IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/64220.html
   My bibliography  Save this paper

A misspecification test for finite-mixture logistic models for clustered binary and ordered responses

Author

Listed:
  • Francesco, Bartolucci
  • Silvia, Bacci
  • Claudia, Pigini

Abstract

An alternative to using normally distributed random effects in modeling clustered binary and ordered responses is based on using a finite-mixture. This approach gives rise to a flexible class of generalized linear mixed models for item responses, multilevel data, and longitudinal data. A test of misspecification for these finite-mixture models is proposed which is based on the comparison between the Marginal and the Conditional Maximum Likelihood estimates of the fixed effects as in the Hausman’s test. The asymptotic distribution of the test statistic is derived; it is of chi-squared type with a number of degrees of freedom equal to the number of covariates that vary within the cluster. It turns out that the test is simple to perform and may also be used to select the number of components of the finite-mixture, when this number is unknown. The approach is illustrated by a series of simulations and three empirical examples covering the main fields of application.

Suggested Citation

  • Francesco, Bartolucci & Silvia, Bacci & Claudia, Pigini, 2015. "A misspecification test for finite-mixture logistic models for clustered binary and ordered responses," MPRA Paper 64220, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:64220
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/64220/1/MPRA_paper_64220.pdf
    File Function: original version
    Download Restriction: no

