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Latent variable models for ordinal data by using the adaptive quadrature approximation

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  • Silvia Cagnone

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  • Paola Monari

Abstract

Latent variable models for ordinal data represent a useful tool in different fields of research in which the constructs of interest are not directly observable so that one or more latent variables are required to reduce the complexity of the data. In these cases problems related to the integration of the likelihood function of the model can arise. Indeed analytical solutions do not exist and in presence of several latent variables the most used classical numerical approximation, the Gauss Hermite quadrature, cannot be applied since it requires several quadrature points per dimension in order to obtain quite accurate estimates and hence the computational effort becomes not feasible. Alternative solutions have been proposed in the literature, like the Laplace approximation and the adaptive quadrature. Different studies demonstrated the superiority of the latter method particularly in presence of categorical data. In this work we present a simulation study for evaluating the performance of the adaptive quadrature approximation for a general class of latent variable models for ordinal data under different conditions of study. A real data example is also illustrated. Copyright Springer-Verlag 2013

Suggested Citation

  • Silvia Cagnone & Paola Monari, 2013. "Latent variable models for ordinal data by using the adaptive quadrature approximation," Computational Statistics, Springer, vol. 28(2), pages 597-619, April.
  • Handle: RePEc:spr:compst:v:28:y:2013:i:2:p:597-619
    DOI: 10.1007/s00180-012-0319-z
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    References listed on IDEAS

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    Cited by:

    1. Silvia Cagnone & Francesco Bartolucci, 2017. "Adaptive Quadrature for Maximum Likelihood Estimation of a Class of Dynamic Latent Variable Models," Computational Economics, Springer;Society for Computational Economics, vol. 49(4), pages 599-622, April.
    2. Cagnone, Silvia & Bartolucci, Francesco, 2013. "Adaptive quadrature for likelihood inference on dynamic latent variable models for time-series and panel data," MPRA Paper 51037, University Library of Munich, Germany.
    3. Marino, Maria Francesca & Alfó, Marco, 2016. "Gaussian quadrature approximations in mixed hidden Markov models for longitudinal data: A simulation study," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 193-209.

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