There are several types of institutional metrics and sources. There are many issues and controversies associated with some of these institutional metrics and rankings. In general, many of the institutional rankings [U.S News & World Report, Times Higher Education (THE), Academic Ranking of World Universities (ARWU), Wall Street Journal/College Pulse, QS World Rankings, SCImago Institutions Rankings, Center for World University Rankings (CWUR), etc.] use what is often called a composite indicator that might include the number of faculty, students, research outputs, citations, collaborations, sponsored research funding, Nobel Prize winners, employability, and reputational surveys to derive a single value, which is perceived by many to be arbitrary, subjective, and not in the best interests of many institutions. It is better to decide what an institution values and believes is important based on their mission, consider what metrics and indicators make sense, and then analyze individually and not as composite indicator (unless those institutional rankings are deemed important by the institution). The SCOPE Framework for Research Evaluation can provide some guidance. These issues are discussed in more detail under the Further Reading section below.
For purely citation-based institutional comparisons, there are the CWTS Leiden Ranking and Essential Science Indicators. Various comparisons can also be performed in Web of Science at the institutional level and for disciplines.
Some professional societies and governmental agencies produce indicators and related data, such as the National Center for Education Statistics, National, NSF's Academic Institution Profiles, and ASEE's Profiles of Engineering & Engineering Technology.
For Texas A&M University institutional data, see the Office of Academic & Business Performance Analytics.