$${\varvec{x}}_{{\varvec{d}}}$$ -index and its variants: a set of overall scholarly expertise diversity indices for the research portfolio management of institutions

During last several decades, various indicators and proxies to measure research output and their impact for different units have been proposed. These measurements may be targeted at individuals, institutions, journals, countries etc. Institutional level assessment is one such area that has always been and will remain a key challenge to a multitude of stakeholders. Various international rankings as well as different bibliometric indicators have been explored in the context of institutional assessments, though each of them has certain criticisms associated. Most of the existing indicators, including h-type indicators, mainly focus on research output and/ or citations to the research output. They do not reveal the expertise of institutions in different subject areas, which is crucial to know the research portfolio of an institution. Recently, a set of expertise measures such as x and x(g) indices were introduced to determine the expertise of institutions with respect to a specific discipline/field considering strengths in different finer level thematic areas of that discipline/field. In this work, an adaptation of the x-index, namely the \(x_{d}\)-index is proposed to determine the overall scholarly expertise of an institution considering its publication pattern and strength in different coarse thematic areas. This indicator helps to identify the core expertise areas and the diversity of the research portfolio of the institution. Further, two variants of the indicator, namely field normalized indicator or \(x_{d}\) (FN)-index and fractional indicator \(x_{d} \left( f \right)\)-index are also introduced to address the effect of field bias and collaborations on the computation of the expertise diversity. The framework can determine the most suitable version of the indicator to use for research portfolio management with the help of correlation analysis. These indicators and the associated framework are demonstrated on a dataset of 136 institutions. Upon rank correlation analysis, no significant difference is noticed between \(x_{d}\) and its variants computed using different publication counting, in this particular dataset, making \(x_{d}\) the most suitable indicator in this case. The possibilities offered by the framework for effective management of the research portfolio of an institution by expanding its diversity and its ability to aid national level policymakers for the effective management of scholarly ecosystem of the country is discussed.