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31.
Dr. Stanley A. Mulaik 《Psychometrika》1981,46(1):105-107
It is proved for the common factor model withr common factors that under certain condition s which maintain the distinctiveness of each common factor a given common factor will be determinate if there exists an unlimited number of variables in the model each having an absolute correlation with the factor greater than some arbitrarily small positive quantity.The author is indebted to R. P. McDonald for suggesting the proof of Guttman's determinantal equation for the squared multiple correlation in predicting a factor from the observed variables used in the parenthetical note. 相似文献
32.
The fixed-interval schedule of reinforcement is one of the more widely studied schedules in the experimental analysis of behavior and is also a common baseline for behavior pharmacology. Despite many intensive studies, the controlling variables and the pattern of behavior engendered are not well understood. The present study examined the microstructure and superstructure of the behavior engendered by a fixed-interval 5- and a fixed-interval 15-minute schedule of food reinforcement in the pigeon. Analysis of performance typical of fixed-interval responding indicated that the scalloped pattern does not result from smooth acceleration in responding, but, rather, from renewed pausing early in the interval. Individual interresponse-time (IRT) analyses provided no evidence of acceleration. There was a strong indication of alternation in shorter-longer IRTs, but these shorter-longer IRTs did not occur at random, reflecting instead a sequential dependency in successive IRTs. Furthermore, early in the interval there was a high relative frequency of short IRTs. Such a pattern of early pauses and short IRTs does not suggest behavior typical of reinforced responding as exemplified by the pattern found near the end of the interval. Thus, behavior from clearly scalloped performance can be classified into three states: postreinforcement pause, interim behavior, and terminal behavior. 相似文献
33.
This paper considers some mathematical aspects of minimum trace factor analysis (MTFA). The uniqueness of an optimal point of MTFA is proved and necessary and sufficient conditions for a point x to be optimal are established. Finally, some results about the connection between MTFA and the classical minimum rank factor analysis will be presented. 相似文献
34.
John G. Arena Edward B. Blanchard Frank Andrasik Bruce C. Dudek 《Journal of psychopathology and behavioral assessment》1982,4(1):55-69
A brief Headache Symptom Questionnaire was administered to 129 chronic headache Sufferers. The questionnaire accurately classified 68.42% of headache subjects in their proper diagnostic category, comparable to, but statistically less accurate than, the 86.4% agreement between expert headache diagnosticians using clinical interviews. Results of a factor analysis of the Headache Symptom Questionnaire lend support for their being two commonly accepted global headache categories—vascular/migraine and muscle contraction—and one headache dimension concerned with duration of headache pain. Combined migraine-muscle contraction headache was found to be related more to migraine than to muscle contraction headache, and cluster headaches emerged as a separate clinical entity, not loading positively on any factor and loading negatively on all three.This research was supported in part by Grant NS-15235 from the National Institute of Neurological and Communicative Disorders and Stroke. 相似文献
35.
Tucker has outlined an application of principal components analysis to a set of learning curves, for the purpose of identifying meaningful dimensions of individual differences in learning tasks. Since the principal components are defined in terms of a statistical criterion (maximum variance accounted for) rather than a substantive one, it is typically desirable to rotate the components to a more interpretable orientation. Simple structure is not a particularly appealing consideration for such a rotation; it is more reasonable to believe that any meaningful factor should form a (locally) smooth curve when the component loadings are plotted against trial number. Accordingly, this paper develops a procedure for transforming an arbitrary set of component reference curves to a new set which are mutually orthogonal and, subject to orthogonality, are as smooth as possible in a well defined (least squares) sense. Potential applications to learning data, electrophysiological responses, and growth data are indicated.Portions of this research were supported by the National Research Council of Canada, Grant A8615 to the second author. We thank Jagdeth Sheth for supplying his raw data. 相似文献
36.
Hoben Thomas 《Psychometrika》1977,42(2):199-206
Individuals are classified in a cross-classification table where two behavioral observations on each individual determine the classification. The problem is to test certain structural models assumed to underlie the cross-classified observations. A minimum chi-square test procedure is proposed. 相似文献
37.
Latent roots of random data correlation matrices with squared multiple correlations on the diagonal: A monte carlo study 总被引:1,自引:0,他引:1
In order to make the parallel analysis criterion for determining the number of factors easy to use, regression equations for predicting the logarithms of the latent roots of random correlation matrices, with squared multiple correlations on the diagonal, are presented. The correlation matrices were derived from distributions of normally distributed random numbers. The independent variables are log (N–1) and log {[n(n–1)/2]–[(i–1)n]}, whereN is the number of observations;n, the number of variables; andi, the ordinal position of the eigenvalue. The results were excellent, with multiple correlation coefficients ranging from .9948 to .9992.This research was supported by the Office of Naval Research under Contract N00014-67-A-0305-0012, Lloyd G. Humphreys, principal investigator, and by the Department of Computer Science of which Richard G. Montanelli, Jr., is a member. 相似文献
38.
Dr. Stanley A. Mulaik 《Psychometrika》1976,41(2):249-262
Guttman's index of indeterminacy (22 – 1) measures the potential amount of uncertainty in picking the right alternative interpretation for a factor. When alternative solutions for a factor are equally likely to be correct, then the squared multiple correlation 2 for predicting the factor from the observed variables is the average correlation
AB
between independently selected alternative solutionsA andB, while var (
AB
)=(1 – 2)2/s, wheres is the dimensionality of the space in which unpredicted components of alternative solutions are to be found. When alternative solutions for the factor are not equally likely to be chosen, 2 is the lower bound for E(
AB
); however, E(
AB
) need not be a modal value in the distribution of
AB
. Guttman's index and E(
AB
) measure different aspects of the same indeterminacy problem. 相似文献
39.
In the last few years, a number of asymptotic results for the distribution of unrotated and rotated factor loadings have been given. This paper investigates the validity of some of these results based on simulation techniques. In particular, it looks at principal component extraction and quartimax rotation on a problem with 13 variables. The indication is that the asymptotic results are quite good. 相似文献
40.
Audrey J. Leroux Christopher J. Cappelli David R. J. Fikis 《The British journal of mathematical and statistical psychology》2021,74(3):404-426
A three-level piecewise growth model (3L-PGM) can be used to break up nonlinear growth into multiple components, providing the opportunity to examine potential sources of variation in individual and contextual growth within different segments of the model. The conventional 3L-PGM assumes that the data are strictly hierarchical in nature, where measurement occasions (level 1) are nested within individuals (level 2) who are members of a single cluster (level 3). However, in longitudinal research, it is sometimes difficult for data structures to remain purely clustered during a study, such as when some students change classrooms or schools over time. One resulting data structure in this situation is known as a multiple membership structure, where some lower-level units are members of more than one higher-level unit. The new multiple membership PGM (MM-PGM) extends the 3L-PGM to handle multiple membership data structures frequently found in the social sciences. This study sought to examine the consequences of ignoring individual mobility across clusters when estimating a 3L-PGM in comparison to estimating a MM-PGM. MM-PGM estimates were less biased (especially in the cluster-level coefficient estimates), although we found substantial bias in cluster-level variance components across some conditions for both models. 相似文献