    File URL: https://mpra.ub.uni-muenchen.de/64787/1/MPRA_paper_64220.pdf
    File Function: revised version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Florian Heiss, 2008. "Sequential numerical integration in nonlinear state space models for microeconometric panel data," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(3), pages 373-389.
    2. Gregori Baetschmann & Kevin E. Staub & Rainer Winkelmann, 2015. "Consistent estimation of the fixed effects ordered logit model," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 178(3), pages 685-703, June.
    3. 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.
    4. 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.
    5. Hausman, Jerry, 2015. "Specification tests in econometrics," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 38(2), pages 112-134.
    6. Laura Azzimonti & Francesca Ieva & Anna Maria Paganoni, 2013. "Nonlinear nonparametric mixed-effects models for unsupervised classification," Computational Statistics, Springer, vol. 28(4), pages 1549-1570, August.
    7. Francesco Bartolucci, 2007. "A class of multidimensional IRT models for testing unidimensionality and clustering items," Psychometrika, Springer;The Psychometric Society, vol. 72(2), pages 141-157, June.
    8. Francesco Bartolucci & Silvia Bacci & Fulvia Pennoni, 2014. "Longitudinal analysis of self-reported health status by mixture latent auto-regressive models," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 63(2), pages 267-288, February.
    9. Agresti, Alan & Caffo, Brian & Ohman-Strickland, Pamela, 2004. "Examples in which misspecification of a random effects distribution reduces efficiency, and possible remedies," Computational Statistics & Data Analysis, Elsevier, vol. 47(3), pages 639-653, October.
    10. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    11. F. Thomas Juster & Richard Suzman, 1995. "An Overview of the Health and Retirement Study," Journal of Human Resources, University of Wisconsin Press, vol. 30, pages 7-56.
    12. Kim, Byung-Do & Blattberg, Robert C & Rossi, Peter E, 1995. "Modeling the Distribution of Price Sensitivity and Implications for Optimal Retail Pricing," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 291-303, July.
    13. Gary Chamberlain, 1980. "Analysis of Covariance with Qualitative Data," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(1), pages 225-238.
    14. Gregori Baetschmann, 2011. "Identification and estimation of thresholds in the fixed effects ordered logit model," ECON - Working Papers 046, Department of Economics - University of Zurich.
    15. Clifford M. Hurvich & Chih‐Ling Tsai, 1993. "A Corrected Akaike Information Criterion For Vector Autoregressive Model Selection," Journal of Time Series Analysis, Wiley Blackwell, vol. 14(3), pages 271-279, May.
    16. Vijverberg, Wim P., 2011. "Testing for IIA with the Hausman-McFadden Test," IZA Discussion Papers 5826, Institute of Labor Economics (IZA).
    17. Chih-Chien Yang & Chih-Chiang Yang, 2007. "Separating Latent Classes by Information Criteria," Journal of Classification, Springer;The Classification Society, vol. 24(2), pages 183-203, September.
    18. Francesco Bartolucci & Antonio Forcina, 2005. "Likelihood inference on the underlying structure of IRT models," Psychometrika, Springer;The Psychometric Society, vol. 70(1), pages 31-43, March.
    19. Bartolucci, Francesco & Belotti, Federico & Peracchi, Franco, 2015. "Testing for time-invariant unobserved heterogeneity in generalized linear models for panel data," Journal of Econometrics, Elsevier, vol. 184(1), pages 111-123.
    20. Heckman, James & Singer, Burton, 1984. "A Method for Minimizing the Impact of Distributional Assumptions in Econometric Models for Duration Data," Econometrica, Econometric Society, vol. 52(2), pages 271-320, March.
    21. Partha Deb, 2001. "A discrete random effects probit model with application to the demand for preventive care," Health Economics, John Wiley & Sons, Ltd., vol. 10(5), pages 371-383, July.
    22. Murray Aitkin, 1999. "A General Maximum Likelihood Analysis of Variance Components in Generalized Linear Models," Biometrics, The International Biometric Society, vol. 55(1), pages 117-128, March.
    23. F. Bartolucci & R. Bellio & A. Salvan & N. Sartori, 2016. "Modified Profile Likelihood for Fixed-Effects Panel Data Models," Econometric Reviews, Taylor & Francis Journals, vol. 35(7), pages 1271-1289, August.
    24. Jain, Dipak C & Vilcassim, Naufel J & Chintagunta, Pradeep K, 1994. "A Random-Coefficients Logit Brand-Choice Model Applied to Panel Data," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(3), pages 317-328, July.
    25. Hamparsum Bozdogan, 1987. "Model selection and Akaike's Information Criterion (AIC): The general theory and its analytical extensions," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 345-370, September.
    26. Alonso, A. & Litière, S. & Molenberghs, G., 2008. "A family of tests to detect misspecifications in the random-effects structure of generalized linear mixed models," Computational Statistics & Data Analysis, Elsevier, vol. 52(9), pages 4474-4486, May.
    27. Patrick J. Heagerty, 1999. "Marginally Specified Logistic-Normal Models for Longitudinal Binary Data," Biometrics, The International Biometric Society, vol. 55(3), pages 688-698, September.
