The use of factor analysis in the statistical analysis of multiple time series

Factor analysis has been proposed and used as a method of statistical analysis of several measurements made on one individual repeatedly over time. This paper discusses some difficulties in applying factor analysis to multiple time series and attempts to indicate to what extent such methods can accomplish the goals of time series analysis. Some other methods are suggested.Research sponsored by contract AF41(657)-214 between the USAF School of Aerospace Medicine and Teachers College, Columbia University.     

Confirmatory factor analysis of the Brunel Mood Scale for use with water-skiing competition

The purpose of the present study was to investigate the factorial validity of the Brunel Mood Scale, which measures anger, confusion, depression, fatigue, tension, and vigor, for water-skiers. Participants were 345 water-skiers (age range 16 to 39 years, men: n=311, women: n=34) who completed the scale approximately 1 hour before a water-skiing competition. Confirmatory factor analysis indicated support for the validity of the 6-factor model, with a Comparative Fit Index of .90 and Root Mean Squared Error of Approximation of .07. Internal consistency coefficients were above the .70 criterion. It is suggested that the Brunel Mood Scale shows factorial validity for use with water-skiers and that researchers should continue to assess validation of the Brunel Mood Scale with other measures and with specific appropriate samples.     

Departures From Sensible Play in Computer Blackjack

Gambling has been viewed as irrational, and even though blackjack offers rational strategies (i.e., Basic [E. Thorp, 1966] and card counting), people exhibit departures from rationality (e.g., “Never Bust” strategies). To determine whether departures from rational behavior reflect ignorance or fatigue, university students were provided with on-line Basic advice while playing a simplified computer blackjack. Although the on-line advice initially affected the totals these players sat on, it was eventually discarded for higher risk strategies. Irrational play did not reflect ignorance or fatigue and was not necessarily conservative. Real fluctuations of odds in blackjack may lead to situations in which Basic is not perceived by players as effective. Because Basic is not a personalized strategy, it seems less likely to be maintained in the face of losses. Players were more optimistic that they might win when utilizing their personalized strategies.     

Exploratory factor analysis: Current use,methodological developments and recommendations for good practice

Current Psychology - Psychological research often relies on Exploratory Factor Analysis (EFA). As the outcome of the analysis highly depends on the chosen settings, there is a strong need for...     

On the Sensible Application of Familywise Alpha Adjustment

This essay responds to Daniel O'Keefe's “Against Familywise Alpha Adjustment.” Whereas O'Keefe maintains that one should never attempt to control Type I error introduced when many statistical tests are conducted, this essay argues that alpha adjustment should be applied only in the narrowly circumscribed instance when the researcher wants to make a strong claim that there is no Type I error in a specific collection of tests.     

Alpha factor analysis

A distinction is made between statistical inference and psychometric inference in factor analysis. After reviewing Rao's canonical factor analysis (CFA), a fundamental statistical method of factoring, a new method of factor analysis based upon the psychometric concept of generalizability is described. This new procedure (alpha factor analysis, AFA) determines factors which have maximum generalizability in the Kuder-Richardson, or alpha, sense. The two methods, CFA and AFA, each have the important property of giving the same factors regardless of the units of measurement of the observable variables. In determining factors, the principal distinction between the two methods is that CFA operates in the metric of the unique parts of the observable variables while AFA operates in the metric of the common (communality) parts.On the other hand, the two methods are substantially different as to how they establish the number of factors. CFA answers this crucial question with a statistical test of significance while AFA retains only those alpha factors with positive generalizability. This difference is discussed at some length. A brief outline of a computer program for AFA is described and an example of the application of AFA is given.The first version of this paper was prepared while the senior author was a U. S. Public Health Service Fellow at the Center for Advanced Study in the Behavioral Sciences and while the junior author was Director of Research of the Palo Alto Public Schools.     

Longitudinal factor analysis

A model is presented for factor analysing scores on a set of psychological tests administered as both pre- and postmeasures in a study of change. The model assumes that the same factors underlie the tests on each occasion, but that factor scores as well as factor loadings may change between occasions. Factors are defined to be orthogonal between as well as within occasions. A two-stage least squares procedure for fitting the model is described, and generally provides a unique rotation solution for the factors on each occasion.We thank M. W. Browne, R. P. McDonald, R. Pruzek, and the Managing Editor for their constructive comments.     

