{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,8,24]],"date-time":"2026-08-24T15:29:03Z","timestamp":1787585343894,"version":"build-2736575974"},"reference-count":44,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2026,8,22]],"date-time":"2026-08-22T00:00:00Z","timestamp":1787356800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The rule of law can be considered as a multidimensional institutional phenomenon, which emerges through interplay between legal, governance and administrative institutions. The paper offers an exploratory statistical modeling approach to find empirical patterns in national rule-of-law profiles according to the 2024 World Justice Project (WJP) Rule of Law Index. Eight dimensions of the index are considered to identify differences between countries and similarities of their multidimensional institutional performance. Principal Component Analysis reveals strong associations between eight dimensions, which are structured along the same performance institutional scale; the first principal component explains 85.7% of the overall variation and two principal components explain 92.5% of it. K-Means, hierarchical and DBSCAN clustering methods are then used to examine the empirical similarities between countries. While the six-cluster solution of K-Means offers distinct group descriptions, low bootstrap stability of this solution suggests that these groups cannot be regarded as fixed rule-of-law regimes. In addition, the Random Forest analysis reveals Regulatory Enforcement, Absence of Corruption, and Criminal Justice as the three dimensions, which contribute to the empirical differentiation of the described profiles the most. In general, the results imply that international variations in rule-of-law performance are viewed as heterogeneous locations in a multidimensional institution space, rather than as stable and distinct legal systems. The above-presented methodology allows for an exploratory approach to analyze international variations in rule-of-law performance that considers the limitations of cross-section data and instability of clusters.<\/jats:p>","DOI":"10.3390\/e28090942","type":"journal-article","created":{"date-parts":[[2026,8,24]],"date-time":"2026-08-24T14:49:34Z","timestamp":1787582974000},"page":"942","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["An Exploratory Statistical Modeling Framework for National Rule-of-Law Profiles"],"prefix":"10.3390","volume":"28","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5468-475X","authenticated-orcid":false,"given":"Sadullah","family":"\u00c7elik","sequence":"first","affiliation":[{"name":"Department of International Trade and Finance, Ayd\u0131n Adnan Menderes University, Ayd\u0131n 09000, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8593-6139","authenticated-orcid":false,"given":"Muhammet Ali","family":"K\u00f6ro\u011flu","sequence":"additional","affiliation":[{"name":"Department of Social Work, U\u015fak University, U\u015fak 64000, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9043-1773","authenticated-orcid":false,"given":"Cemile Zehra","family":"K\u00f6ro\u011flu","sequence":"additional","affiliation":[{"name":"Department of Social Work, U\u015fak University, U\u015fak 64000, T\u00fcrkiye"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2026,8,22]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"North, D.C. (1990). Institutions, Institutional Change and Economic Performance, Cambridge University Press.","DOI":"10.1017\/CBO9780511808678"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Kaufmann, D., Kraay, A., and Mastruzzi, M. (2010). The Worldwide Governance Indicators: Methodology and Analytical Issues, World Bank.","DOI":"10.1596\/1813-9450-5430"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"165","DOI":"10.1111\/j.1468-0491.2008.00391.x","article-title":"What Is Quality of Government? A Theory of Impartial Government Institutions","volume":"21","author":"Rothstein","year":"2008","journal-title":"Governance"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1501\/Intrel_0000000302","article-title":"Rule of Law and Constitutional Democracy","volume":"46","author":"Elena","year":"2015","journal-title":"Turk. Yearb. Int. Relat."},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Reidy, D.A. (2014). Rule of Law. The Cambridge Rawls Lexicon, Cambridge University Press.","DOI":"10.1017\/CBO9781139026741.194"},{"key":"ref_6","unstructured":"Botero, J.C., Ponce, A., Bostrom, A., Campbell, E., Davis, J., Evangelides, A., Fuller, J., Littlejohn, L., Rodr\u00edguez Cajamarca, N., and Wanner, K. (2024). The World Justice Project Rule of Law Index 2024, World Justice Project."},{"key":"ref_7","unstructured":"Botero, J.C., and Ponce, A. (2011). Measuring the Rule of Law. SSRN Electron. J., Available online: https:\/\/papers.ssrn.com\/sol3\/papers.cfm?abstract_id=1966257&__cf_chl_tk=nCrmOfJbC6vv5PZogxzq2f5dw1QPiHCy_0MF2JKhWrQ-1787349374-1.0.1.1-BfQloq0K7Sgz6uel2NpcNYJX5JjKbwmgMNpRHB.6pxk."