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Citation and co-citation indicators of a phased impact of the BCS theory in the physics of superconductivity

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Abstract

An intellectual account of of the physics of superconductivity was compared with citation and co-citation data during two historical periods that coincided with the introduction of its central explanatory theory (BCS). Factor analysis is used to investigate the co-citation data. The results give preliminary support to a hypothesis that distinguishes impact phases in the effect of the theory on the cognitive organization of the specialty. It is also observed that citation and co-citation data are separate types of information which, under some historical conditions, give differing results.

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Notes and references

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  • The question naturally arises here of whether the correlation coefficient is an appropriate measure for citation data. Since citation data is dichotomous (an article is either cited or not), it is part of the general question of the use of dichotomous data in a dependent variable regression model. A good discussion of this question can be found in R. PINDYCK, D. RUBINFELD,Econometric Models and Economic Forecasts, McGraw-Hill, New York, 1976, p. 238–256. Briefly, dichotomous data, when used as a dependent variable, violates the assumption of homoscendasticity of the error variance. Therefore, standard statistical tests cannot be applied to estimated (sample) parameters. This leads to a loss of efficiency in the parameter estimators but these estimates are neither biased nor inconsistent. In practice, the robust results encountered using factor analysis shows this theoretical consideration not to be a major problem. Further, a check was conducted in those time periods where the correlation matrix was non-singular. In such periods, maximum likelihood factor analysis was used for the initial factor extraction. This is an iterative linear programming technique that converages smoothly in Heywood cases (where some of the standard deviations are zero). No difference was found in the results based on this method when compared with the principle components extraction for the same correlation matrix. A further question in multivariate statistical methodology is whether the results are artifactual. If the same data are subjected to various modes of statistical processing, do the results differ? A major processing decision in using factor analysis is the extent that the resultant factors are correlated. See. H. H. HARMON,Modern Factor Analysis, University of Chicago Press, Chicago, 1967; or R. J. RUMMEL,Applied Factor Analysis, Northwestern University Press, Evanston, IL, 1970. Several oblique rotation techniques, using factors correlated to varying degrees, were compared to the conventional orthogonal varimax rotation. These oblique techniques were of the oblimin variety. They include quartimin, and covarim rotations of the structure matrix. This allowed an inspection of low, moderate, and highly correlated structure factors. Factor extraction was made on the basis of the standard principle components method. Where the input correlation matrix was non-singular, maximum likelihood factor extraction was also compared. The oblique rotations using low and medium correlated factors produced the same results as the orthogonal varimax rotation for the cited article correlation matrix in each time period. The loadings changed in absolute size, as did the eigenvalues of the factors, but the same factor was easily identified across the various oblique and orthogonal rotations. This is because the relative loadings remained virtually the same. The same set of articles were highly loaded on a given factor across different rotations. All of the factors produced by the highly correlated oblique rotation, for a given time period, were actually a single factor that was reproduced over and over again. The content of this factor differs from any found on the other oblique or orthogonal rotations. It appears to be a general factor for the matrix and was, therefore, not useful in differentiating various areas of cognitive activity within the specialty. Since the oblique and orthogonal results are the same, only the standard orthogonal varimax results are reported here. Another methodology question is the relation between factor analysis and cluster analysis methodologies when used with co-citation data. Part of this discussion hinges on the adequacy of treating such data as interval rather than ordinal. The robustness of the data and an external face validity check show the interval assumption to be a safe one. A partial comparison with cluster analysis was also conducted. A cluster analysis on the cited article correlation matrix, using a variety of distance and amalgamation criteria, gave very similar results to the factor analysis in the various time periods. This, however, was only a partial comparison since the cluster methodology used by Dr. Small works directly with co-citation frequencies rather than with a correlation matrix. Other tradeoffs are made in choosing cluster over factor analysis. In factor analysis, following the interval assumption, a cited article can be partially incorporated in several different factors, i.e., splitloaded. Also a measure of the overall success in grouping the cited articles, the amount of variance explained, is utilized. (In cluster analysis a cited article is either incorporated into the cluster or not.) The robustness of the data under this partial comparison leads strongly to the opinion that a formal comparison of the two methods will yield little if any differences.

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This research was supported in part by a grant from the National Science Foundation to the Columbia Program in the Sociology of Science NSF SOC 72 05326

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Nadel, E. Citation and co-citation indicators of a phased impact of the BCS theory in the physics of superconductivity. Scientometrics 3, 203–221 (1981). https://doi.org/10.1007/BF02101666

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