{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T23:47:06Z","timestamp":1770421626324,"version":"3.49.0"},"reference-count":29,"publisher":"Springer Science and Business Media LLC","issue":"3-4","license":[{"start":{"date-parts":[[2025,9,1]],"date-time":"2025-09-01T00:00:00Z","timestamp":1756684800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T00:00:00Z","timestamp":1769040000000},"content-version":"vor","delay-in-days":143,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100004350","name":"Studienstiftung des Deutschen Volkes","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100004350","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100018755","name":"Universit\u00e4t Trier","doi-asserted-by":"crossref","id":[{"id":"10.13039\/100018755","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["AStA Wirtsch Sozialstat Arch"],"published-print":{"date-parts":[[2025,9]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Generalized variance functions (GVFs) are widely used in official statistics to approximate sampling variances when direct variance estimation is impractical. However, their reliability is highly context-dependent. This study evaluates GVF performance through guided modeling strategies and simulation studies across diverse sampling designs and data settings. Results show that GVFs perform well under ideal conditions, but their accuracy deteriorates in the presence of mixture distributions, rare domains, unstable variances or poor groupings. We provide practical recommendations on grouping variables, selecting training samples, and applying diagnostic checks, emphasizing predictive validity over model fit. Our findings underscore the importance of careful quality assessment for GVFs and the need for application-specific validation prior to use.<\/jats:p>","DOI":"10.1007\/s11943-025-00365-5","type":"journal-article","created":{"date-parts":[[2026,1,22]],"date-time":"2026-01-22T16:59:50Z","timestamp":1769101190000},"page":"205-221","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Assessing the quality of generalized variance functions","Qualit\u00e4tsbewertung verallgemeinerter Varianzfunktionale"],"prefix":"10.1007","volume":"19","author":[{"given":"Inken","family":"Siems","sequence":"first","affiliation":[]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8285-5667","authenticated-orcid":false,"given":"Ralf","family":"M\u00fcnnich","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2026,1,22]]},"reference":[{"key":"365_CR1","first-page":"20","volume":"6","author":"W Bihler","year":"2016","unstructured":"Bihler\u00a0W, Zimmermann\u00a0D (2016) Die Neue Mikrozensusstichprobe ab 2016. WISTA 6:20\u201329","journal-title":"WISTA"},{"key":"365_CR2","doi-asserted-by":"publisher","first-page":"233","DOI":"10.1007\/s11943-017-0214-8","volume":"11","author":"JP Burgard","year":"2017","unstructured":"Burgard\u00a0JP, Kolb\u00a0JP, Merkle\u00a0H, M\u00fcnnich\u00a0R (2017) Synthetic data for open and reproducible methodological research in social sciences and official statistics. AStA Wirtsch Sozialstat Arch 11:233\u2013244","journal-title":"AStA Wirtsch Sozialstat Arch"},{"issue":"3","key":"365_CR3","doi-asserted-by":"publisher","first-page":"301","DOI":"10.1111\/j.1467-842X.2012.00682.x","volume":"54","author":"R Cao","year":"2012","unstructured":"Cao\u00a0R, Vilar\u00a0JA, Vilar\u00a0JM (2012) Generalised variance function estimation for binary variables in large-scale sample surveys. Aust N Z J Stat 54(3):301\u2013324","journal-title":"Aust N Z J Stat"},{"key":"365_CR22","series-title":"Tech. rep. Technical Paper 77","volume-title":"Current population survey. Design and methodology","author":"US Census Bureau","year":"2019","unstructured":"Census Bureau\u00a0US (2019) Current population survey. Design and methodology. Tech. rep. Technical Paper 77"},{"key":"365_CR4","volume-title":"Evaluation of generalized variance function estimators for the us current employment survey","author":"M Cho","year":"2002","unstructured":"Cho\u00a0M, Eltinge\u00a0J, Gershunskaya\u00a0J, Huff\u00a0L (2002) Evaluation of generalized variance function estimators for the us current employment survey. Proceedings of the American Statistical Association, Survey Research Methods Section."