IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v54y2010i7p1872-1880.html
   My bibliography  Save this article

Goodness-of-fit tests for modeling longitudinal ordinal data

Author

Listed:
  • Lin, Kuo-Chin

Abstract

Longitudinal studies involving categorical responses are extensively applied in many fields of research and are often fitted by the generalized estimating equations (GEE) approach and generalized linear mixed models (GLMMs). The assessment of model fit is an important issue for model inference. The purpose of this article is to extend Pan's (2002a) goodness-of-fit tests for GEE models with longitudinal binary data to the tests for logistic proportional odds models with longitudinal ordinal data. Two proposed methods based on Pearson chi-squared test and unweighted sum of residual squares are developed, and the approximate expectations and variances of the test statistics are easily computed. Four major variants of working correlation structures, independent, AR(1), exchangeable and unspecified, are considered to estimate the variances of the proposed test statistics. Simulation studies in terms of type I error rate and the power performance of the proposed tests are presented for various sample sizes. Furthermore, the approaches are demonstrated by two real data sets.

Suggested Citation

  • Lin, Kuo-Chin, 2010. "Goodness-of-fit tests for modeling longitudinal ordinal data," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1872-1880, July.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:7:p:1872-1880
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167-9473(10)00078-2
    Download Restriction: Full text for ScienceDirect subscribers only.
    ---><---

    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. Wei Pan, 2002. "Goodness‐of‐fit Tests for GEE with Correlated Binary Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 101-110, March.
    2. Zhiying Pan & D. Y. Lin, 2005. "Goodness-of-Fit Methods for Generalized Linear Mixed Models," Biometrics, The International Biometric Society, vol. 61(4), pages 1000-1009, December.
    3. Keunbaik Lee & Michael J. Daniels, 2007. "A Class of Markov Models for Longitudinal Ordinal Data," Biometrics, The International Biometric Society, vol. 63(4), pages 1060-1067, December.
    4. Li C. Liu & Donald Hedeker, 2006. "A Mixed-Effects Regression Model for Longitudinal Multivariate Ordinal Data," Biometrics, The International Biometric Society, vol. 62(1), pages 261-268, March.
    5. Lin, Hui-Yi & Myers, Leann, 2006. "Power and Type I error rates of goodness-of-fit statistics for binomial generalized estimating equations (GEE) models," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3432-3448, August.
    6. Göran Kauermann, 2000. "Modeling Longitudinal Data with Ordinal Response by Varying Coefficients," Biometrics, The International Biometric Society, vol. 56(3), pages 692-698, September.
    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. Chan, Moon-tong & Yu, Dalei & Yau, Kelvin K.W., 2015. "Multilevel cumulative logistic regression model with random effects: Application to British social attitudes panel survey data," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 173-186.
    2. Kuo-Chin Lin & Yi-Ju Chen, 2016. "Goodness-of-fit tests of generalized linear mixed models for repeated ordinal responses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(11), pages 2053-2064, August.

    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. Rana, Subrata & Roy, Surupa & Das, Kalyan, 2018. "Analysis of ordinal longitudinal data under nonignorable missingness and misreporting: An application to Alzheimer’s disease study," Journal of Multivariate Analysis, Elsevier, vol. 166(C), pages 62-77.
    2. Kuo-Chin Lin & Yi-Ju Chen, 2016. "Goodness-of-fit tests of generalized linear mixed models for repeated ordinal responses," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(11), pages 2053-2064, August.
    3. Chaubert, F. & Mortier, F. & Saint André, L., 2008. "Multivariate dynamic model for ordinal outcomes," Journal of Multivariate Analysis, Elsevier, vol. 99(8), pages 1717-1732, September.
    4. Lin, Hui-Yi & Myers, Leann, 2006. "Power and Type I error rates of goodness-of-fit statistics for binomial generalized estimating equations (GEE) models," Computational Statistics & Data Analysis, Elsevier, vol. 50(12), pages 3432-3448, August.
    5. Park, Byeong U. & Mammen, Enno & Härdle, Wolfgang & Borak, Szymon, 2009. "Time Series Modelling With Semiparametric Factor Dynamics," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 284-298.
    6. 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.
    7. Shun Yu & Xianzheng Huang, 2019. "Link misspecification in generalized linear mixed models with a random intercept for binary responses," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 827-843, September.
    8. Song Song & Wolfgang K. Härdle & Ya'acov Ritov, 2010. "High Dimensional Nonstationary Time Series Modelling with Generalized Dynamic Semiparametric Factor Model," SFB 649 Discussion Papers SFB649DP2010-039, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
    9. Somnath Datta & Glen A. Satten, 2008. "A Signed-Rank Test for Clustered Data," Biometrics, The International Biometric Society, vol. 64(2), pages 501-507, June.
    10. Mandal, A. & Huang, W.T. & Bhandari, S.K. & Basu, A., 2011. "Goodness-of-fit testing in growth curve models: A general approach based on finite differences," Computational Statistics & Data Analysis, Elsevier, vol. 55(2), pages 1086-1098, February.
    11. Yu-Zhu Tian & Man-Lai Tang & Wai-Sum Chan & Mao-Zai Tian, 2021. "Bayesian bridge-randomized penalized quantile regression for ordinal longitudinal data, with application to firm’s bond ratings," Computational Statistics, Springer, vol. 36(2), pages 1289-1319, June.
    12. Giorgos Bakoyannis & Ying Zhang & Constantin T. Yiannoutsos, 2020. "Semiparametric regression and risk prediction with competing risks data under missing cause of failure," Lifetime Data Analysis: An International Journal Devoted to Statistical Methods and Applications for Time-to-Event Data, Springer, vol. 26(4), pages 659-684, October.
    13. Keunbaik Lee & Michael J. Daniels, 2007. "A Class of Markov Models for Longitudinal Ordinal Data," Biometrics, The International Biometric Society, vol. 63(4), pages 1060-1067, December.
    14. Alejandra Tapia & Viviana Giampaoli & Víctor Leiva & Yuhlong Lio, 2020. "Data-Influence Analytics in Predictive Models Applied to Asthma Disease," Mathematics, MDPI, vol. 8(9), pages 1-19, September.
    15. Chan, Moon-tong & Yu, Dalei & Yau, Kelvin K.W., 2015. "Multilevel cumulative logistic regression model with random effects: Application to British social attitudes panel survey data," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 173-186.
    16. Ivy Liu & Alan Agresti, 2005. "The analysis of ordered categorical data: An overview and a survey of recent developments," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 14(1), pages 1-73, June.
    17. Lan Wang & Annie Qu, 2009. "Consistent model selection and data‐driven smooth tests for longitudinal data in the estimating equations approach," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 177-190, January.
    18. Andreas Blöchlinger & Markus Leippold, 2011. "A New Goodness-of-Fit Test for Event Forecasting and Its Application to Credit Defaults," Management Science, INFORMS, vol. 57(3), pages 487-505, March.
    19. Cui, Li-E & Zhao, Puying & Tang, Niansheng, 2022. "Generalized empirical likelihood for nonsmooth estimating equations with missing data," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    20. Tang, Min & Slud, Eric V. & Pfeiffer, Ruth M., 2014. "Goodness of fit tests for linear mixed models," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 176-193.

    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:54:y:2010:i:7:p:1872-1880. 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.