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Measure institutional similarity as a change in comparable profiles over repeated periods—not as movement toward the same ranking position. Build an institution-by-period profile covering research topics, people, funding, outputs and collaborations; calculate pairwise similarity for each dimension; then test whether the similarity distribution rises over time. Control for mission, country, size, prestige, discipline mix and database coverage before calling the result convergence.
A university can become more similar to its peers in publication topics while becoming less similar in staffing, funding or collaboration networks. A credible answer therefore reports several dimensions separately and states the population, time windows, field taxonomy, counting rules and uncertainty.
What “becoming more alike” should mean
“More alike” is not a single observable property. It is a claim that the distance between institutions’ profiles is shrinking in a defined population and period. The first decision is therefore substantive: alike in what respect?
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- Specialization: how strongly each institution concentrates on fields relative to a reference research system.
- People: the composition of academic staff and students by discipline, rank, nationality or other available categories.
- Resources: the mix of basic institutional funding, competitive grants and other recorded sources.
- Outputs and impact: publication volume, field-normalized impact, citations and related indicators.
- Collaboration: co-authorship, partner-institution shares, network centrality and community membership.
- Mission and organization: public or private status, teaching and research orientation, degree mix and other structural features.
Each dimension needs its own comparison. Similarity in topic shares does not establish similarity in mission; similar publication counts do not establish similar network positions. State in advance whether “convergence” means a positive average trend in similarity, an upward shift in the entire distribution, or both.
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Define the population, unit and periods before collecting data
Choose the institutions and reference population
Specify the countries or region, institution type and inclusion rule. Decide whether the unit is a whole university, a research institute, a campus or a legally distinct organization. Use a stable identifier rather than a name string. Record mergers, splits, renamings and changes in legal status so that an apparent change is not an artifact of identity matching.
A reference population can be all research institutions in a country, public universities in a field, or a matched set of institutions. The choice changes the meaning of specialization and similarity. An institution can look highly specialized against a national system but ordinary against a global field-specific set.
Set observation windows
Use repeated, comparable periods and keep their length fixed. The 2026 Scientometrics topic-alignment design used four non-overlapping windows—2000–2004, 2005–2009, 2010–2014 and 2015–2019—to avoid overlapping observations. A different design can use annual data or rolling windows, but it must explain why that choice is appropriate and apply it consistently.
Longer windows stabilize small institutions’ profiles; shorter windows reveal faster change but contain more sampling noise. Do not compare a five-year publication profile with a one-year funding profile without an explicit adjustment.
Freeze the classification and counting rules
Choose the database, field or topic taxonomy, document version changes and keep the taxonomy fixed when possible. Decide how multi-field publications are assigned, how interdisciplinary records are treated, and whether outputs are counted in full for every affiliated institution or fractionally divided among institutions. Apply the same rule in every period.
Build an institution-by-period profile
Create one row for each institution-period and one column for every indicator. A practical profile contains several blocks rather than a single score:
| Block | Example variables | Recommended representation |
|---|---|---|
| Research content | Publication share in each field or topic; project share where available | Shares that sum to one within each institution-period |
| People | Staff and student shares by discipline, rank or other stable categories | Separate composition vectors for staff and students |
| Funding | Basic funding, grant funding and other recorded sources | Funding-share vector plus amounts adjusted for size where appropriate |
| Outputs | Publication count, field-normalized citations, citation-impact measures | Counts and rates reported separately; do not substitute volume for profile |
| Collaboration | Shares of co-authorship or institutional partners; network measures | Partner-distribution vector and network-position indicators |
| Context | Country, public/private status, mission, size, prestige and discipline mix | Controls, strata or matching variables |
Keep the raw counts as well as normalized shares. Shares describe composition; counts describe scale. A small specialist institute and a large comprehensive university can have identical topic shares but radically different output and resource levels.
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For composition vectors, divide each category by the institution-period total so that the entries sum to one. For volume variables, report a size measure and a per-staff or per-researcher rate when justified. Citation indicators should be field- and year-normalized before cross-field comparison. Do not normalize away the very difference under study: if institutional scale is part of convergence, analyze it as an outcome as well as a control.
Handle missing and changing coverage
Record missingness by institution, period and variable. A database expansion can make later institutions appear more diverse simply because more records are indexed. Run analyses on a stable coverage subset and report how results change when newly covered institutions or fields are included. Treat mergers and missing years explicitly rather than silently interpolating them.
