Fundamental unit structures: A theory of ratio scalability

A theory of nonassociative measurement structures is developed which produces a natural generalization of associative measurement (i.e., extensive structures), and representation and uniqueness theorems are established for these generalized structures, and it is shown that in many cases these representations are ratio scales. The methods of proof strongly relate the structure of the automorphism group of the nonassociative structure to its underlying concatenation operation.     

The filled-duration illusion: The function of temporal and nontemporal set

Studies of the perception of time have demonstrated that large visual stimuli presented for the same duration as small stimuli will appear to have been presented longer. Two theoretical approaches have been offered to explain this effect. Both have emphasized the absolute amount of information in the stimulus. Thus, both would predict the effect when size is varied between sessions. The present study found no effect of size when size was held constant within sessions, but a substantial effect resulted when size was varied within sessions. Also examined was the range of stimulus durations used within a session. In one condition, patterns of various sizes were presented at 15, 30, or 45 msec, while in a second condition, the same patterns were presented to a different group of subjects at 15, 85, or 155 msec. The size effect was significantly reduced when longer time intervals were presented. A third group of subjects was shown patterns at even longer times but with a reduced range (155, 170, and 185 msec). Here the size effect was of equal magnitude to that of the 15-msec interval condition. The implications of these results are that current theoretical explanations of the filled-duration illusion rely on incorrect assumptions.     

Predicting effectiveness of bayesian classification systems

A model is presented for evaluating potential effectiveness of a Bayesian classification system using the expected value of the posterior probability for true classifications as an evaluation metric. For a given set of input parameters, the value of this complex metric is predictable from a simply computed row variance metric. Prediction equations are given for several representative sets of input parameters.     

Multiple group methods for common-factor analysis: Their basis,computation, and interpretation

In a previous paper (1) were developed three basic theorems which were shown to provide numerical routines, as well as algebraic proof, for existing common-factor methods. New multiple routines were also indicated. The first theorem showed how to extract as many common factors as one wished from the correlation matrix in one operation. The second theorem showed how to do the same from the score matrix. The third proved that factoring the correlation matrix was equivalent to factoring the score matrix. A particular application of these theorems is the multiple group factoring method, which the writer first used in practice on some Army attitude scores during World War II. The present paper explains the basic theorems in more detail with special reference to group factoring. Computations are outlined as consisting of five simple matric operations. The meaning of commonfactor analysis is given in terms of the basic theorems, as well as the relationship to inverted factor theory.     

Some necessary conditions for common-factor analysis

LetR be any correlation matrix of ordern, with unity as each main diagonal element. Common-factor analysis, in the Spearman-Thurstone sense, seeks a diagonal matrixU ² such thatG = R – U ² is Gramian and of minimum rankr. Lets ₁ be the number of latent roots ofR which are greater than or equal to unity. Then it is proved here thatr s ₁. Two further lower bounds tor are also established that are better thans ₁. Simple computing procedures are shown for all three lower bounds that avoid any calculations of latent roots. It is proved further that there are many cases where the rank of all diagonal-free submatrices inR is small, but the minimum rankr for a GramianG is nevertheless very large compared withn. Heuristic criteria are given for testing the hypothesis that a finiter exists for the infinite universe of content from which the sample ofn observed variables is selected; in many cases, the Spearman-Thurstone type of multiple common-factor structure cannot hold.This research was made possible in part by an uncommitted grant-in-aid from the Behavioral Sciences Division of the Ford Foundation.     

