Simplimax: Oblique rotation to an optimal target with simple structure

Factor analysis and principal component analysis are usually followed by simple structure rotations of the loadings. These rotations optimize a certain criterion (e.g., varimax, oblimin), designed to measure the degree of simple structure of the pattern matrix. Simple structure can be considered optimal if a (usually large) number of pattern elements is exactly zero. In the present paper, a class of oblique rotation procedures is proposed to rotate a pattern matrix such that it optimally resembles a matrix which has an exact simple pattern. It is demonstrated that this method can recover relatively complex simple structures where other well-known simple structure rotation techniques fail.This research has been made possible by a fellowship from the Royal Netherlands Academy of Arts and Sciences. The author is obliged to Jos ten Berge for helpful comments on an earlier version.     

Structural analysis of covariance and correlation matrices

A general approach to the analysis of covariance structures is considered, in which the variances and covariances or correlations of the observed variables are directly expressed in terms of the parameters of interest. The statistical problems of identification, estimation and testing of such covariance or correlation structures are discussed.Several different types of covariance structures are considered as special cases of the general model. These include models for sets of congeneric tests, models for confirmatory and exploratory factor analysis, models for estimation of variance and covariance components, regression models with measurement errors, path analysis models, simplex and circumplex models. Many of the different types of covariance structures are illustrated by means of real data.1978 Psychometric Society Presidential Address.This research has been supported by the Bank of Sweden Tercentenary Foundation under the project entitledStructural Equation Models in the Social Sciences, Karl G. Jöreskog, project director.     

Stimulus and reinforcer relativity in multiple schedules: Local and dimensional effects on sensitivity to reinforcement

Pigeons' responses in two successive components of multiple schedules were reinforced according to variable-interval schedules of reinforcement that varied over five different conditions. Within each session of all conditions, line orientations of 0°, 30°, or 45° in Component 1 alternated with orientations of 45°, 60°, or 90° in Component 2. Response rates were recorded in three successive subintervals of each component. Ratios were taken between the response rate in each Component 1 line orientation and the response rate in each Component 2 orientation. These ratios were found to be power functions of the corresponding ratios of obtained reinforcement rates. Sensitivity of response ratios to changes in reinforcer ratios, given by the value of the exponent of the power function, increased systematically with increasing disparity between the dimensional values of orientation stimuli. In addition, sensitivity decreased systematically over successive subintervals of components, that is, with increasing time since component alternation. Dimensional and local (subinterval) effects interacted in that sensitivity increased with stimulus disparity to a far greater extent in the first subinterval than later in components. The data could be described by a combination of rectangular hyperbolae which attributed the interaction between local and dimensional effects to limits set by local effects on the extent that stimulus differences could affect sensitivity.     

概化理论方差分量估计的跨分布分析

方差分量估计是进行概化理论分析的关键。采用MonteCarlo模拟技术,探讨心理与教育测量数据分布对概化理论各种方法估计方差分量的影响。数据分布包括正态、二项和多项分布,估计方法包括Traditional、Jackknife、Bootstrap和MCMC方法。结果表明:(1)Traditional方法估计正态分布和多项分布数据的方差分量相对较好,估计二项分布数据需要校正,Jackknife方法准确地估计了三种分布数据的方差分量,校正的Bootstrap方法和有先验信息的MCMC方法(MCMCinf)估计三种分布数据的方差分量结果较好;(2)心理与教育测量数据分布对四种方法估计概化理论方差分量有影响,数据分布制约着各种方差分量估计方法性能的发挥,需要加以区分地使用。     

Effects of temperature and prior residence on territorial aggression in the convict cichlid Cichlasoma nigrofasciatum

Aggression in the convict cichlid Cichlasoma nigrofasciatum was measured under two different environmental parameters after introduction of a conspecific intruder. Measurements were made after 24-hr and 48-hr teritorial residence times at both 26°C and 30°C. Eight fish established territories in individual tanks each containing one terra cotta pot. Intruders contained in a glass cylinder were introduced into the territories. An opaque divider separating the resident from the intruder was removed after a 15-min acclimation period. At 26°C, we observed a significant difference in the mean number of bites of the cichlids of 24-hr and 48-hr residency durations, whereas, at 30°C, such a difference did not exist. Statistical analysis showed that cichlids exhibited more aggression at 30°C than at 26°C. Increased aggression levels at the higher temperature may be related to the fact that cichlids establish territories and spawn at about 30°C.     

