A note on factor analysis by the method of principal axes

The resolution of a set of variables into principal components may be performed upon variables having arbitrary variances, or upon variables obtained from these by reduction of all variances to unity. The two procedures do not yield the same results even if the principal components are reduced to unit variance in both cases, except when the original variances are all equal.This article was written while the author was on a W.P.A. project at Teacher's College, Columbia University.     

First-order approximation to English,second-order approximation to English,and orthographic neighbor ratio norms for 925 nouns

First- and second-order approximations to English and orthographic neighbor ratio values are provided for Paivio, Yuille, and Madigan’s (1968) 925 nouns. First- and second-order approximations to English are information theory measures of the probability of generating a word on a letter-by-letter basis. The orthographic neighbor ratio is the frequency of a word divided by the sum of the frequencies of all words that can be generated by changing one of its letters. Thus, the orthographic neighbor ratio provides a measure of a sophisticated guessing model in which partial information about a word is obtained and a decision is made on the basis of the relative frequencies of the possible responses. Correlations with existing norms are reported.     

A model-based approach to multivariate principal component regression: Selecting principal components and estimating standard errors for unstandardized regression coefficients

Principal component regression (PCR) is a popular technique in data analysis and machine learning. However, the technique has two limitations. First, the principal components (PCs) with the largest variances may not be relevant to the outcome variables. Second, the lack of standard error estimates for the unstandardized regression coefficients makes it hard to interpret the results. To address these two limitations, we propose a model-based approach that includes two mean and covariance structure models defined for multivariate PCR. By estimating the defined models, we can obtain inferential information that will allow us to test the explanatory power of individual PCs and compute the standard error estimates for the unstandardized regression coefficients. A real example is used to illustrate our approach, and simulation studies under normality and nonnormality conditions are presented to validate the standard error estimates for the unstandardized regression coefficients. Finally, future research topics are discussed.     

A cosine approximation to the normal distribution

A cosine function is suggested to approximate the normal distribution as a device for simplifying algebraic manipulations of the latter. Numerical evaluations remain straightforward and employ only the commonly available trigonometric tables. A method of visual curve fitting requiring only an oscilloscope is also described.     

Comparison of cube rotations around axes inclined relative to the environment or to the cube.

Observers judged whether 2 successive computer-displayed rotations of a cube were the same or different. With respect to the observers, each rotation was about a vertical axis (Y), a horizontal (line-of-sight) axis (Z), an axis tilted just 10 degrees from vertical or horizontal, or a maximally oblique axis. Independently, with respect to the cube, each rotation was about a symmetry axis through opposite faces (F) or through opposite corners (C), an axis tilted 10 degrees from one of these symmetry axes, or an axis of extreme nonsymmetry. Speed and accuracy of comparison decreased as the axes of the successive rotations departed from the canonical axes of the environment (Z, or especially, Y), or even more sharply, from the symmetry axes of the cube (C, or especially, F). The internalized principles that guide the perceptual representation of rigid motions evidently are ones of kinematic geometry more than of physics.     

Emergence and reduction: Reply to Kim

In this paper I examine Jaegwon Kim’s view that emergent properties are irreducible to the base properties on which they supervene. Kim’s view assumes a model of ‘functional reduction’ which he claims to be substantially different from the traditional Nagelian model. I dispute this claim and argue that the two models are only superficially different, and that on either model, properly understood, it is possible to draw a distinction between a property’s being reductively identifiable with its base property and a property’s being reductively explainable in terms of it. I propose that we should take as the distinguishing feature of emergent properties that they be truly novel properties, i.e., ontologically distinct from the ‘base’ properties which they supervene on. This only requires that emergent properties cannot be reductively identified with their base properties, not that they cannot be reductively explained in terms of them. On this conception the set of emergent properties may well include mental properties as conceived by nonreductive physicalists.     

Naive and refined truth approximation

The naive structuralist definition of truthlikeness is an idealization in the sense that it assumes that all mistaken models of a theory are equally bad. The natural concretization is a refined definition based on an underlying notion of structurelikeness.In Section 1 the naive definition of truthlikeness of theories is presented, using a new conceptual justification, in terms of instantial and explanatory mistakes.In Section 2 general constraints are formulated for the notions of structurelikeness and truthlikeness of structures.In Section 3 a refined definition of truthlikeness of theories is presented, based on the notion of structurelikeness, using a sophisticated version of the conceptual justification for the naive definition.In Section 4 it is shown that idealization and concretization is a special kind of potentially refined truth approximation.I would like to acknowledge that van Benthem (1987) played in several respects a crucial role in the research for a new refined definition. Moreover, I like to thank David Miller, Ilkka Niiniluoto, and two referees for their comments on an earlier version. One of the referees notes that the Miller version of the naive approach (in model-theoretic terms, and identifying the truth with the truth about the actual world) has been criticised on several occasions for its failure to accommodate likeness between structures by Oddie (notably Oddie, 1986). The idea that likeness between structures should be a guiding idea behind truthlikeness is said to be a constant theme of Oddie's work. All this may well be true, but I should add however that Oddie's publications did not play any role in my research. The local references to Oddie are based on the suggestions by the referee.     

