{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T22:24:06Z","timestamp":1767997446278,"version":"3.49.0"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"1","license":[{"start":{"date-parts":[[2016,4,1]],"date-time":"2016-04-01T00:00:00Z","timestamp":1459468800000},"content-version":"unspecified","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0"}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["J Classif"],"published-print":{"date-parts":[[2016,4]]},"DOI":"10.1007\/s00357-016-9199-1","type":"journal-article","created":{"date-parts":[[2016,5,2]],"date-time":"2016-05-02T01:19:48Z","timestamp":1462151988000},"page":"30-51","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":48,"title":["Power and Sample Size Computation for Wald Tests in Latent Class Models"],"prefix":"10.1007","volume":"33","author":[{"given":"Dereje W.","family":"Gudicha","sequence":"first","affiliation":[]},{"given":"Fetene B.","family":"Tekle","sequence":"additional","affiliation":[]},{"given":"Jeroen K.","family":"Vermunt","sequence":"additional","affiliation":[]}],"member":"297","published-online":{"date-parts":[[2016,5,2]]},"reference":[{"key":"9199_CR1","doi-asserted-by":"crossref","DOI":"10.1002\/0471249688","volume-title":"Categorical Data Analysis","author":"A AGRESTI","year":"2002","unstructured":"AGRESTI, A. (2002), Categorical Data Analysis, Hoboken NJ: John Wiley & Sons, Inc."},{"key":"9199_CR2","unstructured":"COHEN, J. (1988), Statistical Power Analysis for the Behavioral Sciences (2nd ed.), Hillsdale NJ: Lawrence Erlbaum Associates."},{"key":"9199_CR3","volume-title":"Latent Class and Latent Transition Analysis: With Applications in the Social, Behavioral, and Health Sciences","author":"LM COLLINS","year":"2010","unstructured":"COLLINS, L.M., and LANZA, S.T. (2010), Latent Class and Latent Transition Analysis: With Applications in the Social, Behavioral, and Health Sciences, Hoboken NF: John Wiley & Sons, Inc."},{"key":"9199_CR4","doi-asserted-by":"crossref","unstructured":"DAYTON, C M., and MACREADY, G.B. (1976), \u201cA Probabilistic Model for Validation of Behavioral Hierarchies\u201d, Psychometrika, 41(2), 189\u2013204.","DOI":"10.1007\/BF02291838"},{"issue":"401","key":"9199_CR5","doi-asserted-by":"crossref","first-page":"173","DOI":"10.1080\/01621459.1988.10478584","volume":"83","author":"CM DAYTON","year":"1988","unstructured":"DAYTON, C.M., and MACREADY, G.B. (1988), \u201cConcomitant-Variable Latent-Class Models \u201d, Journal of the American Statistical Association, 83(401), 173\u2013178.","journal-title":"Journal of the American Statistical Association"},{"issue":"18","key":"9199_CR6","doi-asserted-by":"crossref","first-page":"3385","DOI":"10.1002\/sim.2771","volume":"26","author":"E DEMIDENKO","year":"2007","unstructured":"DEMIDENKO, E. (2007), \u201cSample Size Determination for Logistic Regression Revisited\u201d, Statistics in Medicine, 26(18), 3385\u20133397.","journal-title":"Statistics in Medicine"},{"issue":"1","key":"9199_CR7","doi-asserted-by":"crossref","first-page":"36","DOI":"10.1002\/sim.2980","volume":"27","author":"E DEMIDENKO","year":"2008","unstructured":"DEMIDENKO, E. (2008), \u201cSample Size and Optimal Design for Logistic Regression with Binary Interaction \u201d, Statistics in Medicine, 27(1), 36\u201346.","journal-title":"Statistics in Medicine"},{"issue":"12","key":"9199_CR8","doi-asserted-by":"crossref","first-page":"5263","DOI":"10.1016\/j.csda.2008.04.030","volume":"52","author":"A FORCINA","year":"2008","unstructured":"FORCINA, A. (2008), \u201cIdentifability of Extended Latent Class Models with Individual Covariates \u201d, Computational Statistics & Data Analysis, 52(12), 5263\u20135268.","journal-title":"Computational Statistics & Data Analysis"},{"issue":"2","key":"9199_CR9","doi-asserted-by":"crossref","first-page":"171","DOI":"10.1002\/bimj.4710240209","volume":"24","author":"AK FORMANN","year":"1982","unstructured":"FORMANN, A.K. (1982), \u201cLinear Logistic Latent Class Analysis \u201d, Biometrical Journal, 24(2), 171\u2013190.","journal-title":"Biometrical