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"262","DOI":"10.1111\/j.1467-6435.2012.00538.x","article-title":"How to Measure the Rule of Law","volume":"65","author":"Voigt","year":"2012","journal-title":"Kyklos"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S1744137412000148","article-title":"How (Not) to Measure Institutions","volume":"9","author":"Voigt","year":"2013","journal-title":"J. Institutional Econ."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1146\/annurev.polisci.10.081205.095418","article-title":"What Have We Learned About the Causes of Corruption from Ten Years of Cross-National Empirical Research?","volume":"10","author":"Treisman","year":"2007","journal-title":"Annu. Rev. Political Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"347","DOI":"10.1111\/gove.12035","article-title":"What Is Governance?","volume":"26","author":"Fukuyama","year":"2013","journal-title":"Governance"},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"222","DOI":"10.1093\/jleo\/15.1.222","article-title":"The Quality of Government","volume":"15","year":"1999","journal-title":"J. Law Econ. Organ."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1163\/15691330-12341259","article-title":"Sub-Components of the Rule of Law: Reassessing the Relevance of Diminished Subtypes","volume":"12","author":"Skaaning","year":"2013","journal-title":"Comp. Sociol."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"M\u00f8ller, J., and Skaaning, S.-E. (2014). Explaining Cross-National Differences in Adherence to the Rule of Law. The Rule of Law, Palgrave Macmillan UK.","DOI":"10.1057\/9781137320612"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"579","DOI":"10.1017\/S1744137415000545","article-title":"Varieties of Legal Systems: Towards a New Global Taxonomy","volume":"12","author":"Siems","year":"2016","journal-title":"J. Institutional Econ."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"313","DOI":"10.1111\/1475-6765.00085","article-title":"Differentiating the Democratic Performance of the West","volume":"42","author":"Foweraker","year":"2003","journal-title":"Eur. J. Polit. Res."},{"key":"ref_17","first-page":"1","article-title":"International Indices as Models for the Rule of Law Scoreboard of the European Union: Methodological Issues","volume":"21","author":"Jakab","year":"2017","journal-title":"SSRN Electron. J."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"100","DOI":"10.1111\/lsi.12175","article-title":"Measuring the Rule of Law: A Comparison of Indicators","volume":"42","author":"Versteeg","year":"2017","journal-title":"Law Soc. Inq."},{"key":"ref_19","first-page":"73","article-title":"Development And the Rule of Law: A Comparative Study","volume":"BI","year":"2017","journal-title":"Rev. Fac. Direito UFMG"},{"key":"ref_20","doi-asserted-by":"crossref","unstructured":"Jakab, A., and Lorincz, V.O. (2020). Rule of Law Indices and How They Could Be Used in the EU Rule of Law Crisis. SSRN Electron. J., 4\u20135.","DOI":"10.2139\/ssrn.3513250"},{"key":"ref_21","first-page":"278","article-title":"Rule of Law and Economic Growth","volume":"1","author":"Shevchuk","year":"2021","journal-title":"Financ. Credit. Act. Probl. Theory Pract."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"146","DOI":"10.32914\/i.55.1-2.12","article-title":"Public Interest and Good Governance in the Rule of Law Aspect","volume":"55","author":"Berendieieva","year":"2022","journal-title":"Informatologia"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"56","DOI":"10.69893\/gjle.2023.000049","article-title":"Strengthening Rule of Law to Control Crime: A Cross Country Analysis","volume":"VI","author":"Pai","year":"2023","journal-title":"Gnlu J. Law Econ."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"191","DOI":"10.1007\/s40803-022-00181-x","article-title":"Triangulation of Theoretical and Empirical Conceptualizations Related to the Rule of Law","volume":"15","author":"Lacko","year":"2023","journal-title":"Hague J. Rule Law"},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"9","DOI":"10.31338\/1641-2478pe.2.23.1","article-title":"The Rule of Law in the National and Supranational Context","volume":"2023","year":"2023","journal-title":"Przegl\u0105d Eur."