Matrix manipulation and interpretation of data related to AIDS transmission

This research describes how a currently available spreadsheet program can be set up to analyze sociographic data. An algorithm developed by Jamrich (1960) is presented, along with both the mathematical and the spreadsheet equations. An example of the application of the algorithm and equations to AIDS transmission data is presented.     

校长领导行为与校长类型

对3800名中小学教师和200名校长进行问卷施测,考察校长工作角色五个方面的相互关系,并在此基础上对校长领导行为进行聚类分析,得到四个类型。四种类型校长所在学校的组织气氛和学校效能感均有显著差异。     

The role of axes of elongation and symmetry in rotated object naming

Many theorists have postulated that axes of elongation and/or symmetry play an important role in the recognition of objects. In this paper, evidence is presented that mitigates this claim from independent assessments of the effects of axes of elongation or symmetry on the time to name rotated line drawings of common objects. This conclusion was further supported in a stronger test in which both of these variables were orthogonally controlled, the aspect ratio of elongation was manipulated,and only objects that were completely geometrically symmetrical or asymmetrical were used. In all the experiments, objects were named for several blocks to determine the influence of these variables on effects of orientation with practice. Symmetry was found to diminish the effects of orientation after practice in naming the object set, and the effects of the most extreme orientation tested (120 degrees from upright) were diminished when both axes defined the same orientation, relative to when they defined different orientations. Contrary to many theories, these findings relegate the axes of symmetry and elongation to relatively minor roles during object identification.     

A unified approach to multiple‐set canonical correlation analysis and principal components analysis

Multiple‐set canonical correlation analysis and principal components analysis are popular data reduction techniques in various fields, including psychology. Both techniques aim to extract a series of weighted composites or components of observed variables for the purpose of data reduction. However, their objectives of performing data reduction are different. Multiple‐set canonical correlation analysis focuses on describing the association among several sets of variables through data reduction, whereas principal components analysis concentrates on explaining the maximum variance of a single set of variables. In this paper, we provide a unified framework that combines these seemingly incompatible techniques. The proposed approach embraces the two techniques as special cases. More importantly, it permits a compromise between the techniques in yielding solutions. For instance, we may obtain components in such a way that they maximize the association among multiple data sets, while also accounting for the variance of each data set. We develop a single optimization function for parameter estimation, which is a weighted sum of two criteria for multiple‐set canonical correlation analysis and principal components analysis. We minimize this function analytically. We conduct simulation studies to investigate the performance of the proposed approach based on synthetic data. We also apply the approach for the analysis of functional neuroimaging data to illustrate its empirical usefulness.     

Nonlinear principal components analysis: introduction and application

The authors provide a didactic treatment of nonlinear (categorical) principal components analysis (PCA). This method is the nonlinear equivalent of standard PCA and reduces the observed variables to a number of uncorrelated principal components. The most important advantages of nonlinear over linear PCA are that it incorporates nominal and ordinal variables and that it can handle and discover nonlinear relationships between variables. Also, nonlinear PCA can deal with variables at their appropriate measurement level; for example, it can treat Likert-type scales ordinally instead of numerically. Every observed value of a variable can be referred to as a category. While performing PCA, nonlinear PCA converts every category to a numeric value, in accordance with the variable's analysis level, using optimal quantification. The authors discuss how optimal quantification is carried out, what analysis levels are, which decisions have to be made when applying nonlinear PCA, and how the results can be interpreted. The strengths and limitations of the method are discussed. An example applying nonlinear PCA to empirical data using the program CATPCA (J. J. Meulman, W. J. Heiser, & SPSS, 2004) is provided.     

Referentiality and Matrix Semantics

Referential semantics importantly subscribes to the programme of theory of logical calculi. Defined by Wójcicki in [8], it has been subsequently studied in a series of papers of the author, till the full exposition of the framework in [9] and its intuitive characterisation in [10].     

Reference-related inhibition produces enhanced position discrimination and fast repulsion near axes of symmetry

Models proposed to account for reference frame effects in spatial cognition often account for performance in some tasks well, but fail to generalize to other tasks. Here, we demonstrate that a new process account of spatial working memory--the dynamic field theory (DFT)--can bridge the gap between perceptual and memory processes in position discrimination and spatial recall, highlighting that the processes underlying spatial recall also operate in position discrimination. In six experiments, we tested two novel predictions of the DFT: first, that discrimination is enhanced near symmetry axes, especially when the perceptual salience of the axis is increased; and second, that performance far from a reference axis depends on the direction in which the second stimulus is presented. The DFT also predicts the magnitude of this direction-dependent modulation. These effects arise from reference-related inhibition in the theory. We discuss how the processes captured by the DFT relate to existing psychophysical models and operate across a diverse array of spatial tasks.