Measure topic and disciplinary similarity
Use cosine similarity for transparent profile alignment
Represent institution i in period t by a field-share vector Ai,t = (a1, a2, …, ak). For institutions i and j, calculate:
cos(A,B) = (A · B) / (||A|| × ||B||)
With non-negative share vectors, the value approaches 1 when profiles point in the same direction and approaches 0 when they have little overlap. Calculate every institution pair in every period, then summarize the pairwise values with the mean, median, standard deviation or interquartile range, and selected percentiles.
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Turn similarity into a convergence test
For each pair, compute the change between periods, such as ΔSij = Sij,t2 − Sij,t1. Report the average and median change, the proportion of pairs with positive change, and the confidence interval for the trend. A positive average can hide a polarized distribution in which some institutions converge and others diverge, so show the full distribution or its quantiles.
The topic-alignment literature uses positive change in cosine similarity as evidence that institutions’ research profiles are becoming more aligned. That interpretation is valid only for the chosen taxonomy, database and population; it is not a universal convergence threshold.
Check alternative similarity measures
Cosine similarity is easy to interpret, but it ignores some distributional features. Add profile-overlap measures or a distance measure suited to compositional data when the research question requires it. Use the same measure across periods and explain how zeros, rare fields and interdisciplinary records are handled.
Measure specialization and internal diversity together
Relative Specialization Index
For each institution and field, compare the institution’s field share with that field’s share in the reference system. Document the exact convention; one common form is RSI = (institution field share ÷ reference-system field share) − 1. Positive values indicate over-representation relative to the reference system, while negative values indicate under-representation. The index describes position, not convergence by itself. Convergence requires comparing the entire RSI profile across institutions and periods.
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Profile overlap
Calculate how much of two institutions’ field distributions occupies the same categories. Overlap can be easier to explain to non-specialists than a distance metric, but it remains sensitive to the granularity of the taxonomy. A broad six-field classification will usually show more overlap than a fine-grained topic classification.
Within-institution diversity and Rao’s quadratic diversity
Between-institution similarity can rise because institutions are broadening, or because all institutions are narrowing toward the same specialty. Measure internal diversity separately. Rao’s quadratic diversity combines category shares with a distance between categories, commonly represented as RaoQ = Σ pi pj dij. Use a documented field-distance matrix and report how the result changes under alternative matrices.
The distinction matters: high pairwise overlap with low internal diversity indicates homogenized specialization, while high pairwise overlap with high internal diversity indicates broad profiles that happen to contain similar proportions.
Test organizational convergence variable by variable
Do not collapse staff, students and money into one institutional-isomorphism score. Build separate vectors for each structural dimension and compare them over time.
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Staff composition
Compare shares by discipline, academic rank, contract type or other categories consistently available across periods. A shift toward similar disciplinary staffing can occur even when publication topics remain different.
Student composition
Use the same logic for student fields, levels and other stable categories. Distinguish enrollment composition from research-student composition when the data permit; they represent different institutional functions.
Basic and grant funding
Calculate the share of resources supplied through basic institutional funding and competitive grants separately. Also retain inflation-adjusted amounts and size-normalized rates where possible. A common funding mix can reflect policy design rather than institutional imitation, so interpret the mechanism only after controlling for country and institution type.
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A longitudinal study of German public universities covering 1995–2020 demonstrates why this variable-by-variable design is necessary: some institutional variables can become more isomorphic while others do not. An aggregate score would conceal that pattern.
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Publication volume is an output level, not a research profile. Two institutions may publish the same number of papers while specializing in different fields. Report at least three separate views:
- Volume: total publications or projects, with the counting rule stated.
- Composition: field or topic shares used for similarity.
- Impact: field- and year-normalized citation indicators or other documented impact measures.
Use full counting when the unit is institutional participation and fractional counting when you want contributions to sum across co-affiliations. Present both in a robustness check if the choice could alter the conclusion. Do not treat higher citation counts as evidence that institutions are more alike; impact can rise while profiles diverge.
