[Paper Review] Citation indices and dimensional homogeneity

Gangan Prathap|arXiv (Cornell University)|Jan 3, 2017

scientometrics and bibliometrics research15 references3 citations

TL;DR

This paper argues that citation indices in bibliometrics must adhere to dimensional homogeneity, a principle from physics, to ensure scientific validity. It demonstrates that most h-type indices have dimensions of [P] (papers), while the Euclidean index has dimensions of [P^{3/2}], and provides an empirical example to validate the framework, highlighting the importance of consistent units in citation metrics.

ABSTRACT

The importance of dimensional analysis and dimensional homogeneity in bibliometric studies is always overlooked. In this paper, we look at this issue systematically and show that most h-type indices have the dimensions of [P], where [P] is the basic dimensional unit in bibliometrics which is the unit publication or paper. The newly introduced Euclidean index, based on the Euclidean length of the citation vector has the dimensions [P3/2]. An empirical example is used to illustrate the concepts.

Motivation & Objective

• To highlight the overlooked importance of dimensional analysis in bibliometric studies.
• To establish that citation indices must be dimensionally homogeneous to be scientifically meaningful.
• To classify the dimensional units of various citation indices, particularly h-type and Euclidean indices.
• To provide a systematic framework for evaluating the dimensional consistency of bibliometric indicators.
• To demonstrate through an empirical example that dimensional homogeneity improves the interpretability and validity of citation metrics.

Proposed method

• Applies principles of dimensional analysis from physics to bibliometric citation indices.
• Defines the basic unit of bibliometrics as the publication or paper, denoted [P].
• Analyzes the dimensional structure of h-type indices, showing they have dimensions [P].
• Derives the dimensional structure of the Euclidean citation index, showing it has dimensions [P^{3/2}].
• Uses an empirical dataset to illustrate the dimensional classification and validate the theoretical framework.
• Compares different citation indices based on their dimensional consistency and physical plausibility.

Experimental results

Research questions

• RQ1 Why is dimensional homogeneity important in bibliometric indices, and what are its implications?
• RQ2 What are the dimensional units of common h-type citation indices in bibliometrics?
• RQ3 How does the Euclidean citation index differ in dimensional structure from traditional h-type indices?
• RQ4 Can dimensional analysis improve the validity and interpretability of citation metrics?
• RQ5 What empirical evidence supports the dimensional classification of citation indices?

Key findings

• Most h-type citation indices are dimensionally homogeneous and have the unit [P], representing the number of papers.
• The Euclidean citation index, based on the Euclidean norm of the citation vector, has dimensions [P^{3/2}].
• Dimensional inconsistency in citation indices can lead to flawed interpretations and invalid comparisons.
• The paper provides an empirical example demonstrating the dimensional classification of indices in practice.
• The study establishes that dimensional homogeneity is a necessary criterion for scientifically sound bibliometric evaluation.
• The framework enables clearer distinction and classification of citation indices based on their physical dimensions.