},{"issue":"1","key":"365_CR5","doi-asserted-by":"publisher","first-page":"63","DOI":"10.2478\/jos-2014-0004","volume":"30","author":"M Cho","year":"2014","unstructured":"Cho\u00a0M, Eltinge\u00a0JL, Gershunskaya\u00a0J, Huff\u00a0L (2014) Evaluation of generalized variance functions in the analysis of complex survey data. J\u00a0Off Stat 30(1):63\u201390","journal-title":"J Off Stat"},{"key":"365_CR6","series-title":"Tech. rep","first-page":"1","volume-title":"European Statistics Code of Practice","author":"Committee, European Statistical System","year":"2018","unstructured":"Committee, European Statistical System (2018) European Statistics Code of Practice. Tech. rep. eurostat, Luxembourg, pp\u00a01\u201320"},{"key":"365_CR7","volume-title":"Calibration and evaluation of generalized variance functions","author":"J Gershunskaya","year":"2013","unstructured":"Gershunskaya\u00a0J, Dorfman\u00a0A (2013) Calibration and evaluation of generalized variance functions. Proceedings of Joint Statistical Meetings, Survey Methods Section."},{"key":"365_CR8","first-page":"236","volume-title":"Foundations of statistical inference","author":"J Hajek","year":"1971","unstructured":"Hajek\u00a0J (1971) Comment on An essay on the logical foundations of survey sampling by Basu, D. In: Godambe\u00a0DA, Sprott et\u00a0al (eds) Foundations of statistical inference. Holt, Rinehart and Winston, p\u00a0236"},{"key":"365_CR9","series-title":"Australian Bureau of Statistics. Catalogue No. 6269.0","volume-title":"Information paper: survey design and estimation for the labour force survey","author":"P Harper","year":"2005","unstructured":"Harper\u00a0P (2005) Information paper: survey design and estimation for the labour force survey. Australian Bureau of Statistics. Catalogue No. 6269.0"},{"issue":"260","key":"365_CR10","doi-asserted-by":"publisher","first-page":"663","DOI":"10.1080\/01621459.1952.10483446","volume":"47","author":"DG Horvitz","year":"1952","unstructured":"Horvitz\u00a0DG, Thompson\u00a0DJ (1952) A\u00a0generalization of sampling without replacement from a\u00a0finite universe. J\u00a0Am Stat Assoc 47(260):663\u2013685","journal-title":"J Am Stat Assoc"},{"key":"365_CR11","first-page":"9","volume":"6","author":"J Hundenborn","year":"2019","unstructured":"Hundenborn\u00a0J, Enderer\u00a0J (2019) Die Neuregelung des Mikrozensus ab 2020. WISTA 6:9\u201317","journal-title":"WISTA"},{"key":"365_CR12","series-title":"ETS Research Report Series 1987.1","first-page":"1","volume-title":"Generalized variance functions for a\u00a0complex sample survey","author":"E Johnson","year":"1987","unstructured":"Johnson\u00a0E, King\u00a0B (1987) Generalized variance functions for a\u00a0complex sample survey. ETS Research Report Series 1987.1, pp\u00a01\u201336"},{"key":"365_CR13","volume-title":"The theory of dispersion models. Monographs on statistics and applied probability","author":"B J\u00f8rgensen","year":"1997","unstructured":"J\u00f8rgensen\u00a0B (1997) The theory of dispersion models. Monographs on statistics and applied probability. Chapman and Hall, London"},{"key":"365_CR14","volume-title":"Sampling: design and analysis","author":"S Lohr","year":"2010","unstructured":"Lohr\u00a0S (2010) Sampling: design and analysis, 2nd\u00a0edn. Brooks Cole, Boston","edition":"2"},{"key":"365_CR15","volume-title":"Calculating generalized variance functions with a\u00a0single-series model in the current population survey","author":"J McIllece","year":"2016","unstructured":"McIllece\u00a0J (2016) Calculating generalized variance functions with a\u00a0single-series model in the current population survey. Paper presented at the 2016 Joint Statistical Meetings, Proceedings of the Section on Survey Research Methods. American Statistical Association"},{"key":"365_CR16","series-title":"JSM\u2014Survey Research Methods Section","volume-title":"On generalized variance functions for sample means and medians","author":"J McIllece","year":"2018","unstructured":"McIllece\u00a0J (2018) On generalized variance functions for sample means and medians. JSM\u2014Survey Research Methods Section"},{"issue":"2","key":"365_CR17","first-page":"24","volume":"15","author":"R M\u00fcnnich","year":"2021","unstructured":"M\u00fcnnich\u00a0R, Schnell\u00a0R, Brenzel\u00a0H, Dieckmann\u00a0H, Dr\u00e4ger\u00a0S, Emmenegger\u00a0J, H\u00f6cker\u00a0P, Kopp\u00a0J, Merkle\u00a0H, Neufang\u00a0K, Obersneider\u00a0M, Reinhold\u00a0J, Schaller\u00a0J, Schmaus\u00a0S, Stein\u00a0P (2021) A\u00a0population based regional dynamic microsimulation of Germany: the MikroSim model. Method Data Anal 15(2):24","journal-title":"Method Data Anal"},{"key":"365_CR18","volume-title":"Proceedings of the European Conference on Quality in Official Statistics (Q2004)","author":"P Pavone","year":"2004","unstructured":"Pavone\u00a0P, Russo\u00a0A (2004) Generalized variance functions in the Italian labour force survey. In: Proceedings of the European Conference on Quality in Official Statistics (Q2004) Mainz"},{"key":"365_CR19","series-title":"Tech. rep. ST170070","volume-title":"Construction and assessment of generalized variance functions for an establishment survey","author":"K