There are several parameters to assess the research reputation of the academic staff such as scientific publications, citation index, etc. Is there a unique and reliable measure to determine the research output?
I am not aware of any unique and reliable quantitative *measure* of the research reputation. Even if it existed, one should also bear in mind the Goodhart's law (http://en.wikipedia.org/wiki/Goodhart's_law): "When a measure becomes a target, it ceases to be a good measure."
In the hard sciences to date the most reliable (although not perfect) indicator of one's academic reputation is probably just the opinion of the leading experts in the field.
You can pile up a bunch of statistical parameters, all of which are indicative of something. They are much less useful between fields than within a single field. You probably cannot get a single quantitative value. Of course, the use to which the number or whatever is to be put may be a helpful guide in answering your question. I would also have real reservations about asking a few 'leading experts'.
Several indicators/measures are proposed, studied and given in:
Information Management Model for Intellectual Capital of HEIs in Oman: Theoretical Quantitative Approach and Practical Results. J. of Information and Knowledge Management, 2018, Vol. 17, No. 1, pp.1-38. (World Scientific).
· HEIs Quality Improvement Through Students and Academic Staff’s Perception: Data Analysis and Robustness of the Results. International Journal for Quality Research, 2017, Vol.11, No.2, pp.261-278.
· Al-Farahidi Performative model to assess HEIs. 4th OQNHE Conference 2017, pp.1-15.
· A Framework for Fostering the Quality of HEIs: Data Collection, Evaluation, Indication and Validation. Int. J. of Quality and Innovation, 2016, Vol.3, No.1, pp.42-66 (Inderscience).
. Developing and Establishing Statistical Indicators for Fostering the Quality of Omani HEIs. International Journal for Cross-Disciplinary Subjects in Education (IJCDSE), 2015, Volume 6, Issue 2, pp. 2142-2151.
. Quantitative and qualitative indicators to assess
the performance of higher education institutions. Int. J. of Information and Decision sciences, 2014, Vol.6, No. 4, pp.369-392.