Upper bound of the uncertainty interval of the Rao-Stirling diversity index.

Description

This function computes the upper bound of the uncertainty interval of the Rao-Stirling diversity index, as explained in Calatrava et al. (2016). The computation involves the redistribution of uncategorized references to various disciplines. In order to avoid improbable redistributions of disciplines, a set of permissible disciplines for redistribution can be defined. Furthermore, the number of disciplines redistributed to uncategorized references can be limited.

Usage

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UpperIndexBound(known.ref.counts, uncat.ref.count, similarity,
  permissible.disciplines = NULL, redistribution.limit = 4)

Arguments

known.ref.counts

A vector of positive integers. Each element represents the count of references to each discipline.

uncat.ref.count

A positive integer denoting the number of references that are not categorized into disciplines.

similarity

A positive semi-definite matrix that encodes the similarity between disciplines, as explained in Porter and Rafols (2009). The dimensions of this matrix are n x n, being n the total number of disciplines. The self-similarities (i.e. the diagonal elements) have to be 1.

permissible.disciplines

A logical vector denoting to which disciplines uncategorized references can be distributed. Its length needs to be equal to the length of known.ref.counts. This argument is optional and leaving it unspecified or supplying NULL permits redistribution to all disciplines.

redistribution.limit

A positive integer that limits the number of disciplines that each uncategorized reference can have redistributed. This argument is optional and leaving it unspecified will set the redistribution.limit to default.

Value

The upper bound of the uncertainty interval of the Rao-Stirling diversity index.

References

Calatrava Moreno, M.C., Auzinger, T. and Werthner, H. (2016) On the uncertainty of interdisciplinarity measurements due to incomplete bibliographic data. Scientometrics. DOI:10.1007/s11192-016-1842-4

Porter, A. and Rafols, I. (2009) Is science becoming more interdisciplinary? Measuring and mapping six research fields over time. Scientometrics, Vol. 81, No. 3 (719-745). DOI:10.1007/s11192-008-2197-2

Examples

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#Load data
data(pubdata1)

#Get counts of citations of one of the publications in the dataset
counts <- pd1.count.matrix[,1]

#Get number of uncategorized references in the publication
uncat <- pd1.uncat.refs[1]

#Get vector of permissible disciplines.
logic.disciplines <- counts > 0
permissible <- PruneDisciplines(logic.disciplines, 0.233, pd1.similarity)

UpperIndexBound(counts, uncat, pd1.similarity, permissible)