IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v127y2018icp248-257.html
   My bibliography  Save this article

Asymptotic null distribution of the modified likelihood ratio test for homogeneity in finite mixture models

Author

Listed:
  • Wong, Tony S.T.
  • Lam, Kwok Fai
  • Zhao, Victoria X.

Abstract

Likelihood-based methods play a central role in statistical inference for parametric models. Among these, the modified likelihood ratio test is preferred in testing for homogeneity in finite mixture models. The test statistic is related to the maximum of a quadratic function under general regularity conditions. Re-parameterization is shown to have overcome the difficulty when linear independence is not satisfied. Models with parameter constraints are also considered. The asymptotic null distribution of the test statistic is shown to have a chi-bar-squared distribution in both constrained and unconstrained cases. We extend the result to linear models and demonstrate that the chi-bar-squared distribution is also applicable. The general asymptotic result provides a much simpler testing procedure with an exact form of the asymptotic distribution compared to re-sampling approach in the literature. It also offers accurate p-value as shown in simulation. The results are checked by extensive simulation and are supplemented by a breast cancer data example.

Suggested Citation

  • Wong, Tony S.T. & Lam, Kwok Fai & Zhao, Victoria X., 2018. "Asymptotic null distribution of the modified likelihood ratio test for homogeneity in finite mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 127(C), pages 248-257.
    • Handle: RePEc:eee:csdana:v:127:y:2018:i:c:p:248-257
    DOI: 10.1016/j.csda.2018.05.010
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947318301191
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2018.05.010?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. Shaoting Li & Jiahua Chen & Jianhua Guo & Bing-Yi Jing & Shui-Ying Tsang & Hong Xue, 2015. "Likelihood Ratio Test for Multi-Sample Mixture Model and Its Application to Genetic Imprinting," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 867-877, June.
    2. P. Li & J. Chen & P. Marriott, 2009. "Non-finite Fisher information and homogeneity: an EM approach," Biometrika, Biometrika Trust, vol. 96(2), pages 411-426.
    3. 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.
    4. Hiroyuki Kasahara & Katsumi Shimotsu, 2015. "Testing the Number of Components in Normal Mixture Regression Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(512), pages 1632-1645, December.
    5. G. J. McLachlan, 1987. "On Bootstrapping the Likelihood Ratio Test Statistic for the Number of Components in a Normal Mixture," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 36(3), pages 318-324, November.
    6. Wong, Tony Siu Tung & Li, Wai Keung, 2014. "Test for homogeneity in gamma mixture models using likelihood ratio," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 127-137.
    7. McLachlan, G. J. & Khan, N., 2004. "On a resampling approach for tests on the number of clusters with mixture model-based clustering of tissue samples," Journal of Multivariate Analysis, Elsevier, vol. 90(1), pages 90-105, July.
    8. Hong‐Tu Zhu & Heping Zhang, 2004. "Hypothesis testing in mixture regression models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(1), pages 3-16, February.
    Full references (including those not matched with items on IDEAS)

