field, as well as their relationships. The results are based on frequency of citations, co-authorships and numbers of papers referenced in the chapters of the handbooks. They show that a detailed network of attachment researchers exists and that it is getting denser. Major areas of attachment research have been relatively stable in the last decade.