IDEAS home Printed from https://ideas.repec.org/a/spr/aistmt/v67y2015i4p745-772.html
   My bibliography  Save this article

Empirical identifiability in finite mixture models

Author

Listed:
  • Daeyoung Kim
  • Bruce Lindsay

Abstract

Although the parameters in a finite mixture model are unidentifiable, there is a form of local identifiability guaranteeing the existence of the identifiable parameter regions. To verify its existence, practitioners use the Fisher information on the estimated parameters. However, there exist model/data situations where local identifiability based on Fisher information does not correspond to that based on the likelihood. In this paper, we propose a method to empirically measure degree of local identifiability on the estimated parameters, empirical identifiability, based on one’s ability to construct an identifiable likelihood set. From a detailed topological study of the likelihood region, we show that for any given data set and mixture model, there typically exists limited range of confidence levels where the likelihood region has a natural partition into identifiable subsets. At confidence levels that are too high, there is no natural way to use the likelihood to resolve the identifiability problem. Copyright The Institute of Statistical Mathematics, Tokyo 2015

Suggested Citation

  • 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.
    • Handle: RePEc:spr:aistmt:v:67:y:2015:i:4:p:745-772
    DOI: 10.1007/s10463-014-0474-9
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1007/s10463-014-0474-9
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1007/s10463-014-0474-9?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. Hanfeng Chen & Jiahua Chen & John D. Kalbfleisch, 2001. "A modified likelihood ratio test for homogeneity in finite mixture models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(1), pages 19-29.
    3. Dankmar Böhning & Ekkehart Dietz & Rainer Schaub & Peter Schlattmann & Bruce Lindsay, 1994. "The distribution of the likelihood ratio for mixtures of densities from the one-parameter exponential family," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(2), pages 373-388, June.
    4. Rothenberg, Thomas J, 1971. "Identification in Parametric Models," Econometrica, Econometric Society, vol. 39(3), pages 577-591, May.
    5. Yao, Weixin & Lindsay, Bruce G., 2009. "Bayesian Mixture Labeling by Highest Posterior Density," Journal of the American Statistical Association, American Statistical Association, vol. 104(486), pages 758-767.
    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. Alexandra Badea & Catalina Bolancé & Raluca Vernic, 2022. "On the Bivariate Composite Gumbel–Pareto Distribution," Stats, MDPI, vol. 5(4), pages 1-22, October.
    2. Omerovic, Sanela & Friedl, Herwig & Grün, Bettina, 2022. "Modelling Multiple Regimes in Economic Growth by Mixtures of Generalised Nonlinear Models," Econometrics and Statistics, Elsevier, vol. 22(C), pages 124-135.

    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. 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.
    2. Seo, Byungtae & Kim, Daeyoung, 2012. "Root selection in normal mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 56(8), pages 2454-2470.
    3. Jia-Chiun Pan & Guan-Hua Huang, 2014. "Bayesian Inferences of Latent Class Models with an Unknown Number of Classes," Psychometrika, Springer;The Psychometric Society, vol. 79(4), pages 621-646, October.
    4. Antonio Punzo & Paul. D. McNicholas, 2017. "Robust Clustering in Regression Analysis via the Contaminated Gaussian Cluster-Weighted Model," Journal of Classification, Springer;The Classification Society, vol. 34(2), pages 249-293, July.
    5. Gonzalez-Valdes, Felipe & Heydecker, Benjamin G. & Ortúzar, Juan de Dios, 2022. "Quantifying behavioural difference in latent class models to assess empirical identifiability: Analytical development and application to multiple heuristics," Journal of choice modelling, Elsevier, vol. 43(C).
    6. Angelo Mazza & Antonio Punzo, 2020. "Mixtures of multivariate contaminated normal regression models," Statistical Papers, Springer, vol. 61(2), pages 787-822, April.
    7. Nguimkeu, Pierre & Denteh, Augustine & Tchernis, Rusty, 2019. "On the estimation of treatment effects with endogenous misreporting," Journal of Econometrics, Elsevier, vol. 208(2), pages 487-506.
    8. Kocięcki, Andrzej & Kolasa, Marcin, 2023. "A solution to the global identification problem in DSGE models," Journal of Econometrics, Elsevier, vol. 236(2).
    9. Carvalho Lopes, Celia Mendes & Bolfarine, Heleno, 2012. "Random effects in promotion time cure rate models," Computational Statistics & Data Analysis, Elsevier, vol. 56(1), pages 75-87, January.
    10. Neusser, Klaus, 2016. "A topological view on the identification of structural vector autoregressions," Economics Letters, Elsevier, vol. 144(C), pages 107-111.
    11. Orazio Attanasio & Sarah Cattan & Emla Fitzsimons & Costas Meghir & Marta Rubio-Codina, 2020. "Estimating the Production Function for Human Capital: Results from a Randomized Controlled Trial in Colombia," American Economic Review, American Economic Association, vol. 110(1), pages 48-85, January.
    12. Chrysanthos Dellarocas & Charles A. Wood, 2008. "The Sound of Silence in Online Feedback: Estimating Trading Risks in the Presence of Reporting Bias," Management Science, INFORMS, vol. 54(3), pages 460-476, March.
    13. Xiaohong Chen & Victor Chernozhukov & Sokbae Lee & Whitney K. Newey, 2014. "Local Identification of Nonparametric and Semiparametric Models," Econometrica, Econometric Society, vol. 82(2), pages 785-809, March.
    14. 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.
    15. Naimoli, Antonio & Storti, Giuseppe, 2019. "Heterogeneous component multiplicative error models for forecasting trading volumes," International Journal of Forecasting, Elsevier, vol. 35(4), pages 1332-1355.
    16. Andrew Chesher & Adam Rosen, 2015. "Characterizations of identified sets delivered by structural econometric models," CeMMAP working papers 63/15, Institute for Fiscal Studies.
    17. Zirogiannis, Nikolaos & Tripodis, Yorghos, 2013. "A Generalized Dynamic Factor Model for Panel Data: Estimation with a Two-Cycle Conditional Expectation-Maximization Algorithm," Working Paper Series 142752, University of Massachusetts, Amherst, Department of Resource Economics.
    18. Gary Koop & M. Hashem Pesaran & Ron P. Smith, 2013. "On Identification of Bayesian DSGE Models," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 31(3), pages 300-314, July.
    19. Abadir, Karim M. & Distaso, Walter, 2007. "Testing joint hypotheses when one of the alternatives is one-sided," Journal of Econometrics, Elsevier, vol. 140(2), pages 695-718, October.
    20. Yao, Weixin & Wei, Yan & Yu, Chun, 2014. "Robust mixture regression using the t-distribution," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 116-127.

    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:aistmt:v:67:y:2015:i:4:p:745-772. 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.