Journal"},{"issue":"2","key":"9199_CR10","doi-asserted-by":"crossref","first-page":"215","DOI":"10.1093\/biomet\/61.2.215","volume":"61","author":"LA GOODMAN","year":"1974","unstructured":"GOODMAN, L.A. (1974), \u201cExploratory Latent Structure Analysis Using Both Identifiable and Unidentifiable Models \u201d, Biometrika, 61(2), 215\u2013231.","journal-title":"Biometrika"},{"issue":"3","key":"9199_CR11","doi-asserted-by":"crossref","first-page":"379","DOI":"10.1177\/0049124188016003002","volume":"16","author":"JA HAGENAARS","year":"1988","unstructured":"HAGENAARS, J.A. (1988), \u201cLatent Structure Models with Direct Effects Between Indicators Local Dependence Models \u201d, Sociological Methods & Research, 16(3), 379\u2013405.","journal-title":"Sociological Methods & Research"},{"issue":"3","key":"9199_CR12","doi-asserted-by":"crossref","first-page":"207","DOI":"10.1177\/0269758012446984","volume":"18","author":"H HIRTENLEHNER","year":"2012","unstructured":"HIRTENLEHNER, H., STARZER, B., and WEBER, C. (2012), \u201cA Differential Phenomenology of Stalking Using Latent Class Analysis to Identify Different Types of Stalking Victimization \u201d, International Review of Cictimology, 18(3), 207\u2013227.","journal-title":"International Review of Cictimology"},{"issue":"3","key":"9199_CR13","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1177\/014662168901300301","volume":"13","author":"JA HOLT","year":"1989","unstructured":"HOLT, J.A., and MACREADY, G.B. (1989), \u201cA Simulation Study of the Difference Chi-Square Statistic for Comparing Latent Class Models Under Violation of Regularity Conditions \u201d, Applied Psychological Measurement, 13(3), 221\u2013231.","journal-title":"Applied Psychological Measurement"},{"issue":"2","key":"9199_CR14","doi-asserted-by":"crossref","first-page":"192","DOI":"10.1001\/archpsyc.61.2.192","volume":"61","author":"PK KEEL","year":"2004","unstructured":"KEEL, P.K., FICHTER, M., QUADIEG, N., BULIK, C.M., BAXTER, M.G., THORNTON, L., HALMI, K.A., KAPLAN, A.S., STROBER, M., WOODSIDE, D.B., et al. (2004), \u201cApplication of a Latent Class Analysis to Empirically Define Eating Disorder Phenotypes \u201d, Archives of General Psychiatry, 61(2), 192.","journal-title":"Archives of General Psychiatry"},{"key":"9199_CR15","doi-asserted-by":"crossref","unstructured":"LANZA, S.T., COLLINS, L M., LEMMON, D.R., and SCHAFER, J.L. (2007), \u201cProc LCA: A SAS Procedure for Latent Class Analysis \u201d, Structural Equation Modeling, 14(4), 671\u2013694.","DOI":"10.1080\/10705510701575602"},{"key":"9199_CR16","unstructured":"LAZARSFELD, P. (1950), \u201cThe Logical and Mathematical Foundation of Latent Stricture Analysis and the Interpretation and Mathematical Foundation of Latent Structure Analysis\u201d, in Measurement and Predictions, eds. S.A. Stoufer et al., pp. 362\u2013472."},{"issue":"10","key":"9199_CR17","first-page":"1","volume":"42","author":"DA LINZAR","year":"2011","unstructured":"LINZAR, D.A., and LEWIS, J.B. (2011), \u201cpoLCA: An r Package for Polytomous Variable Latent Class Analysis \u201d, Journal of Statistical Software, 42(10), 1\u201329.","journal-title":"Journal of Statistical Software"},{"key":"9199_CR18","doi-asserted-by":"crossref","unstructured":"MAGIDSON, J., and VERMUNT, J.K. (2004), \u201cLatent Class Models \u201d, in The Sage Handbook of Quantitative Methodology for the Social Sciences, ed. D. Kaplan, Thousand Oaks CA: Sage, pp. 175\u2013198.","DOI":"10.4135\/9781412986311.n10"},{"issue":"3","key":"9199_CR19","doi-asserted-by":"crossref","first-page":"217","DOI":"10.1214\/aoms\/1177731415","volume":"14","author":"HB MANN","year":"1943","unstructured":"MANN, H.B., and WALD, A. (1943), \u201cOn Stochastic Limit and Order Relationships \u201d, The Annals of Mathematical Statistics, 14(3), 217\u2013226.","journal-title":"The Annals of Mathematical Statistics"},{"key":"9199_CR20","doi-asserted-by":"crossref","DOI":"10.4135\/9781412984713","volume-title":"Latent Class Analysis","author":"AL MCCUTCHTEON","year":"1987","unstructured":"MCCUTCHTEON, A.L. (1987), Latent Class Analysis, Newbury Park CA: SAGE Publications."