论马克思对康德自由概念的感性证明

自由是贯穿整个西方文化的价值目标,是主体之为主体的根据,它发展到德国古典哲学时期已经取得了巨大成果,康德和马克思的自由观就宛如德国近代自由思想的两个点:康德自由概念的核心是自由意志,并且它是纯粹理性的唯一事实,但对它的证明始终是个问题;马克思对康德的"自由"进行了感性证明。     

Establishing Sensible and Practical Guidelines for Desk Rejections

Publishing has become, in several respects, more challenging in recent years. Academics are faced with evolving ethics that appear to be more stringent in a bid to reduce scientific fraud, the emergence of science watchdogs that are now scrutinizing the published literature with critical eyes to hold academics, editors and publishers more accountable, and a barrage of checks and balances that are required between when a paper is submitted and eventually accepted, to ensure quality control. Scientists are often under increasing pressure to produce papers in an increasingly stringent publishing environment. In such a climate, timing is everything, as is the efficiency of the process. Academics appreciate that rejections are part of the fabric of attempting to get a paper published, but they expect the reason to be clear, based on careful evaluation of their work, and not on superficial or unsubstantiated excuses. A desk rejection occurs when a paper gets rejected even before it has entered the peer review process. This paper examines the features of some desk rejections and offers some guidelines that would make desk rejections valid, fair and ethical. Academics who publish are under constant pressure to do so quickly, but effectively. They are dependent on the editors’ good judgment and the publisher’s procedures. Unfair, unsubstantiated, or tardy desk rejections disadvantage academics, and editors and publishers must be held accountable for wasting their time, resources, and patience.     

Sensible Atoms: A Techno-aesthetic Approach to Representation

This essay argues that nano-images would be best understood with an aesthetical approach rather than with an epistemological critique. For this aim, I propose a ‘techno-aesthetical’ approach: an enquiry into the way instruments and machines transform the logic of the sensible itself and not just the way by which it represents something else. Unlike critical epistemology, which remains self-evidently grounded on a representationalist philosophy, the approach developed here presents the advantage of providing a clear-cut distinction between image-as-representation and other modes of existence of images, such as the one of ‘imaginaction’ that I draw from a comparison between far-field and near-field microscopies. Once this regime of imaginaction is distinguished from representation, I focus on nanotechnological percepts and argue that they follow a transmodal logic. I then draw the implications of this enquiry in terms of a new sensible condition that changes the way we think of non-living objects. Finally, I conclude that if techno-aesthetics dares to posit and articulate sensibility beyond the privileged sphere of subject/object relationships, it simultaneously engages us to consider the political character of our responsibilities towards the design of nano-engineered sensorial spaces.     

Measuring motivations for intercollegiate athlete alcohol use: a confirmatory factor analysis of the drinking motives measure

This study examined the psychometric properties of the Drinking Motives Measure (DMM) on a sample of 227 collegiate athletes. Confirmatory factor analyses indicated that the 4-factor structure of the DMM provided a better fit than either 2- or 1-factor models, but the overall fit of the 4-factor model was moderate at best. A revised 3-factor model consistent with prior research (M. L. Cooper, M. Russell, J. B. Skinner, & M. Windle, 1992) provided the best fit. Hierarchical multiple regression analyses indicated that the 3 DMM factors included in the revised model accounted for 17%-21% of the unique variance on alcohol consumption variables. Results provide preliminary evidence supporting the internal consistency, construct validity, and convergent validity of the revised 3-factor DMM with collegiate athletes.     

Relations of factor score estimates to their use

Considerations of factor score estimates have concentrated on internal characteristics. This report considers external characteristics of four methods for determining factor score estimates; that is, relations of these estimates to measures on attributes not entered into the factor analysis. These external characteristics are important for many uses of factor score estimates. Findings are that different ones of the methods are appropriate for different uses.Supported in part by the Personnel and Training Branch of the Office of Naval Research under contract number 00014-67-A-0305-0003.     

Orthogonal inter-battery factor analysis

It is the purpose of this paper to present a method of analysis for obtaining (i) inter-battery factors and (ii) battery specific factors for two sets of tests when the complete correlation matrix including communalities is given. In particular, the procedure amounts to constructing an orthogonal transformation such that its application to an orthogonal factor solution of the combined sets of tests results in a factor matrix of a certain desired form. The factors isolated are orthogonal but may be subjected to any suitable final rotation, provided the above classification of factors into (i) and (ii) is preserved. The general coordinate-free solution of the problem is obtained with the help of methods pertaining to the theory of linear spaces. The actual numerical analysis determined by the coordinate-free solution turns out to be a generalization of the formalism of canonical correlation analysis for two sets of variables. A numerical example is provided.This investigation has been supported by the U.S. Office of Naval Research under Contract Nonr-2752(00).     

Note on factor analysis

Certain assumptions and procedures basic to factor analysis are examined from the point of view of the mathematician. It is demonstrated that the Hotelling method does not yield meaningful traits, and an example from the theory of gas mixtures with convertible components is cited as evidence. The justification of current methods for determining the adequacy of the reproduction of a correlation matrix by a factorial matrix is questioned, and ax ² criterion, practical only for a small matrix, is proposed. By means of a hypothetical example from geometry, it is shown that results of a Hotelling analysis are necessarily relative to the population at hand. The factorial effects of the adjunction of a total test to a group of tests are considered. Some of the general considerations and questions raised are pertinent to types of analysis other than the Hotelling.The calculations which lie in the background of thisNote, but of which only relatively few are in evidence, were made possible by a grant from the Carnegie Corporation of New York to whom grateful acknowledgment is hereby made.