IDEAS home Printed from https://ideas.repec.org/a/spr/advdac/v7y2013i3p267-279.html
   My bibliography  Save this article

A Monte Carlo evaluation of three methods to detect local dependence in binary data latent class models

Author

Listed:
  • Daniel Oberski
  • Geert Kollenburg
  • Jeroen Vermunt

Abstract

Binary data latent class analysis is a form of model-based clustering applied in a wide range of fields. A central assumption of this model is that of conditional independence of responses given latent class membership, often referred to as the “local independence” assumption. The results of latent class analysis may be severely biased when this crucial assumption is violated; investigating the degree to which bivariate relationships between observed variables fit this hypothesis therefore provides vital information. This article evaluates three methods of doing so. The first is the commonly applied method of referring the so-called “bivariate residuals” to a Chi-square distribution. We also introduce two alternative methods that are novel to the investigation of local dependence in latent class analysis: bootstrapping the bivariate residuals, and the asymptotic score test or “modification index”. Our Monte Carlo simulation indicates that the latter two methods perform adequately, while the first method does not perform as intended. Copyright Springer-Verlag Berlin Heidelberg 2013

Suggested Citation

  • Daniel Oberski & Geert Kollenburg & Jeroen Vermunt, 2013. "A Monte Carlo evaluation of three methods to detect local dependence in binary data latent class models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 7(3), pages 267-279, September.
  • Handle: RePEc:spr:advdac:v:7:y:2013:i:3:p:267-279
    DOI: 10.1007/s11634-013-0146-2
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s11634-013-0146-2
    Download Restriction: Access to full text is restricted to subscribers.

