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Explicit estimating equations for semiparametric generalized linear latent variable models

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  • Yanyuan Ma
  • Marc G. Genton

Abstract

Summary. We study generalized linear latent variable models without requiring a distributional assumption of the latent variables. Using a geometric approach, we derive consistent semiparametric estimators. We demonstrate that these models have a property which is similar to that of a sufficient complete statistic, which enables us to simplify the estimating procedure and explicitly to formulate the semiparametric estimating equations. We further show that the explicit estimators have the usual root n consistency and asymptotic normality. We explain the computational implementation of our method and illustrate the numerical performance of the estimators in finite sample situations via extensive simulation studies. The advantage of our estimators over the existing likelihood approach is also shown via numerical comparison. We employ the method to analyse a real data example from economics.

Suggested Citation

  • Yanyuan Ma & Marc G. Genton, 2010. "Explicit estimating equations for semiparametric generalized linear latent variable models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(4), pages 475-495, September.
    • Handle: RePEc:bla:jorssb:v:72:y:2010:i:4:p:475-495
    DOI: 10.1111/j.1467-9868.2010.00741.x
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    1. Verbeke, Geert & Lesaffre, Emmanuel, 1997. "The effect of misspecifying the random-effects distribution in linear mixed models for longitudinal data," Computational Statistics & Data Analysis, Elsevier, vol. 23(4), pages 541-556, February.
    2. Youngjo Lee & John A. Nelder, 2006. "Double hierarchical generalized linear models (with discussion)," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 55(2), pages 139-185, April.
    3. Newey, Whitney K, 1990. "Semiparametric Efficiency Bounds," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 5(2), pages 99-135, April-Jun.
    4. Philippe Huber & Elvezio Ronchetti & Maria‐Pia Victoria‐Feser, 2004. "Estimation of generalized linear latent variable models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 66(4), pages 893-908, November.
    5. Anastasios A. Tsiatis & Yanyuan Ma, 2004. "Locally efficient semiparametric estimators for functional measurement error models," Biometrika, Biometrika Trust, vol. 91(4), pages 835-848, December.
    6. Irini Moustaki & Martin Knott, 2000. "Generalized latent trait models," Psychometrika, Springer;The Psychometric Society, vol. 65(3), pages 391-411, September.
    7. Moustaki, Irini & Victoria-Feser, Maria-Pia, 2006. "Bounded-Influence Robust Estimation in Generalized Linear Latent Variable Models," Journal of the American Statistical Association, American Statistical Association, vol. 101, pages 644-653, June.
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    Cited by:

    1. Silvia Cagnone & Cinzia Viroli, 2014. "A factor mixture model for analyzing heterogeneity and cognitive structure of dementia," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 98(1), pages 1-20, January.
    2. 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.
    3. Vock, David & Davidian, Marie & Tsiatis, Anastasios, 2014. "SNP_NLMM: A SAS Macro to Implement a Flexible Random Effects Density for Generalized Linear and Nonlinear Mixed Models," Journal of Statistical Software, Foundation for Open Access Statistics, vol. 56(c02).
    4. Bianconcini, Silvia & Cagnone, Silvia, 2012. "Estimation of generalized linear latent variable models via fully exponential Laplace approximation," Journal of Multivariate Analysis, Elsevier, vol. 112(C), pages 183-193.
    5. Yanyuan Ma & Jeffrey D. Hart & Ryan Janicki & Raymond J. Carroll, 2011. "Local and omnibus goodness‐of‐fit tests in classical measurement error models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 73(1), pages 81-98, January.
    6. Francis K.C. Hui & Nicole A. Hill & A.H. Welsh, 2022. "Assuming independence in spatial latent variable models: Consequences and implications of misspecification," Biometrics, The International Biometric Society, vol. 78(1), pages 85-99, March.

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