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What “becoming more alike” should mean
“Alike” is not a single observable property. Two universities can publish in the same fields while having different staff structures, funding sources or collaboration networks. Conversely, they can have similar budgets and student numbers but sharply different research portfolios. A credible study therefore defines convergence dimension by dimension.
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For institutions i and j in period t, create a vector of comparable measures and calculate a similarity score. Repeat this for every institution pair and every period. Convergence is supported when the average or median similarity increases, the lower-similarity tail shrinks, or the whole distribution shifts upward. State in advance which of those outcomes is your definition.
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| Dimension | What the profile contains | Question answered |
|---|---|---|
| Research topics and disciplines | Shares of publications or grants by a fixed field or topic taxonomy | Are institutions working in increasingly similar areas? |
| People and organization | Staff and student shares by category, career stage or discipline | Are their internal populations becoming more alike? |
| Funding | Basic institutional funding and competitive-grant shares | Are their financial structures converging? |
| Outputs and impact | Publication volume, field-normalized citations and related indicators | Are they producing similar kinds and levels of output? |
| Collaboration | Co-authorship, partner shares, network centrality and communities | Are they occupying similar positions in research networks? |
| Mission and context | Public or private status, teaching or research mission, country, size and prestige | Is an apparent trend caused by changing composition rather than convergence? |
Do not combine these dimensions into one index until you have examined them separately. A single score can hide a result in which topic profiles converge but organizational structures diverge.
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1. Define the population and observation periods
Choose institutions and a stable unit
Specify the countries or region, institution types and inclusion rules. Decide whether the unit is a whole university, a research institute, a campus or a legally distinct organization. Use a persistent identifier rather than a name alone. Record mergers, splits, renamings and changes in legal status; otherwise a new identifier can look like a sudden rise or fall in similarity.
Fix the time windows
Use equal, non-overlapping periods when possible. The topic-alignment study in Scientometrics used 2000–2004, 2005–2009, 2010–2014 and 2015–2019. A German public-university analysis in Quantitative Science Studies followed 1995–2020. A European disciplinary-profile study in the Journal of Informetrics covered 1996–2011. These periods illustrate the principle: a five-year window smooths annual volatility, but the best length depends on publication volume and the lag between funding, staffing and output.
Keep the window length fixed for the primary analysis. If you also test rolling or overlapping windows, label them as a robustness analysis because overlapping observations are not independent.
Freeze the comparison frame
Record the database, field taxonomy, document types, language filters, affiliation rules and counting method before calculating profiles. A change in any of these can create artificial convergence. If coverage changes during the study, show the break and run a sensitivity analysis rather than silently joining incompatible series.
2. Build comparable institutional profiles
Convert counts into shares
Raw publication or staff counts mainly measure size. For a profile, divide each category by the institution’s total in the same period. If university i has 400 indexed papers and 80 are in chemistry, its chemistry share is 0.20. The resulting vector might be (0.20, 0.15, 0.10, …), with categories summing to one.
Apply the same rule to staff, students, basic funding, grants and collaboration partners. Keep a separate size variable—such as total publications, staff or funding—so that normalization does not erase meaningful scale differences.
Choose a counting rule
Full counting gives every institution one credit for a multi-affiliated paper. Fractional counting divides credit among institutions or authors. Neither is universally correct. Full counting reflects participation and is easy to explain; fractional counting better represents institutional contribution when papers have many affiliations. Report both when co-authorship or international affiliation is substantial.
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Keep categories comparable
Field and topic categories must remain stable across all periods. If a database revises its classification, map the old and new categories to a common taxonomy and document the mapping. Run the analysis with at least one alternative taxonomy when the result could depend on disciplinary boundaries.
3. Measure topic and disciplinary similarity
Cosine similarity for topic alignment
Cosine similarity compares the angle between two share vectors and ignores their total size:
cosine(i,j,t) = (xi,t · xj,t) / (||xi,t|| ||xj,t||)
For non-negative shares, the value ranges from 0 (no overlap) to 1 (identical composition). Calculate it for every pair in every period. Report the mean, median, interquartile range and the proportion of pairs whose score increased from the first to the last period. The Scientometrics topic-alignment design uses this type of comparison to identify positive change in institutional similarity.
Cosine similarity is transparent, but it does not explain why profiles changed. A university can become more similar because it entered a new field, because a previously dominant field declined, or because the reference taxonomy was altered. Inspect category-level changes alongside the score.
Relative specialization
Use a Relative Specialization Index, or a comparable location-quotient measure, to describe an institution’s position against the reference system. A value above the system benchmark indicates relative concentration in a field; a value below it indicates under-representation. Compare the index across periods to distinguish a shift in an institution’s own specialization from a shift in the entire system.