Measure collaboration convergence as a network outcome
Construct co-authorship and institutional-partner networks for each period. Compare the distribution of partners, not just the number of collaborations. Useful outcomes include:
- the share of collaborations involving domestic, international, public, private or sector-specific partners, when consistently coded;
- pairwise similarity in partner-distribution vectors;
- degree, betweenness or other centrality measures, with the network definition stated;
- community or cluster membership and the stability of those communities over time;
- the concentration of partnerships, using a documented concentration index.
The EU-candidate institution study based on Scopus-indexed publications examines research activity and collaboration patterns together. Its design illustrates why collaboration should remain a separate outcome: institutions can publish similar volumes yet occupy different positions in the collaboration network.
Decide whether a co-authored paper contributes one tie per institution pair, fractional tie weight, or another rule. Apply the same treatment to all periods and distinguish missing partnership data from genuine absence of collaboration.
Estimate trends and uncertainty
Pairwise trend models
At the simplest level, regress pairwise similarity on time and report the slope with a confidence interval. For panel data, include institution-pair fixed effects when appropriate, so the estimate reflects within-pair change rather than a different mix of pairs in each period. Cluster uncertainty at a level consistent with the repeated observations.
Bootstrap the pairs
Because pairwise observations are not independent—each institution appears in many pairs—ordinary standard errors can be too small. Resample institutions, recompute all pairwise similarities, and use the resulting distribution for confidence intervals. State whether the bootstrap resamples institutions, institution pairs or both.
Test distributional change
Report more than a mean. Compare medians, dispersion, lower and upper quantiles, and the share of pairs whose similarity increased. A stochastic-distribution comparison can show whether the entire distribution shifted upward or whether only a small group moved.
Pre-specify the convergence rule
Before examining results, write the decision rule: for example, a positive time slope with a confidence interval excluding zero and an upward shift in the median. There is no universal convergence threshold established across all research institutions, so the threshold and reference population must be justified rather than imported from another study.
Run robustness checks that expose fragile conclusions
Re-estimate the result under plausible alternatives and place the choices next to the reported estimates:
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- Counting: compare full and fractional publication or collaboration counting.
- Taxonomy: repeat the analysis with a broad and a fine field classification, and with an alternative topic model if available.
- Database: compare the main database with a stable-coverage subset or another documented source.
- Window: test non-overlapping periods against an alternative window length.
- Size: compare raw profiles, size-normalized rates and analyses weighted or unweighted by institution.
- Outliers: repeat results after excluding mergers, very small institutions and extreme multidisciplinary institutions, while reporting how many were removed.
- Diversity measure: compare cosine or overlap results with a documented diversity index and Rao’s quadratic diversity.
A comparison of 42 universities using Web of Science subject categories found that conclusions can vary by diversity and interdisciplinarity measure. That sensitivity is a substantive result, not a nuisance: it tells the reader which definition of “alike” drives the finding.
Compare like with like
Aggregate similarity can rise simply because the institutional mix changed. Stratify, match or adjust for:
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- country, region and regulatory system;
- research mission and teaching orientation;
- discipline mix and presence of medical, technical or social-science units;
- size, age and resource base;
- prestige or prior research position.
Then report both within-stratum convergence and between-stratum differences. Evidence from Russian institutions shows why this matters: private and state universities can have different diversity profiles, so an overall trend can conceal compositional change.
Matching institutions on baseline profile and size can make the comparison more credible, but matching also changes the target population. State clearly whether the estimate applies to all institutions or only to comparable pairs.
Explain mechanisms without overstating causality
Similarity is descriptive. To argue why it occurred, connect the timing of convergence to plausible institutional pressures and test competing explanations.
Coercive pressure
Regulation, accreditation rules, funding formulas or reporting requirements can push institutions toward common structures. Examine policy start dates and exposure differences, rather than assuming every post-policy change is caused by the policy.
Mimetic pressure
Institutions may imitate prominent peers under uncertainty, especially when adopting research centers, performance targets or strategic fields. Test whether later adopters move toward earlier leaders, controlling for shared national trends.
Normative pressure
Professional standards, disciplinary organizations and common career expectations can align staffing, evaluation and research practices. Compare fields with different professional structures where possible.
Rankings and metric regimes
Rankings can narrow diversity when institutions optimize for the same measured outputs, but the mechanism must be demonstrated rather than inferred from a rising similarity score. Test whether convergence is concentrated in ranking-related indicators and whether mission-specific dimensions remain distinct.
