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An EM algorithm for the estimation of parametric and nonparametric hierarchical nonlinear models

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  • Jeroen K. Vermunt

Abstract

It is shown how to implement an EM algorithm for maximum likelihood estimation of hierarchical nonlinear models for data sets consisting of more than two levels of nesting. This upward–downward algorithm makes use of the conditional independence assumptions implied by the hierarchical model. It cannot only be used for the estimation of models with a parametric specification of the random effects, but also to extend the two‐level nonparametric approach – sometimes referred to as latent class regression – to three or more levels. The proposed approach is illustrated with an empirical application.

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  • Jeroen K. Vermunt, 2004. "An EM algorithm for the estimation of parametric and nonparametric hierarchical nonlinear models," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 58(2), pages 220-233, May.
    • Handle: RePEc:bla:stanee:v:58:y:2004:i:2:p:220-233
    DOI: 10.1046/j.0039-0402.2003.00257.x
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    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. 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.
    3. Begoña A. Farizo & John Joyce & Mario Soliño, 2014. "Dealing with Heterogeneous Preferences Using Multilevel Mixed Models," Land Economics, University of Wisconsin Press, vol. 90(1), pages 181-198.
    4. Hilger, James & Hanemann, Michael, 2006. "Heterogeneous Preferences for Water Quality: A Finite Mixture Model of Beach Recreation in Southern California," Department of Agricultural & Resource Economics, UC Berkeley, Working Paper Series qt0565c0b2, Department of Agricultural & Resource Economics, UC Berkeley.
    5. Carlos Forero & Josué Almansa & Núria Adroher & Jeroen Vermunt & Gemma Vilagut & Ron Graaf & Josep-Maria Haro & Jordi Alonso Caballero, 2014. "Partial Likelihood Estimation of IRT Models with Censored Lifetime Data: An Application to Mental Disorders in the ESEMeD Surveys," Psychometrika, Springer;The Psychometric Society, vol. 79(3), pages 470-488, July.
    6. Dylan Molenaar & Conor Dolan & Paul Boeck, 2012. "The Heteroscedastic Graded Response Model with a Skewed Latent Trait: Testing Statistical and Substantive Hypotheses Related to Skewed Item Category Functions," Psychometrika, Springer;The Psychometric Society, vol. 77(3), pages 455-478, July.

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