The weighted oblimin rotation

Cureton & Mulaik (1975) proposed the Weighted Varimax rotation so that Varimax (Kaiser, 1958) could reach simple solutions when the complexities of the variables in the solution are larger than one. In the present paper the weighting procedure proposed by Cureton & Mulaik (1975) is applied to Direct Oblimin (Clarkson & Jennrich, 1988), and the rotation method obtained is called Weighted Oblimin. It has been tested on artificial complex data and real data, and the results seem to indicate that, even though Direct Oblimin rotation fails when applied to complex data, Weighted Oblimin gives good results if a variable with complexity one can be found for each factor in the pattern. Although the weighting procedure proposed by Cureton & Mulaik is based on Landahl's (1938) expression for orthogonal factors, Weighted Oblimin seems to be adequate even with highly oblique factors. The new rotation method was compared to other rotation methods based on the same weighting procedure and, whenever a variable with complexity one could be found for each factor in the pattern, Weighted Oblimin gave the best results. When rotating a simple empirical loading matrix, Weighted Oblimin seemed to slightly increase the performance of Direct Oblimin.The author is obliged to Henk A. L. Kiers and three anonymous reviewers for helpful comments on an earlier version of this paper.     

The typical rank of tall three-way arrays

The rank of a three-way array refers to the smallest number of rank-one arrays (outer products of three vectors) that generate the array as their sum. It is also the number of components required for a full decomposition of a three-way array by CANDECOMP/PARAFAC. The typical rank of a three-way array refers to the rank a three-way array has almost surely. The present paper deals with typical rank, and generalizes existing results on the typical rank ofI × J × K arrays withK = 2 to a particular class of arrays withK ≥ 2. It is shown that the typical rank isI when the array is tall in the sense thatJK − J < I < JK. In addition, typical rank results are given for the case whereI equalsJK − J. The author is obliged to Henk Kiers, Tom Snijders, and Philip Thijsse for helpful comments.     

The ontogeny of cumulative culture: Individual toddlers vary in faithful imitation and goal emulation

The success of human culture depends on early emerging mechanisms of social learning, which include the ability to acquire opaque cultural knowledge through faithful imitation, as well as the ability to advance culture through flexible discovery of new means to goal attainment. This study explores whether this mixture of faithful imitation and goal emulation is based in part on individual differences which emerge early in ontogeny. Experimental measurements and parental reports were collected for a group of 2‐year‐old children (N = 48, age = 23–32 months) on their imitative behavior as well as other aspects of cognitive and social development. Results revealed individual differences in children's imitative behavior across trials and tasks which were best characterized by a model that included two behavioral routines; one corresponding to faithful imitation, and one to goal emulation. Moreover, individual differences in faithful imitation and goal emulation were correlated with individual differences in theory of mind, prosocial behavior, and temperament. These findings were discussed in terms of their implications for understanding the mechanisms of social learning, ontogeny of cumulative culture, and the benefit of analyzing individual differences for developmental experiments.     

Generate,maintain, manipulate? Exploring the multidimensional nature of motor imagery

Motor imagery (MI), the mental rehearsal of a motor task, is thought to be a synergistic interaction between processes that allow for the generation, maintenance, and manipulation, of motor images. While our understanding of the multidimensional nature of MI stems from research examining various methods to assess MI ability, limited research has been conducted employing multiple assessments across participants to probe the underlying dimensions of MI. Accordingly, the current study sought to explore the multidimensional nature of MI using an exploratory approach that would allow for the dimensions of imagery to be examined and linked to each assessment measure. Specifically, participants (N = 81) underwent a battery of MI-assessments (including questionnaires, mental chronometry, a hand laterality judgment task, and a MI-based learning task), and data was analyzed via principal component analysis (PCA). Three components resulted, which were named based on which outcome measures loaded on to the component: generation, maintenance, and manipulation of motor images. We further discuss a fourth component, named ‘temporal sequencing’ of motor images, identified via the initial component solution. Concordant with previous research, we highlight the importance of employing multiple measures when assessing imagery ability prior to its use in training. Notably, this work allowed us to link assessments of MI to the different dimensions of MI, informing on the nature of MI.