    28. Rasmus Waagepetersen, 2006. "A Simulation‐based Goodness‐of‐fit Test for Random Effects in Generalized Linear Mixed Models," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 33(4), pages 721-731, December.
    29. Eric J. Tchetgen & Brent A. Coull, 2006. "A diagnostic test for the mixing distribution in a generalised linear mixed model," Biometrika, Biometrika Trust, vol. 93(4), pages 1003-1010, December.
    30. Stanley Sclove, 1987. "Application of model-selection criteria to some problems in multivariate analysis," Psychometrika, Springer;The Psychometric Society, vol. 52(3), pages 333-343, September.
    31. repec:bla:econom:v:65:y:1998:i:260:p:535-56 is not listed on IDEAS
    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. Shun Yu & Xianzheng Huang, 2017. "Random-intercept misspecification in generalized linear mixed models for binary responses," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(3), pages 333-359, 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. Bartolucci, Francesco & Bacci, Silvia & Pigini, Claudia, 2017. "Misspecification test for random effects in generalized linear finite-mixture models for clustered binary and ordered data," Econometrics and Statistics, Elsevier, vol. 3(C), pages 112-131.
    2. Shun Yu & Xianzheng Huang, 2017. "Random-intercept misspecification in generalized linear mixed models for binary responses," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 26(3), pages 333-359, August.
    3. Reza Drikvandi & Geert Verbeke & Geert Molenberghs, 2017. "Diagnosing misspecification of the random-effects distribution in mixed models," Biometrics, The International Biometric Society, vol. 73(1), pages 63-71, March.
    4. Lin, Kuo-Chin & Chen, Yi-Ju, 2015. "Detecting misspecification in the random-effects structure of cumulative logit models," Computational Statistics & Data Analysis, Elsevier, vol. 92(C), pages 126-133.
    5. Huang, Xianzheng, 2011. "Detecting random-effects model misspecification via coarsened data," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 703-714, January.
    6. Baltas, George & Doyle, Peter, 2001. "Random utility models in marketing research: a survey," Journal of Business Research, Elsevier, vol. 51(2), pages 115-125, February.
    7. Claudia Pigini & Alessandro Pionati & Francesco Valentini, 2023. "Specification testing with grouped fixed effects," Papers 2310.01950, arXiv.org.
    8. 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.
    9. Bartolucci, Francesco & Belotti, Federico & Peracchi, Franco, 2015. "Testing for time-invariant unobserved heterogeneity in generalized linear models for panel data," Journal of Econometrics, Elsevier, vol. 184(1), pages 111-123.
    10. Tanya P. Garcia & Yanyuan Ma, 2016. "Optimal Estimator for Logistic Model with Distribution-free Random Intercept," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 43(1), pages 156-171, March.
    11. Francesco Bartolucci & Francesco Valentini & Claudia Pigini, 2023. "Recursive Computation of the Conditional Probability Function of the Quadratic Exponential Model for Binary Panel Data," Computational Economics, Springer;Society for Computational Economics, vol. 61(2), pages 529-557, February.
    12. Li Donni, P., 2010. "Risk Preference Heterogeneity And Multiple Demand For Insurance," Health, Econometrics and Data Group (HEDG) Working Papers 10/17, HEDG, c/o Department of Economics, University of York.
    13. C. Giannetti & M. Madia & L. Moretti, 2013. "Job Insecurity and Financial Distress," Working Papers wp887, Dipartimento Scienze Economiche, Universita' di Bologna.
    14. Leonardo Grilli & Carla Rampichini, 2015. "Specification of random effects in multilevel models: a review," Quality & Quantity: International Journal of Methodology, Springer, vol. 49(3), pages 967-976, May.
    15. Po-Hsien Huang, 2017. "Asymptotics of AIC, BIC, and RMSEA for Model Selection in Structural Equation Modeling," Psychometrika, Springer;The Psychometric Society, vol. 82(2), pages 407-426, June.
    16. William H. Greene & David A. Hensher, 2008. "Modeling Ordered Choices: A Primer and Recent Developments," Working Papers 08-26, New York University, Leonard N. Stern School of Business, Department of Economics.
    17. Xianzheng Huang, 2009. "Diagnosis of Random-Effect Model Misspecification in Generalized Linear Mixed Models for Binary Response," Biometrics, The International Biometric Society, vol. 65(2), pages 361-368, June.
    18. Wang, Yong, 2010. "Fisher scoring: An interpolation family and its Monte Carlo implementations," Computational Statistics & Data Analysis, Elsevier, vol. 54(7), pages 1744-1755, July.
    19. Minelli, Liliana & Pigini, Claudia & Chiavarini, Manuela & Bartolucci, Francesco, 2014. "Employment status and perceived health condition: longitudinal data from Italy," MPRA Paper 55788, University Library of Munich, Germany.
    20. Nicolas Depraetere & Martina Vandebroek, 2014. "Order selection in finite mixtures of linear regressions," Statistical Papers, Springer, vol. 55(3), pages 871-911, August.

    More about this item

    Keywords

    Generalized Linear Mixed Models; Hausman Test; Item Response Theory; Latent Class model; Longitudinal data; Multilevel data;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    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:pra:mprapa:64220. 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: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    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.