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Estimation of generalized linear latent variable models via fully exponential Laplace approximation

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  • Bianconcini, Silvia
  • Cagnone, Silvia

Abstract

Latent variable models represent a useful tool in different fields of research in which the constructs of interest are not directly observable. In such models, problems related to the integration of the likelihood function can arise since analytical solutions do not exist. Numerical approximations, like the widely used Gauss–Hermite (GH) quadrature, are generally applied to solve these problems. However, GH becomes unfeasible as the number of latent variables increases. Thus, alternative solutions have to be found. In this paper, we propose an extended version of the Laplace method for approximating the integrals, known as fully exponential Laplace approximation. It is computational feasible also in presence of many latent variables, and it is more accurate than the classical Laplace approximation. The method is developed within the Generalized Linear Latent Variable Models (GLLVM) framework.

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  • 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.
    • Handle: RePEc:eee:jmvana:v:112:y:2012:i:c:p:183-193
    DOI: 10.1016/j.jmva.2012.06.005
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    References listed on IDEAS

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    3. Jenni Niku & David I. Warton & Francis K. C. Hui & Sara Taskinen, 2017. "Generalized Linear Latent Variable Models for Multivariate Count and Biomass Data in Ecology," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 22(4), pages 498-522, December.
    4. Kelava, Augustin & Kohler, Michael & Krzyżak, Adam & Schaffland, Tim Fabian, 2017. "Nonparametric estimation of a latent variable model," Journal of Multivariate Analysis, Elsevier, vol. 154(C), pages 112-134.
    5. Andersson, Björn & Jin, Shaobo & Zhang, Maoxin, 2023. "Fast estimation of multiple group generalized linear latent variable models for categorical observed variables," Computational Statistics & Data Analysis, Elsevier, vol. 182(C).

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