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"37","DOI":"10.25019\/perspol\/24.17.0.4","article-title":"Deterioration of the Rule of Law and the Effects Over Economic Development-A Comparative Analysis on the United States of America, Singapore and Romania","volume":"17","author":"Brad","year":"2024","journal-title":"Perspect. Politice"},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"714","DOI":"10.1080\/13501763.2025.2451365","article-title":"Unravelling National Governments\u2019 Positions on EU Rule of Law Enforcement: Structural, Semi-Structural and Ideological Factors","volume":"33","author":"Closa","year":"2025","journal-title":"J. Eur. Public Policy"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"399","DOI":"10.1163\/15718123-bja10219","article-title":"Clearing Muddied Waters: The Relationship Between the Rule of Law and the Fight against Corruption in the Jurisprudence of the European Court of Human Rights","volume":"25","author":"Jungfleisch","year":"2025","journal-title":"Int. Crim. Law Rev."},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"38","DOI":"10.22158\/elp.v8n1p38","article-title":"Research on the Integration of Ecological Environment Space Governance and Rule of Law","volume":"8","author":"Sun","year":"2025","journal-title":"Econ. Law Policy"},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1080\/13572334.2024.2443882","article-title":"The Role of National Parliaments and European Parliament as Guardians of European Values: The Case of Democracy and the Rule of Law in Cyprus","volume":"31","author":"Kalaitzaki","year":"2025","journal-title":"J. Legis. Stud."},{"key":"ref_31","doi-asserted-by":"crossref","unstructured":"Acemoglu, D., and Robinson, J. (2012). Why Nations Fail: The Origins of Power, Prosperity, and Poverty, Random House.","DOI":"10.1355\/ae29-2j"},{"key":"ref_32","doi-asserted-by":"crossref","unstructured":"Levitsky, S., and Way, L.A. (2010). Competitive Authoritarianism, Cambridge University Press.","DOI":"10.1017\/CBO9780511781353"},{"key":"ref_33","doi-asserted-by":"crossref","unstructured":"Le Clercq, J.A., and Abreu Sacramento, J.P. (2020). Rebuilding the State Institutions, Springer International Publishing.","DOI":"10.1007\/978-3-030-31314-2"},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"20150202","DOI":"10.1098\/rsta.2015.0202","article-title":"Principal Component Analysis: A Review and Recent Developments","volume":"374","author":"Jolliffe","year":"2016","journal-title":"Philos. Trans. R. Soc. A Math. Phys. Eng. Sci."},{"key":"ref_35","doi-asserted-by":"crossref","unstructured":"Jolliffe, I.T. (2006). Principal Component Analysis, Springer.","DOI":"10.1002\/0470013192.bsa501"},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1016\/0377-0427(87)90125-7","article-title":"Silhouettes: A Graphical Aid to the Interpretation and Validation of Cluster Analysis","volume":"20","author":"Rousseeuw","year":"1987","journal-title":"J. Comput. Appl. Math."},{"key":"ref_37","first-page":"281","article-title":"Some Methods for Classification and Analysis of Multivariate Observations","volume":"Volume 1","author":"MacQueen","year":"1967","journal-title":"Proceedings of the 5th Berkeley Symposium on Mathematical Statistics and Probability"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1109\/TIT.1982.1056489","article-title":"Least Squares Quantization in PCM","volume":"28","author":"Lloyd","year":"1982","journal-title":"IEEE Trans. Inf. Theory"},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"100","DOI":"10.2307\/2346830","article-title":"Algorithm AS 136: A K-Means Clustering Algorithm","volume":"28","author":"Hartigan","year":"1979","journal-title":"Appl. Stat."},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Hastie, T., Tibshirani, R., and Friedman, J. (2009). The Elements of Statistical Learning, Springer.","DOI":"10.1007\/978-0-387-84858-7"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"3595","DOI":"10.1080\/03610929008830400","article-title":"A Class of Invariant Consistent Tests for Multivariate Normality","volume":"19","author":"Henze","year":"1990","journal-title":"Commun. Stat. Theory Methods"},{"key":"ref_42","unstructured":"Tabachnick, B.G., and Fidell, L.S. (2019). Using Multivariate Statistics, Pearson. [7th ed.]."},{"key":"ref_43","doi-asserted-by":"crossref","first-page":"583","DOI":"10.1080\/01621459.1952.10483441","article-title":"Use of Ranks in One-Criterion Variance Analysis","volume":"47","author":"Kruskal","year":"1952","journal-title":"J. Am. Stat. Assoc."},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"5","DOI":"10.1023\/A:1010933404324","article-title":"Random Forests","volume":"45","author":"Breiman","year":"2001","journal-title":"Mach. Learn."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/9\/942\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,8,24]],"date-time":"2026-08-24T14:53:03Z","timestamp":1787583183000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/28\/9\/942"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,8,22]]},"references-count":44,"journal-issue":{"issue":"9","published-online":{"date-parts":[[2026,9]]}},"alternative-id":["e28090942"],"URL":"https:\/\/doi.org\/10.3390\/e28090942","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,22]]}}}