},{"issue":"4","key":"9199_CR21","doi-asserted-by":"crossref","first-page":"331","DOI":"10.1007\/BF02296300","volume":"21","author":"RB MCHUGH","year":"1956","unstructured":"MCHUGH, R.B. (1956), \u201cEfficient Estimation and Local Identification in Latent Class Analysis \u201d, Psychometrika, 21(4), 331\u2013347.","journal-title":"Psychometrika"},{"key":"9199_CR22","doi-asserted-by":"crossref","DOI":"10.1002\/0471721182","volume-title":"Finite Mixture Models","author":"G MCLACHLAN","year":"2000","unstructured":"MCLACHLAN, G., and PEEL, D. (2000), Finite Mixture Models, New York: John Wiley."},{"key":"9199_CR23","unstructured":"MUTH\u00c9N, L.K., and MUTH\u00c9N, B.O. (2012), Mplus. The Comprehensive Modelling Program for Applied Researchers: Users Guide 5, Los Angeles CA: Muth\u00e9n & Muth\u00e9n."},{"issue":"2","key":"9199_CR24","first-page":"103","volume":"7","author":"S NAKAGAWA","year":"2004","unstructured":"NAKAGAWA, S., and FOSTER, T.M. (2004), \u201cThe Case Against Retrospective Statistical Power Analyses with an Introduction to Power Analysis \u201d, Actathologica, 7(2), 103\u2013108.","journal-title":"Actathologica"},{"issue":"4","key":"9199_CR25","doi-asserted-by":"crossref","first-page":"535","DOI":"10.1080\/10705510701575396","volume":"14","author":"KL NYLUND","year":"2007","unstructured":"NYLUND, K.L., ASPAROUHOV, T., and MUTH\u00c9N, B. O. (2007), \u201cDeciding on the Number of Classes in Latent Class Analysis and Growth Mixture Modeling: A Monte Carlo Simulation Study \u201d, Structural Equation Modeling, 14(4), 535\u2013569.","journal-title":"Structural Equation Modeling"},{"key":"9199_CR26","unstructured":"\u00d3 BRIEN, R.G. (1986), \u201cUsing the SAS System to Perform Power Analyses for Log-Linear Models\u201d, in Proceedings of the 11th Annual SAS Users Group Conference, pp. 778\u2013784."},{"issue":"1","key":"9199_CR27","doi-asserted-by":"crossref","first-page":"225","DOI":"10.1214\/aos\/1176345353","volume":"9","author":"R RENDER","year":"1981","unstructured":"RENDER, R. (1981), \u201cNote on the Consistency of the Maximum Likelihood Estimate for Non-Identifiable Distributions \u201d, The Annals of Statistics, 9(1), 225\u2013228.","journal-title":"The Annals of Statistics"},{"key":"9199_CR28","volume-title":"Linear Models in Statistics","author":"AC RENCHER","year":"2000","unstructured":"RENCHER, A.C. (2000), Linear Models in Statistics, New York: John Wiley."},{"issue":"1","key":"9199_CR29","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1002\/sim.4780050105","volume":"5","author":"D RINDSKOPF","year":"1986","unstructured":"RINDSKOPF, D., and RINDSKOPF, W. (1986), \u201cThe Value of Latent Class Analysis in Medical Diagnosis \u201d, Statistics in Medicine, 5(1), 21\u201327.","journal-title":"Statistics in Medicine"},{"key":"9199_CR30","unstructured":"TOFIGHI, D., and ENDERS, C.K. (2008), \u201cIdentifying the Correct Number of Classes in Growth Mixture Models \u201d, Advances in Latent Variable Mixture Models, 317\u2013341."},{"issue":"5","key":"9199_CR31","doi-asserted-by":"crossref","first-page":"559","DOI":"10.1002\/sim.4780090509","volume":"9","author":"JS UEBERSAX","year":"1990","unstructured":"UEBERSAX, J.S., and GROVE, W.M. (1990), \u201cLatent Class Analysis of Diagnostic Agreement\u201d, Statistics in Medicine, 9(5), 559\u2013572.","journal-title":"Statistics in Medicine"},{"key":"9199_CR32","volume-title":"Log-Linear Event History Analysis: A General Approach with Missing Data, Latent Variables, and Unobserved Heterogeneity","author":"JK VERMUNT","year":"1996","unstructured":"VERMUNT, J.K. (1996), Log-Linear Event History Analysis: A General Approach with Missing Data, Latent Variables, and Unobserved Heterogeneity, Tilburg: Tilburg University Press."},{"key":"9199_CR33","volume-title":"LEM: A General Program for the Analysis of Categorical Data","author":"JK VERMUNT","year":"1997","unstructured":"VERMUNT, J.K. (1997), LEM: A General Program for the Analysis of Categorical Data, Tilburg: Tilburg University."