Factor analysis by generalized least squares

Aitken's generalized least squares (GLS) principle, with the inverse of the observed variance-covariance matrix as a weight matrix, is applied to estimate the factor analysis model in the exploratory (unrestricted) case. It is shown that the GLS estimates are seale free and asymptotically efficient. The estimates are computed by a rapidly converging Newton-Raphson procedure. A new technique is used to deal with Heywood cases effectively.The work on this project was done when the first author was Research Statistician at Educational Testing Service, Princeton, N. J. The second author was in part supported by a grant from the Research Committee of the University of Wisconsin Graduate School. The authors wish to thank Michael Browne for many helpful comments and Marielle van Thillo for valuable assistance in the numerical computations.     

An individual difference model for the multidimensional analysis of preference data

A model for the analysis of paired comparison data is presented which combines features of the BTL-model with features of the Unfolding model. The model is metric, mathematically tractable, and has an exact algebraic solution. Since it is multidimensional and allows for individual differences, it is thought to be more realistic for some choice situations than either the Thurstone model or the BTL-model. No claim is made that the present model will be appropriate for all conceivable choice situations. Rather, it is argued that the fact that it is explicitly falsifiable is a point in its favor.This work was supported by a grant of the United States Public Health Service (1 R03 MH19139 01 MSM) and a David Ross (XR) grant of the Purdue Research Foundation (PRF 2132), both of which are gratefully acknowledged. We also owe thanks to Dr. Terry Cooper, whose careful scrutiny of an earlier draft of this paper allowed us to reduce the number of errors from n to n-1.     

Some new results on factor indeterminacy

Some relations between maximum likelihood factor analysis and factor indeterminacy are discussed. Bounds are derived for the minimum average correlation between equivalent sets of correlated factors which depend on the latent roots of the factor intercorrelation matrix . Empirical examples are presented to illustrate some of the theory and indicate the extent to which it can be expected to be relevant in practice.     

Negation of Park's transformations

Zusammenfassung Parks Kritik beruht, meiner Ansicht nach, auf einem entscheidenden Mißverständnis meiner Intentionen: es geht mir überhaupt nicht um eine Argumentation gegen eine Transformationsgrammatik à la Chomsky, und nicht einmal in erster Linie gegen die Absicht mancher Psycholinguisten, eine derartige Theorie in ihren psychischen Funktionen aufzuzeigen. Ich möchte lediglich dafür plädieren, daß die Psycholinguistik in erster Linie psychologische (und nicht linguistische) Überlegungen und Modellvorstellungen als Leitlinien verwendet.     

Differential-psychologische Untersuchungen zum Vigilanzverhalten

Zusammenfassung Mit Hilfe von Korrelationsmethoden wurden inter-individuelle Leistungsunterschiede in einer ein- und einer mehrflächigen Vigilanzaufgabe untersucht. In beiden Aufgaben korrelieren bestimmte Vigilanzscores mit Interferenzindikatoren im Stroop-Versuch. In der mehrflächigen Anordnung zeigte sich eine negative Korrelation zwischen der Entdeckungswahrscheinlichkeit und der Rate der falschen Alarme. Hinsichtlich der zeitlichen Merkmale der Vigilanzleistung ergab sich, daß die Vpn den geringsten Abfall der Entdeckungswahrscheinlichkeit erkennen lassen, die zu Beginn der Vigilanzaufgabe die Rate der falschen Alarme am stärksten reduzieren konnten. Die Ergebnisse wurden im Rahmen des detection-Modells interpretiert.

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Experiments in individual differences of vigilance behavior

Summary This paper is concerned with individual differences of vigilance performance in a simple and a complex vigilance task. In both tasks certain aspects of vigilance behavior were correlated with interference in the Color Word Test by Stroop. In the complex vigilance task there was a negative correlation between the probabilities of signal detections and false alarms rates. With regard to the temporal characteristics of vigilance behavior it was found out that subjects with the least decrease of detection rate showed the greatest reduction of their false alarms rate to the beginning of the vigilance task. The results were discussed in the context of the detection model.

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Teil II der Dissertation, die im Januar 1969 der Philosophischen Fakultät der Freien Universität Berlin vorgelegt wurde.     

Polydipsia induced in the rat by a second-order schedule

Drinking was studied in rats pressing a bar on a second-order schedule in which every third completion of a 1-min fixed interval was followed by food presentation. A brief flash of light signaled the completion of each fixed-interval component. The rats drank not only after the food presentations but also after presentations of the light flash alone. A high rate of steady drinking followed intervals terminated by a food presentation. Drinking that followed intervals terminated by a light flash alone was of comparable rate, but characteristically interrupted by bar pressing. When 250-mg food pellets were used instead of 45-mg pellets, both drinking and bar-pressing rates increased substantially.     

A general approach to confirmatory maximum likelihood factor analysis

We describe a general procedure by which any number of parameters of the factor analytic model can be held fixed at any values and the remaining free parameters estimated by the maximum likelihood method. The generality of the approach makes it possible to deal with all kinds of solutions: orthogonal, oblique and various mixtures of these. By choosing the fixed parameters appropriately, factors can be defined to have desired properties and make subsequent rotation unnecessary. The goodness of fit of the maximum likelihood solution under the hypothesis represented by the fixed parameters is tested by a large samplex ² test based on the likelihood ratio technique. A by-product of the procedure is an estimate of the variance-covariance matrix of the estimated parameters. From this, approximate confidence intervals for the parameters can be obtained. Several examples illustrating the usefulness of the procedure are given.This work was supported by a grant (NSF-GB 1985) from the National Science Foundation to Educational Testing Service.