Profile overlap and internal diversity
Pairwise overlap measures how much two institutions share. It should be accompanied by a within-institution measure such as Rao’s quadratic diversity or a self-overlap statistic. This distinction matters:
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- High between-institution similarity plus high internal diversity can mean broad institutions are covering the same fields.
- High between-institution similarity plus falling internal diversity can mean institutions are narrowing toward the same specialties.
- Low between-institution similarity with falling internal diversity can indicate increasing specialization without convergence.
The disciplinary-profile work in the Journal of Informetrics and a 42-university comparison in the Journal of Data and Information Science show why diversity and interdisciplinarity measures can yield different conclusions. Treat the choice of index as a substantive decision, not a cosmetic one.
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Staff and student composition
Construct vectors for academic ranks, administrative staff, doctoral researchers, undergraduate students and other categories relevant to the institutions being compared. Use shares within the institution and, where available, discipline-specific composition. A rise in the share of doctoral researchers may make two universities look more alike even when their research topics remain different.
Basic and grant funding
Separate recurring basic funding from competitive grants. Compare the proportions and, in a second analysis, inflation-adjusted amounts per staff member or researcher. A common grant profile does not prove a common mission: grant portfolios can converge because the same national schemes are available to institutions with different teaching roles.
Variable-by-variable interpretation
The German 1995–2020 study demonstrates the value of this decomposition. Institutional variables can become more isomorphic in one dimension while remaining distinct in another. Report a table of trends for staff, students, basic funding and grants rather than collapsing them into one organizational-convergence number.
| Measure | Primary normalization | Useful companion |
|---|---|---|
| Staff categories | Share of total staff | Total staff and staff per researcher |
| Student categories | Share of enrolled students | Total enrollment and student-to-staff ratio |
| Basic funding | Share of institutional income | Real amount per staff member |
| Competitive grants | Share of research income | Grant amount per researcher and field mix |
5. Compare outputs without confusing volume and similarity
Publication counts, citation counts and field-normalized impact are outcomes, not substitutes for a research profile. Include them as separate variables or vectors. Two institutions may publish the same number of papers while one concentrates on a few fields and the other spreads output broadly.
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6. Measure collaboration as a network outcome
Partner distributions
Build a vector of each institution’s co-authorship or institutional-partner shares. Partners can be grouped by country, sector, institution or network community. Compare those vectors with cosine similarity or overlap, just as with topic shares.
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Network position
Add centrality, brokerage, component membership and community structure. A university can have an output profile similar to its peers while occupying a different network position—for example, acting as a bridge between otherwise separate communities. The EU-candidate study of Scopus-indexed publications illustrates why research activity and collaboration patterns should be examined together rather than inferred from publication volume.
Keep network construction consistent
Define whether an edge requires one co-authored paper, whether repeated collaborations are weighted, and how multi-institution papers are counted. Recalculate results under full and fractional counting. Network measures are especially sensitive to database coverage and to the inclusion of very large consortia.
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7. Estimate the trend and its uncertainty
Pairwise change
For each pair, calculate the change between periods, such as ΔSij = Sij,last − Sij,first. Summarize the distribution, not only its mean. Report the median change, confidence interval, percentage of positive changes and changes by institution type.
Panel models
With repeated periods, estimate a model in which pairwise similarity is the outcome and time is the predictor. Add pair fixed effects when the question is within-pair change, period effects for system-wide shocks, and controls for size, country, mission, discipline mix and prestige. Standard errors should account for the fact that each institution appears in many pairs; a naive independence assumption makes uncertainty look too small.
Bootstrap and permutation checks
Bootstrap institution pairs or institutions to obtain intervals that reflect the sample structure. A permutation test can ask whether the observed time shift is larger than expected after randomly reassigning periods or labels, provided the exchangeability assumptions are stated. Pre-specify whether the primary claim requires a positive average slope, an upward shift in the full distribution, or both.
Independent reader supportYour contribution helps us test, update, and keep practical guides available for everyone.8. Compare like with like
An aggregate increase in similarity may simply reflect a changing institutional mix. Stratify, match or weight institutions by:
- Public or private status and legal form.
- Teaching, research or mixed mission.
- Country, region and national funding regime.
- Discipline mix and degree of medical or technical specialization.
- Publication, staff and funding size.
- Prestige or prior research intensity, using a measure fixed before the outcome period.
Evidence from Russian institutions shows that private and state universities can have different diversity profiles. Pooling them without adjustment can therefore turn compositional change into an apparent convergence trend. Present both the overall result and the stratified results.
