A Study On The Linear Methods For Field Normalization Of Publication’s Citation Impact

Citation count, an indicator for publication’s impact, is the most important and commonly used indicator in research evaluation since it is a good proxy of publication’s quality. However, due to the differences in citation practices among scientific fields, citation counts are not comparable across fields. In order to make a transdisciplinary comparison of publications’ impact, the field differences in citation counts should be eliminated by field normalization methods to make the normalized citations comparable across fields.The process of field normalization is essentially a mathematical transformation to the citation counts of publications. Field normalization methods can be classified as linear and nonlinear methods from the perspective of whether the transformation is linear. The aggregate normalized citation performance for a set of publications(such as the publications of a university or a department) is usually defined as the sum or average of individual publications’ normalized citations. The operation of summing and averaging are based on the assumption that the normalized citation of individual publications is an equidistant metric. Since the normalized citations under nonlinear methods are not equidistant, so it’s more reasonable to use linear normalization methods when evaluating the citation performance at the aggregate level. Based on this fact, this study focuses on linear normalization methods.The fairness of research evaluation has a close relationship with the normalization effect of normalization methods. Though relevant studies showed that mean-based method has an edge over many linear normalization methods, such as median-based method etc., few studies give a thorough comparison of the normalization effect between mean-based method and z-score. In this context, this study first conducted a systematic comparison of their normalization effect based on 236 Web of Science subject categories. The result shows that mean-based method performs better than z-score as a whole.Mean-based method and z-score are both special cases of the general linear method y = kx + b. Starting from the form of general linear method, this study established an optimization model from which more effective linear normalization methods are expected to be derived. This study derived the scaling normalization method y = kx and affine normalization method y = kx + b for the 236 fields under separate unweighted and weighted optimization models. In the unweighted model all distinct citations contribute equally to the objective function. The contribution of a publication’s citation is irrelevant to its position in the citat ion distribution. In the weighted model the contribution of a publication’s citation is weighted by its position in the citation distribution. It turns out that while the normalization performance of unweighted-optimization-based linear methods is unbalanced along the citation distributions, the weighted-optimization-based scaling method shows trivial but affine method shows significant advantages over mean-based method.To evaluate the impact of the weighted-optimization-based linear method’s advantage on normalization effect to the results of practical research evaluation, this study investigated the differences among the publication citation impact rankings of 39 " Project 985" universities obtained under separate mean-based method, weightedoptimization-based scaling method and affine method. It turns out that when the normalized citation performance at the aggregate level is defined as the average of individual publications’ normalized citations, the university rankings are sensitive to the differences in normalization effect, but when the aggregate citation performance is defined as the sum of individual publications’ normalized citations the rankings are insensitive to the differences in normalization effect. So, the weighted-optimizationbased affine method is a better choice in research evaluation when the aggregate citation performance is obtained by averaging individual publications’ normalized citations, but when the aggregate citation performance is obtained by summing individual publications’ normalized citations, the simple mean-based method can be used instead.