},{"key":"9199_CR34","doi-asserted-by":"crossref","unstructured":"VERMUNT, J.K. (2010a), \u201cLatent Class Modeling with Covariates: Two Improved Three-Step Approaches \u201d, Political Analysis, 18(4), 450\u2013469.","DOI":"10.1093\/pan\/mpq025"},{"key":"9199_CR35","doi-asserted-by":"crossref","unstructured":"VERMUNT, J.K. (2010b), \u201cLatent Class Models\u201d, in International Encyclopedia of Education, 7, eds. P. Peterson, E. Baker, and B. McGaw, pp. 238\u2013244.","DOI":"10.1016\/B978-0-08-044894-7.01340-3"},{"key":"9199_CR36","unstructured":"VERMUNT, J.K., and Magidson, J. (2013a), LG-Syntax User\u2019s Guide: Manual for Latent GOLD 5.0 Syntax Module, Belmont MA: Statistical Innovations Inc."},{"key":"9199_CR37","unstructured":"VERMUNT, J.K., and Magidson, J. (2013b), Technical Guide for Latent GOLD 5.0: Basic, Advanced, and Syntax, Belmont MA: Statistical Innovations Inc."},{"issue":"3","key":"9199_CR38","doi-asserted-by":"crossref","first-page":"426","DOI":"10.1090\/S0002-9947-1943-0012401-3","volume":"54","author":"A WALD","year":"1943","unstructured":"WALD, A. (1943), \u201cTests of Statistical Hypotheses Concerning Several Parameters When the Number of Observations is Large \u201d, Transactions of the American Mathematical Society, 54(3), 426\u2013482.","journal-title":"Transactions of the American Mathematical Society"},{"issue":"1","key":"9199_CR39","doi-asserted-by":"crossref","first-page":"1","DOI":"10.2307\/1912526","volume":"50","author":"H WHITE","year":"1982","unstructured":"WHITE, H. (1982), \u201cMaximum Likelihood Estimation of Misspecified Models \u201d, Econometrica: Journal of the Econometric Society, 50(1), 1\u201325.","journal-title":"Econometrica: Journal of the Econometric Society"},{"issue":"373","key":"9199_CR40","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1080\/01621459.1981.10477597","volume":"76","author":"AS WHITTEMORE","year":"1981","unstructured":"WHITTEMORE, A.S. (1981), \u201cSample Size for Logistic Regression with Small Response Probability \u201d, Journal of the American Statistical Association, 76(373), 27\u201332.","journal-title":"Journal of the American Statistical Association"},{"issue":"3","key":"9199_CR41","doi-asserted-by":"crossref","first-page":"329","DOI":"10.1207\/s15327906mbr0503_6","volume":"5","author":"JH WOLFE","year":"1970","unstructured":"WOLFE, J.H. (1970), \u201cPattern Clustering by Multivariate Mixture Analysis \u201d, Multivariate Behavioral Research, 5(3), 329\u2013350.","journal-title":"Multivariate Behavioral Research"},{"issue":"4","key":"9199_CR42","doi-asserted-by":"crossref","first-page":"1090","DOI":"10.1016\/j.csda.2004.11.004","volume":"50","author":"CC YANG","year":"2006","unstructured":"YANG, C.C. (2006), \u201cEvaluating Latent Class Analysis Models in Qualitative Phenotype Identification \u201d, Computational Statistics and Data Analysis, 50(4), 1090\u20131104.","journal-title":"Computational Statistics and Data Analysis"},{"issue":"3","key":"9199_CR43","doi-asserted-by":"crossref","first-page":"948","DOI":"10.2307\/2533555","volume":"53","author":"I YANG","year":"1997","unstructured":"YANG, I., and BECKER,M.P. (1997), \u201cLatent Variable Modeling of Diagnostic Accuracy\u201d, Biometrics, 53(3) 948\u2013958.","journal-title":"Biometrics"}],"container-title":["Journal of Classification"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00357-016-9199-1.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s00357-016-9199-1\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s00357-016-9199-1","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2019,9,7]],"date-time":"2019-09-07T02:43:44Z","timestamp":1567824224000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s00357-016-9199-1"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,4]]},"references-count":43,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2016,4]]}},"alternative-id":["9199"],"URL":"https:\/\/doi.org\/10.1007\/s00357-016-9199-1","relation":{},"ISSN":["0176-4268","1432-1343"],"issn-type":[{"value":"0176-4268","type":"print"},{"value":"1432-1343","type":"electronic"}],"subject":[],"published":{"date-parts":[[2016,4]]}}}