9. Run robustness checks before drawing a conclusion
Recalculate the main result under the following alternatives:
- Full versus fractional publication and collaboration counting.
- At least two field or topic taxonomies.
- Different databases or documented coverage subsets.
- Raw shares versus size-adjusted indicators.
- Shorter, longer and non-overlapping time windows.
- Inclusion and exclusion of multidisciplinary journals, reviews and conference papers.
- All institutions versus matched or stratified samples.
A conclusion that survives reasonable choices is more credible than one produced by a single index. When estimates disagree, show the disagreement and explain which substantive property each measure captures. Diversity indices are sensitive to how categories are defined; this sensitivity was visible in the 42-university comparison across Web of Science subject categories.
10. Explain possible mechanisms without overclaiming causality
Similarity is an outcome. To explain it, test whether changes coincide with institutional pressures described by institutional-isomorphism theory:
Coercive pressure
Regulation, accreditation requirements and funding rules can make organizational structures or reporting categories more uniform. Look for policy timing and exposure differences between institutions.
Mimetic pressure
Under uncertainty, institutions may imitate visible peers. Examine whether changes follow adoption by high-prestige institutions, while recognizing that correlation does not establish imitation.
Normative pressure
Professional standards, shared career systems and common evaluation practices can align staffing, publication and grant behavior. Compare fields with different professional norms where data permit.
Ranking and metric pressure
Rankings can reward a narrow set of publication, citation, internationalization or income indicators. If institutions respond to those incentives, they may become more similar on measured outputs while becoming less diverse in mission. Test this by comparing ranking-sensitive variables with dimensions that rankings do not measure, and by examining changes before and after a metric or policy is introduced.
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- Write the estimand. State whether you are measuring topic convergence, organizational isomorphism, network convergence or a combination.
- Register the frame. List institutions, identifiers, countries, types, periods, databases, taxonomies and document rules.
- Assemble raw data. Keep source counts, affiliation strings, field labels, staff categories, funding components and partner records.
- Resolve identities. Map mergers, splits and name changes to stable institution histories.
- Create period profiles. Convert each category to a share and retain totals for size controls.
- Calculate primary metrics. Use cosine similarity for topic and partner vectors; add specialization, overlap and internal diversity.
- Model change. Report pairwise differences and a panel or trend estimate with uncertainty.
- Stratify and adjust. Compare like with like and show whether the result survives controls.
- Run robustness analyses. Change counting rules, taxonomies, databases and windows.
- Publish an audit table. Include definitions, missingness, exclusions, sensitivity results and the exact interpretation of convergence.
12. How to report the result clearly
A defensible conclusion should identify the dimension, population and period in the same sentence. For example: “Among the defined public universities, topic-vector cosine similarity increased across the four five-year periods, while staff and funding profiles showed different trends.” Do not write “universities became more alike” without naming what became alike.
Include the following in a results table:
| Item | Minimum disclosure |
|---|---|
| Population | Institution types, countries, inclusion and exclusion rules |
| Time | Period boundaries and whether windows overlap |
| Data | Database, coverage date, document types and affiliation treatment |
| Profile | Categories, normalization and counting rule |
| Similarity | Metric, pair aggregation and interpretation of its scale |
| Inference | Trend model, controls, clustering or bootstrap method and interval |
| Robustness | Alternative taxonomies, databases, windows and sample restrictions |
Common failure modes and fixes
- Using rankings as the definition of similarity. Fix: measure profiles directly; rankings compress many dimensions into one order.
- Comparing raw counts. Fix: use shares for composition and retain size as a separate control.
- Changing the taxonomy mid-series. Fix: map to a stable taxonomy and report a sensitivity run.
- Ignoring mergers and name changes. Fix: maintain institution histories and stable identifiers.
- Pooling unlike institutions. Fix: stratify or match by mission, country, type and size.
- Treating publication similarity as mission similarity. Fix: add staff, students, funding and collaboration dimensions.
- Reporting only a mean. Fix: show median, dispersion, positive-pair share and the full distribution shift.
- Claiming a cause from a trend. Fix: align policy or ranking changes with timing and use designs that support stronger inference.
- Hiding database limits. Fix: state coverage and repeat the analysis on alternative data where possible.
What counts as convincing evidence?
There is no universal convergence threshold and no single global dataset that measures every dimension consistently. Set the threshold and reference population before looking at the result. Strong evidence combines a transparent rise in pairwise similarity with stable definitions, uncertainty intervals, like-for-like comparisons and robustness across reasonable specifications. It also shows where convergence does not occur. That pattern—rather than one headline number—tells you whether institutions are becoming more alike, in which respects, and at what cost to internal diversity.
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