Performance of expert abacus operators

Ten expert abacus operators were given various restrictions and distractions during addition of ten numbers of 3–5 figures. All subjects except one could calculate very rapidly without an abacus, probably relying upon its mental representation. Some of those at an intermediate level of mastery moved their fingers as if they had been manipulating a real abacus, and prohibition of this movement or interfering finger-tapping reduced their performance. All the subjects could answer simple non-mathematical questions during abacus calculation without increasing time or errors, but answering extraneous mathematical questions was very hard.     

The principal components of mixed measurement level multivariate data: An alternating least squares method with optimal scaling features

A method is discussed which extends principal components analysis to the situation where the variables may be measured at a variety of scale levels (nominal, ordinal or interval), and where they may be either continuous or discrete. There are no restrictions on the mix of measurement characteristics and there may be any pattern of missing observations. The method scales the observations on each variable within the restrictions imposed by the variable's measurement characteristics, so that the deviation from the principal components model for a specified number of components is minimized in the least squares sense. An alternating least squares algorithm is discussed. An illustrative example is given.Copies of this paper and of the associated PRINCIPALS program may be obtained by writing to Forrest W. Young, Psychometric Laboratory, Davie Hall 013-A, Chapel Hill, NC 27514.     

Constrained DEDICOM

The DEDICOM method for the analysis of asymmetric data tables gives representations that are identified only up to a nonsingular transformation. To identify solutions it is proposed to impose subspace constraints on the stimulus coefficients. Most attention is paid to the case where different subspace constraints are imposed on different dimensions. The procedures are discussed both for the case where the complete table is fitted, and for cases where only offdiagonal elements are fitted. The case where the data table is skew-symmetric is treated separately as well.The research of H. A. L. Kiers has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. The research of Y. Takane has been supported by the Natural Sciences and Engineering Research Council of Canada, grant number A6394, and by the McGill-IBM Cooperative Grant. The authors are obliged to Richard A. Harshman for helpful comments on an earlier version.     

A monotonically convergent algorithm for factals

Takane, Young, and de Leeuw proposed a procedure called FACTALS for the analysis of variables of mixed measurement levels (numerical, ordinal, or nominal). Mooijaart pointed out that their algorithm does not necessarily converge, and Nevels proposed a new algorithm for the case of nominal variables. In the present paper it is shown that Nevels' procedure is incorrect, and a new procedure for handling nominal variables is proposed. In addition, a procedure for handling ordinal variables is proposed. Using these results, a monotonically convergent algorithm is constructed for FACTALS of any mixture of variables.The authors are obliged to Jos ten Berge for stimulating comments on an earlier version of this paper. The research of H. A. L. Kiers has been made possible by a fellowship of the Royal Netherlands Academy of Arts and Sciences. The research of Y. Takane has been supported by the Natural Sciences and Engineering Research Council of Canada, grant number A6394, and by the McGill-IBM Cooperative Grant.     

Generalized structured component analysis

We propose an alternative method to partial least squares for path analysis with components, called generalized structured component analysis. The proposed method replaces factors by exact linear combinations of observed variables. It employs a well-defined least squares criterion to estimate model parameters. As a result, the proposed method avoids the principal limitation of partial least squares (i.e., the lack of a global optimization procedure) while fully retaining all the advantages of partial least squares (e.g., less restricted distributional assumptions and no improper solutions). The method is also versatile enough to capture complex relationships among variables, including higher-order components and multi-group comparisons. A straightforward estimation algorithm is developed to minimize the criterion.The work reported in this paper was supported by Grant A6394 from the Natural Sciences and Engineering Research Council of Canada to the second author. We wish to thank Richard Bagozzi for permitting us to use his organizational identification data and Wynne Chin for providing PLS-Graph 3.0.     

On a test of dimensionality in redundancy analysis

Lazraq and Cléroux (Psychometrika, 2002, 411–419) proposed a test for identifying the number of significant components in redundancy analysis. This test, however, is ill-conceived. A major problem is that it regards each redundancy component as if it were a single observed predictor variable, which cannot be justified except for the rare situations in which there is only one predictor variable. Consequently, the proposed test leads to drastically biased results, particularly when the number of predictor variables is large, and it cannot be recommended for use. This is shown both theoretically and by Monte Carlo studies.The work reported in this paper was supported by Grant A6394 to the first author from the Natural Sciences and Engineering Research Council of Canada.     

A new stacking motif in the decagonal approximant Mn3Ga5

The structure of the decagonal approximant Mn₃Ga₅     

Investor's Pessimistic and False Belief About Trustworthiness and Stake Size in Trust Decision1

Trust is a vital element of any society. Previous studies using trust games have provided insight into understandings of trusting behavior. However, investors' behaviors can be confounded by their risk preferences in the game, and little is known about the relationship between stake size and beliefs of others' good intentions underlying trust. We thus used a variant of the trust game and conducted two experiments to examine how stake size affects investors' beliefs about receivers' trustworthiness, with model-based analyses. We showed that, when holding all else equal, investors trusted more, but their expectations of reciprocation declined as stake size increased. However, actual receivers' reciprocation rates showed the opposite trend to investors' pessimistic beliefs. Furthermore, following previous studies in social psychology, we hypothesized that investors' social preferences (social value orientation) moderated the beliefs underlying trust, but they had no explanatory powers in investors' expectations of reciprocation. These results suggest that peoples' naive beliefs about stake size play a more important role in trust decisions than expected.