    File URL: https://libkey.io/10.1007/s11634-013-0146-2?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Guan-Hua Huang & Karen Bandeen-Roche, 2004. "Building an identifiable latent class model with covariate effects on underlying and measured variables," Psychometrika, Springer;The Psychometric Society, vol. 69(1), pages 5-32, March.
    2. Forcina, Antonio, 2008. "Identifiability of extended latent class models with individual covariates," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5263-5268, August.
    3. Cees Glas, 1999. "Modification indices for the 2-PL and the nominal response model," Psychometrika, Springer;The Psychometric Society, vol. 64(3), pages 273-294, September.
    4. Paul S. Albert & Lori E. Dodd, 2004. "A Cautionary Note on the Robustness of Latent Class Models for Estimating Diagnostic Error without a Gold Standard," Biometrics, The International Biometric Society, vol. 60(2), pages 427-435, June.
    5. Ahlquist, John S. & Breunig, Christian, 2012. "Model-based Clustering and Typologies in the Social Sciences," Political Analysis, Cambridge University Press, vol. 20(1), pages 92-112, January.
    6. Wim Linden & Cees Glas, 2010. "Statistical Tests of Conditional Independence Between Responses and/or Response Times on Test Items," Psychometrika, Springer;The Psychometric Society, vol. 75(1), pages 120-139, March.
    7. Albert Satorra, 1989. "Alternative test criteria in covariance structure analysis: A unified approach," Psychometrika, Springer;The Psychometric Society, vol. 54(1), pages 131-151, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Huiping Xu & Xiaochun Li & Zuoyi Zhang & Shaun Grannis, 2022. "Score test for assessing the conditional dependence in latent class models and its application to record linkage," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 71(5), pages 1663-1687, November.
    2. Maike Damme & Dimitris Pavlopoulos, 2022. "Gender Ideology in Europe: Plotting Normative Types in a Multidimensional Space," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 164(2), pages 861-891, November.
    3. Zinn, Andrew, 2015. "A typology of supervision in child welfare: Multilevel latent class and confirmatory analyses of caseworker–supervisor relationship type," Children and Youth Services Review, Elsevier, vol. 48(C), pages 98-110.
    4. Martin Lukac & Nadja Doerflinger & Valeria Pulignano, 2019. "Developing a Cross-National Comparative Framework for Studying Labour Market Segmentation: Measurement Equivalence with Latent Class Analysis," Social Indicators Research: An International and Interdisciplinary Journal for Quality-of-Life Measurement, Springer, vol. 145(1), pages 233-255, August.
    5. Guastadisegni, Lucia & Cagnone, Silvia & Moustaki, Irini & Vasdekis, Vassilis, 2022. "Use of the Lagrange multiplier test for assessing measurement invariance under model misspecification," LSE Research Online Documents on Economics 110358, London School of Economics and Political Science, LSE Library.
    6. Sands, Sean & Ferraro, Carla & Campbell, Colin & Pallant, Jason, 2016. "Segmenting multichannel consumers across search, purchase and after-sales," Journal of Retailing and Consumer Services, Elsevier, vol. 33(C), pages 62-71.
    7. Alonso-González, María J. & Hoogendoorn-Lanser, Sascha & van Oort, Niels & Cats, Oded & Hoogendoorn, Serge, 2020. "Drivers and barriers in adopting Mobility as a Service (MaaS) – A latent class cluster analysis of attitudes," Transportation Research Part A: Policy and Practice, Elsevier, vol. 132(C), pages 378-401.
    8. Claudio Castro-López & Purificación Vicente-Galindo & Purificación Galindo-Villardón & Oscar Borrego-Hernández, 2022. "TAID-LCA: Segmentation Algorithm Based on Ternary Trees," Mathematics, MDPI, vol. 10(4), pages 1-16, February.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Guastadisegni, Lucia & Cagnone, Silvia & Moustaki, Irini & Vasdekis, Vassilis, 2022. "Use of the Lagrange multiplier test for assessing measurement invariance under model misspecification," LSE Research Online Documents on Economics 110358, London School of Economics and Political Science, LSE Library.
    2. Dardanoni, V & Li Donni, P, 2008. "Testing For Asymmetric Information In Insurance Markets With Unobservable Types," Health, Econometrics and Data Group (HEDG) Working Papers 08/26, HEDG, c/o Department of Economics, University of York.
    3. Dardanoni, Valentino & Li Donni, Paolo, 2012. "Incentive and selection effects of Medigap insurance on inpatient care," Journal of Health Economics, Elsevier, vol. 31(3), pages 457-470.
    4. Sandip Sinharay & Peter W. van Rijn, 2020. "Assessing Fit of the Lognormal Model for Response Times," Journal of Educational and Behavioral Statistics, , vol. 45(5), pages 534-568, October.
    5. Paolo Li Donni & Ranjeeta Thomas, 2020. "Latent class models for multiple ordered categorical health data: testing violation of the local independence assumption," Empirical Economics, Springer, vol. 59(4), pages 1903-1931, October.
    6. Ting Wang & Carolin Strobl & Achim Zeileis & Edgar C. Merkle, 2018. "Score-Based Tests of Differential Item Functioning via Pairwise Maximum Likelihood Estimation," Psychometrika, Springer;The Psychometric Society, vol. 83(1), pages 132-155, March.
    7. Wang, Zheyu & Sebestyen, Krisztian & Monsell, Sarah E., 2017. "Model-based clustering for assessing the prognostic value of imaging biomarkers and mixed type tests," Computational Statistics & Data Analysis, Elsevier, vol. 113(C), pages 125-135.
    8. Mengbing Li & Daniel E. Park & Maliha Aziz & Cindy M. Liu & Lance B. Price & Zhenke Wu, 2023. "Integrating sample similarities into latent class analysis: a tree‐structured shrinkage approach," Biometrics, The International Biometric Society, vol. 79(1), pages 264-279, March.
    9. Forcina, Antonio, 2017. "A Fisher-scoring algorithm for fitting latent class models with individual covariates," Econometrics and Statistics, Elsevier, vol. 3(C), pages 132-140.
    10. Paul S. Albert, 2007. "Random Effects Modeling Approaches for Estimating ROC Curves from Repeated Ordinal Tests without a Gold Standard," Biometrics, The International Biometric Society, vol. 63(2), pages 593-602, June.
    11. Seungwoo Han, 2022. "Spatial stratification and socio-spatial inequalities: the case of Seoul and Busan in South Korea," Palgrave Communications, Palgrave Macmillan, vol. 9(1), pages 1-14, December.
    12. Kai Hong & Peter A. Savelyev & Kegon T. K. Tan, 2020. "Understanding the Mechanisms Linking College Education with Longevity," Journal of Human Capital, University of Chicago Press, vol. 14(3), pages 371-400.
    13. Daeyoung Kim & Bruce Lindsay, 2015. "Empirical identifiability in finite mixture models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 67(4), pages 745-772, August.
    14. Donal O'Neill & Olive Sweetman, 2013. "Estimating Obesity Rates in Europe in the Presence of Self-Reporting Errors," Economics Department Working Paper Series n236-13.pdf, Department of Economics, National University of Ireland - Maynooth.
    15. A. Béguin & C. Glas, 2001. "MCMC estimation and some model-fit analysis of multidimensional IRT models," Psychometrika, Springer;The Psychometric Society, vol. 66(4), pages 541-561, December.
    16. Lisa Blaydes, 2023. "Assessing the Labor Conditions of Migrant Domestic Workers in the Arab Gulf States," ILR Review, Cornell University, ILR School, vol. 76(4), pages 724-747, August.
    17. Inhan Kang & Paul Boeck & Roger Ratcliff, 2022. "Modeling Conditional Dependence of Response Accuracy and Response Time with the Diffusion Item Response Theory Model," Psychometrika, Springer;The Psychometric Society, vol. 87(2), pages 725-748, June.
    18. Francesco BARTOLUCCI & Silvia BACCI & Claudia PIGINI, 2015. "A Misspecification Test for Finite-Mixture Logistic Models for Clustered Binary and Ordered Responses," Working Papers 410, Universita' Politecnica delle Marche (I), Dipartimento di Scienze Economiche e Sociali.
    19. Forcina, Antonio, 2008. "Identifiability of extended latent class models with individual covariates," Computational Statistics & Data Analysis, Elsevier, vol. 52(12), pages 5263-5268, August.
    20. Brisa N. Sánchez & Shan Kang & Bhramar Mukherjee, 2012. "A Latent Variable Approach to Study Gene–Environment Interactions in the Presence of Multiple Correlated Exposures," Biometrics, The International Biometric Society, vol. 68(2), pages 466-476, June.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:advdac:v:7:y:2013:i:3:p:267-279. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.