Abstract
In a previous paper a static model for the relations among science indicators was discussed. From the perspective of science dynamics, we are interested not in relations among variables or indicators, but in the prediction of an event, given comparable events about which we already have knowledge. The quality of the prediction can be measured by the expected information valueI of the message, which converts thea priori probabilities of the events stored in the knowledge base into thea posteriori probabilities of the event. The possibility of predicting in terms of specified variables with hindsight, gives a quantitative measure for testing hypotheses concerning the reconstruction of scientific developments. Some implications for the construction of artificial intelligence using textual archives, as a knowledge base will be discussed.
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References
L. Leydesdorff, Relations among science indicators. Or, more generally among anything one might wish to count about texts. I. The static model,Scientometrics 18 (1990) 281–307
See also:H. Theil,Statistical Decomposition Analysis, North Holland, Amsterdam etc., 1972.
Op. cit. note 1.
See:Theil,Op. cit., 1972, pp. 56ff
Ibid., pp. 59f.
Op. cit., note 2.
In reaction to a draft of the manuscriptVan Driel also commented that word usage is “a bit” dependent upon the journal, to which one wants to submit the article.
By conventiono log o is equal to zero, which is the value of the limit forp→ 0.
See with respect to a similar problem, for example:D. de Solla Price, The analysis of square matrices of scientometric transactions,Scientometrics, 31981, p. 57: “If any cells of the matrix are vacant, unity may be inserted to replace the blank for this stage only.”
Actually, we should then replace them with 0.5 to the power of 2/N, since if the prior relative frequency is 2, the correspondingq is equal to 2/N, and hence:\({2 \mathord{\left/ {\vphantom {2 {N\log {2 \mathord{\left/ {\vphantom {2 1}} \right. \kern-\nulldelimiterspace} 1}}}} \right. \kern-\nulldelimiterspace} {N\log {2 \mathord{\left/ {\vphantom {2 1}} \right. \kern-\nulldelimiterspace} 1}}} = {2 \mathord{\left/ {\vphantom {2 {N\log {1 \mathord{\left/ {\vphantom {1 {0.5}}} \right. \kern-\nulldelimiterspace} {0.5}} = {2 \mathord{\left/ {\vphantom {2 {N\log 1 - \log ((0.5)\exp {2 \mathord{\left/ {\vphantom {2 N}} \right. \kern-\nulldelimiterspace} N}).}}} \right. \kern-\nulldelimiterspace} {N\log 1 - \log ((0.5)\exp {2 \mathord{\left/ {\vphantom {2 N}} \right. \kern-\nulldelimiterspace} N}).}}}}} \right. \kern-\nulldelimiterspace} {N\log {1 \mathord{\left/ {\vphantom {1 {0.5}}} \right. \kern-\nulldelimiterspace} {0.5}} = {2 \mathord{\left/ {\vphantom {2 {N\log 1 - \log ((0.5)\exp {2 \mathord{\left/ {\vphantom {2 N}} \right. \kern-\nulldelimiterspace} N}).}}} \right. \kern-\nulldelimiterspace} {N\log 1 - \log ((0.5)\exp {2 \mathord{\left/ {\vphantom {2 N}} \right. \kern-\nulldelimiterspace} N}).}}}}\) With increasingN, 2/N→0, and hence, (0.5 exp 2N) → 1. Therefore, if one wants to meet the specified criterion zero's should be replaced with a value between 0.52 (=0.25) and 1, depending on theN of the distribution. A more precise mathematical formulation would be needed.
Op. cit., note 2..
M. Hesse,Revolutions and Reconstruction in the Philosophy of Science, Harvester Books, London, 1980;L. Leydesdorff, “In search of epistemic networks,”Social Studies of Science (forthcoming)
These problems are a consequence of the magnitude of errors when using averages in small smaples only.
Ibid. These problems are a consequence of the magnitude of errors when using averages in small samples only.
See also:Leydesdorff,op. cit., note 12. “In search of epistemic networks,”Social Studies of Science (forthcoming)
Since in co-authored articles it is common practice that each author is responsible for particular parts, it may well be that this is the part which was brought in byVan Haastert as one of the coauthors of theJanssens et al., 1986-article, and not byVan Driel.
See:Op. cit. note 1
Leydesdorff,Op. cit., notes1 and 12.
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Leydesdorff, L. Relations among science indicators or more generally among anything one might wish to count about texts. Scientometrics 19, 271–296 (1990). https://doi.org/10.1007/BF02095352
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DOI: https://doi.org/10.1007/BF02095352