Panel, matched or policy-exposure designs can strengthen a causal explanation. A descriptive similarity trend alone cannot identify which pressure produced it.
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- Write the estimand. State whether the target is topic convergence, organizational isomorphism, collaboration convergence or a combination reported as separate outcomes.
- Register the population and periods. List institutions, countries, institution types, years, identifiers and rules for mergers or exits.
- Assemble raw records. Retain publication, staff, student, funding and collaboration records before aggregation.
- Freeze definitions. Record database versions, field taxonomy, topic assignment, counting rule, currency treatment and missing-data rules.
- Create profiles. Produce institution-period vectors for each dimension and preserve totals for scale analysis.
- Calculate pairwise measures. Compute cosine similarity and at least one overlap or distance measure for each relevant vector.
- Calculate specialization and diversity. Produce RSI profiles, profile overlap and within-institution Rao diversity.
- Analyze networks. Build period-specific collaboration networks and calculate partner similarity and network position.
- Estimate change. Report pairwise slopes, median and quantile shifts, positive-change shares and uncertainty.
- Stress-test the result. Repeat the analysis with alternative taxonomies, databases, counting rules, windows and size treatments.
- Stratify and interpret. Compare like institutions, then examine policy, ranking, professional or imitation mechanisms.
- Publish an audit trail. Provide a data dictionary, inclusion list, formulas, code or reproducible calculation description, and every sensitivity result needed to reproduce the conclusion.
How to report the result
A reader should be able to tell exactly what became more alike, among whom and under which definition. A compact reporting table can use this structure:
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| Question | Report |
|---|---|
| Which institutions? | Population, country or region, institution type, identifier rules and exclusions |
| Which periods? | Start and end dates, window length and whether windows overlap |
| Which profile? | Fields, topics, staff, students, funding, outputs or collaboration variables |
| Which comparison? | Cosine, overlap, RSI, Rao diversity, network measure or another named statistic |
| What changed? | Mean, median, dispersion, quantiles, positive-change share and slope |
| How certain? | Confidence interval, bootstrap or panel specification and clustering choice |
| Could composition explain it? | Strata or controls for mission, country, size, prestige and discipline mix |
| Is it robust? | Alternative taxonomy, database, counting rule, window and normalization results |
Use a chart of the pairwise-similarity distribution for each period alongside the numerical estimates. A single upward line can hide widening inequality, a cluster of converging institutions or a database-coverage break.
Common failure modes and fixes
Using rankings as the convergence measure
Problem: Similar ranks can result from different research portfolios, and rank formulas change. Fix: Treat rankings, if used at all, as one contextual variable; measure profiles directly.
Calling higher publication volume convergence
Problem: Growth in output says nothing about whether topic mixes or organizations are alike. Fix: Analyze composition and scale separately.
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Problem: A revised field taxonomy can manufacture apparent convergence or divergence. Fix: map records to a stable taxonomy and run a sensitivity analysis for unavoidable changes.
Ignoring internal diversity
Problem: Institutions may overlap more because each is narrowing to a common specialty. Fix: report Rao diversity or another within-institution measure beside pairwise overlap.
Treating all pairs as independent
Problem: Reusing each institution in many pairs understates uncertainty. Fix: bootstrap institutions or use an appropriate panel model.
Combining unlike institutions without controls
Problem: A changing share of private, specialist or newly founded institutions can drive the aggregate result. Fix: stratify or match by status, mission, country, size, prestige and discipline mix.
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Overclaiming a mechanism
Problem: A positive similarity slope does not prove regulation, rankings or imitation caused it. Fix: align timing, compare exposed and less-exposed institutions and describe the evidence as associative unless the design supports causality.
What a defensible conclusion looks like
A strong conclusion names the dimension and population: for example, “Among the defined institutions, topic-share cosine similarity increased across the four five-year periods, while staff and funding profiles showed different trends.” It reports the uncertainty and sensitivity, identifies whether the full distribution shifted, and states the database, taxonomy, counting rule and controls.
There is no single global dataset or threshold that establishes convergence across every institutional dimension. The most defensible answer is therefore a profile-based, multi-dimensional result: institutions are becoming more alike only where a pre-specified similarity measure rises consistently, survives reasonable robustness checks and is not explained solely by a changing mix of institutions or data coverage.
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