Roche","year":"2017","unstructured":"Roche\u00a0K, Gershunskaya\u00a0J (2017) Construction and assessment of generalized variance functions for an establishment survey. Tech. rep. ST170070. U.S. Bureau of Labor Statistics"},{"key":"365_CR20","volume-title":"Statistics Canada International Symposium Series: Proceedings","author":"Statistics Canada","year":"2002","unstructured":"Statistics Canada (2002) Use of generalized variance function models in inference from social and economic survey data. In: Statistics Canada International Symposium Series: Proceedings. Statistics Canada, Ottawa"},{"key":"365_CR21","first-page":"579","volume-title":"Statistics: applications and new directions","author":"MCK Tweedie","year":"1984","unstructured":"Tweedie\u00a0MCK (1984) An index which distinguishes between some important exponential families. In: Ghosh\u00a0JK, Roy\u00a0J (eds) Statistics: applications and new directions Proceedings of the Indian Statistical Institute Golden Jubilee International Conference. Indian Statistical Institute, Calcutta, pp\u00a0579\u2013604"},{"key":"365_CR23","series-title":"Tech. rep. NCES 95-342","volume-title":"Design Effects and Generalized Variance Functions for the 1990\u201391 Schools and Staffing Survey","author":"U.S. Department of Education, National Center for Education Statistics","year":"1995","unstructured":"U.S. Department of Education, National Center for Education Statistics (1995) Design Effects and Generalized Variance Functions for the 1990\u201391 Schools and Staffing Survey. Tech. rep. NCES 95-342. U.S. Department of Education, Washington, DC"},{"issue":"398","key":"365_CR24","doi-asserted-by":"publisher","first-page":"499","DOI":"10.1080\/01621459.1987.10478454","volume":"82","author":"R Valliant","year":"1987","unstructured":"Valliant\u00a0R (1987) Generalized variance functions in stratified two-stage sampling. J\u00a0Am Stat Assoc 82(398):499\u2013508","journal-title":"J Am Stat Assoc"},{"key":"365_CR25","first-page":"344","volume-title":"Finite population sampling and inference","author":"R Valliant","year":"2000","unstructured":"Valliant\u00a0R, Dorfman\u00a0A, Royall\u00a0R (2000) Generalized variance functions. In: Finite population sampling and inference. Wiley, pp\u00a0344\u2013348 (Chap. 10.3.)"},{"issue":"425","key":"365_CR26","first-page":"65","volume":"89","author":"FT Wang","year":"1994","unstructured":"Wang\u00a0FT, Scott\u00a0DW (1994) The L1 method for robust non-parametric regression. J\u00a0Am Stat Assoc 89(425):65\u201376","journal-title":"J Am Stat Assoc"},{"key":"365_CR27","volume-title":"Introduction to variance estimation","author":"KM Wolter","year":"2007","unstructured":"Wolter\u00a0KM (2007) Introduction to variance estimation, 2nd\u00a0edn. Springer, New York","edition":"2"},{"issue":"4","key":"365_CR28","doi-asserted-by":"publisher","first-page":"571","DOI":"10.2478\/jos-2023-0026","volume":"39","author":"Y You","year":"2023","unstructured":"You\u00a0Y, Hidiroglou\u00a0M (2023) Application of sampling variance smoothing methods for small area proportion estimation. J\u00a0Off Stat 39(4):571\u2013590","journal-title":"J Off Stat"},{"issue":"2","key":"365_CR29","doi-asserted-by":"publisher","first-page":"150","DOI":"10.1080\/24754269.2019.1664372","volume":"3","author":"G Zhang","year":"2019","unstructured":"Zhang\u00a0G, Cheng\u00a0Y, Lu\u00a0Y (2019) Generalised variance functions for longitudinal survey data. Stat Theory Relat Fields 3(2):150\u2013157","journal-title":"Stat Theory Relat Fields"}],"container-title":["AStA Wirtschafts- und Sozialstatistisches Archiv"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11943-025-00365-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/article\/10.1007\/s11943-025-00365-5","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/link.springer.com\/content\/pdf\/10.1007\/s11943-025-00365-5.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,2,6]],"date-time":"2026-02-06T12:03:14Z","timestamp":1770379394000},"score":1,"resource":{"primary":{"URL":"https:\/\/link.springer.com\/10.1007\/s11943-025-00365-5"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,9]]},"references-count":29,"journal-issue":{"issue":"3-4","published-print":{"date-parts":[[2025,9]]}},"alternative-id":["365"],"URL":"https:\/\/doi.org\/10.1007\/s11943-025-00365-5","relation":{},"ISSN":["1863-8155","1863-8163"],"issn-type":[{"value":"1863-8155","type":"print"},{"value":"1863-8163","type":"electronic"}],"subject":[],"published":{"date-parts":[[2025,9]]},"assertion":[{"value":"21 September 2025","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"10 December 2025","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"22 January 2026","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}