Image theory for the structure of quantitative variates

A universe of infinitely many quantitative variables is considered, from which a sample ofn variables is arbitrarily selected. Only linear least-squares regressions are considered, based on an infinitely large population of individuals or respondents. In the sample of variables, the predicted value of a variablex from the remainingn – 1 variables is called the partial image ofx, and the error of prediction is called the partial anti-image ofx. The predicted value ofx from the entire universe, or the limit of its partial images asn , is called the total image ofx, and the corresponding error is called the total anti-image. Images and anti-images can be used to explain why any two variablesx _j andx _k are correlated with each other, or to reveal the structure of the intercorrelations of the sample and of the universe. It is demonstrated that image theory is related to common-factor theory but has greater generality than common-factor theory, being able to deal with structures other than those describable in a Spearman-Thurstone factor space. A universal computing procedure is suggested, based upon the inverse of the correlation matrix.This paper introduces one of three new structural theories, each of which generalizes common-factor analysis in a different direction.Nodular theory extends common-factor analysis to qualitative data and to data with curvilinear regressions (6).Order-factor theory introduces the notions oforder among the observed variables and ofseparable factors (7). The presentimage theory is relevant also to the other two.Attention may be called to empirical results published since this paper was written: Louis Guttman, Two new approaches to factor analysis, Annual Technical Report on contract Nonr—731(00). The present research was aided by an uncommitted grant-in-aid from the Ford Foundation.     

Multiple rectilinear prediction and the resolution into components: II

Given a battery ofn tests that has already been resolved intor orthogonal common factors andn unique factors, procedures are outlined for computing the following types of linear multiple regressions directly from the factor loadings: (i) the regression of any one test on then?1 remaining tests; (ii) all then different regressions of ordern?1 for then tests, computed simultaneously; (iii) the regression of any common factor on then tests; (iv) the regressions of all the common factors on then tests computed simultaneously; (v) the regression of any unique factor on then tests; (vi) the regressions of all the unique factors on then tests, computed simultaneously. Multiple and partial correlations are then determined by ordinary formulas from the regression coefficients. A worksheet with explicit instructions is provided, with a completely worked out example. Computing these regressions directly from the factor loadings is a labor-saving device, the efficiency of which increases as the number of tests increases. The amount of labor depends essentially on the number of common factors. This is in contrast to computations based on the original test intercorrelations, where the amount of labor increases more than proportionately as the number of tests increases. The procedures evaluate formulas developed in a previous paper (2). They are based essentially on a shortened way of computing the inverse of the test intercorrelation matrix by use of the factor loadings.     

Development of the self-system: How children perceive their own and others' ideas about themselves

The purpose of this article is to present a model for the development of the self-system in which six concepts within and related to the self-system are distinguished as follows: Four intraindividual self-concepts involving the real and the ideal self-concepts, the perceived real concepts of others about the self, and the perceived ideal concepts or expectancies of others about the self and two environmental concepts involving the actual ideas of others about the child and the others' ideal concepts of or expectancies toward the child. The development and interrelationships among these concepts were studied with 204 children from six age groups (i.e., 6-, 8-, 10-, 12-, 14- and 16-year-olds) with respect to their fit. The intraindividual self-concepts of the children were assessed by means of a Repertory Grid procedure presented to the children. The environmental concepts were obtained by interviewing both parents. The results suggest that although adolescents believe that they do not fulfill their parents expectations, their parents are reasonably satisfied with the extent to which their children have met their ideal expectations.     

The politics of physiological psychology Ivan Pavlov’s suppressed defense of scientific freedom and its consequences

This statement, first presented at a plenary session of the Pavlovian Society on 9 October 1992, in Los Angeles, California, attempts to assess the recently released speech delivered by Ivan Pavlov in 1923, but publicly brought to light only in 1991, on the subject of “Communist Dogmatism and the Autonomy of Science.” This speech, noteworthy for the courage of the delivery under adverse circumstances no less than the contents of its remarks, compels a new estimate of the place of science in a totalitarian system boasting an ideology of physiological psychology. It also sheds new light on the Russian Nobel laureate and pioneer in the areas of behavior modification induced by the functions of the higher nervous system. These remarks take an in-depth view of American radical and Marxian appraisals — how they followed the Soviet lead in harnessing Pavlov to the Communist cause, and in attempting to discredit the work of Sigmund Freud. This lethal combination of Communist political needs and ideological proclivities served to rationalize the implementation of slave labor as work therapy during the Stalinist era. The linkage of Pavlov to Makarenko in education and Michurin in biology serves as a case study in the manufacture of tradition. The collapse of the Soviet system permits a recasting of the history of science and Pavlov’s place in Russian life. Such new conditions also provide a lesson in the distortive role of ideology in the evolution of modern science.