    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. Hiroyuki Kasahara & Katsumi Shimotsu, 2017. "Testing the Order of Multivariate Normal Mixture Models," CIRJE F-Series CIRJE-F-1044, CIRJE, Faculty of Economics, University of Tokyo.
    2. Wong, Tony Siu Tung & Li, Wai Keung, 2014. "Test for homogeneity in gamma mixture models using likelihood ratio," Computational Statistics & Data Analysis, Elsevier, vol. 70(C), pages 127-137.
    3. Alexander D. Stead & Phill Wheat & William H. Greene, 2023. "On hypothesis testing in latent class and finite mixture stochastic frontier models, with application to a contaminated normal-half normal model," Journal of Productivity Analysis, Springer, vol. 60(1), pages 37-48, August.
    4. Kasahara Hiroyuki & Shimotsu Katsumi, 2012. "Testing the Number of Components in Finite Mixture Models," Global COE Hi-Stat Discussion Paper Series gd12-259, Institute of Economic Research, Hitotsubashi University.
    5. Chuan Hong & Yang Ning & Shuang Wang & Hao Wu & Raymond J. Carroll & Yong Chen, 2017. "PLEMT: A Novel Pseudolikelihood-Based EM Test for Homogeneity in Generalized Exponential Tilt Mixture Models," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 112(520), pages 1393-1404, October.
    6. Ye, Mao & Lu, Zhao-Hua & Li, Yimei & Song, Xinyuan, 2019. "Finite mixture of varying coefficient model: Estimation and component selection," Journal of Multivariate Analysis, Elsevier, vol. 171(C), pages 452-474.
    7. Dante Amengual & Xinyue Bei & Marine Carrasco & Enrique Sentana, 2022. "Score-type tests for normal mixtures," Working Papers wp2022_2213, CEMFI.
    8. Hoshino Tadao & Yanagi Takahide, 2022. "Estimating marginal treatment effects under unobserved group heterogeneity," Journal of Causal Inference, De Gruyter, vol. 10(1), pages 197-216, January.
    9. Derek S. Young & Xi Chen & Dilrukshi C. Hewage & Ricardo Nilo-Poyanco, 2019. "Finite mixture-of-gamma distributions: estimation, inference, and model-based clustering," 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. 13(4), pages 1053-1082, December.
    10. Charnigo, Richard & Fan, Qian & Bittel, Douglas & Dai, Hongying, 2013. "Testing unilateral versus bilateral normal contamination," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 163-167.
    11. Juan Shen & Xuming He, 2015. "Inference for Subgroup Analysis With a Structured Logistic-Normal Mixture Model," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(509), pages 303-312, March.
    12. Meitz, Mika & Saikkonen, Pentti, 2021. "Testing for observation-dependent regime switching in mixture autoregressive models," Journal of Econometrics, Elsevier, vol. 222(1), pages 601-624.
    13. Wichitchan, Supawadee & Yao, Weixin & Yang, Guangren, 2019. "Hypothesis testing for finite mixture models," Computational Statistics & Data Analysis, Elsevier, vol. 132(C), pages 180-189.
    14. Lo, Yungtai, 2005. "Likelihood ratio tests of the number of components in a normal mixture with unequal variances," Statistics & Probability Letters, Elsevier, vol. 71(3), pages 225-235, March.
    15. Yu Hao & Hiroyuki Kasahara, 2022. "Testing the Number of Components in Finite Mixture Normal Regression Model with Panel Data," Papers 2210.02824, arXiv.org, revised Jun 2023.
    16. Jin Seo Cho & Peter C. B. Phillips & Juwon Seo, 2019. "Parametric Inference on the Mean of Functional Data Applied to Lifetime Income Curves," Working papers 2019rwp-153, Yonsei University, Yonsei Economics Research Institute.
    17. Jin Seo Cho & Peter C. B. Phillips & Juwon Seo, 2022. "Parametric Conditional Mean Inference With Functional Data Applied To Lifetime Income Curves," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 63(1), pages 391-456, February.
    18. Pan, Lanfeng & Li, Yehua & He, Kevin & Li, Yanming & Li, Yi, 2020. "Generalized linear mixed models with Gaussian mixture random effects: Inference and application," Journal of Multivariate Analysis, Elsevier, vol. 175(C).
    19. Polymenis, Athanase, 2014. "A combined likelihood ratio/information ratio bootstrap technique for estimating the number of components in finite mixtures," Computational Statistics & Data Analysis, Elsevier, vol. 71(C), pages 107-115.
    20. Jiaying Gu & Roger Koenker & Stanislav Volgushev, 2017. "Testing for homogeneity in mixture models," CeMMAP working papers 39/17, Institute for Fiscal Studies.

    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:eee:csdana:v:127:y:2018:i:c:p:248-257. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/csda .

    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.