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Gaussian quadrature approximations in mixed hidden Markov models for longitudinal data: A simulation study

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  • Marino, Maria Francesca
  • Alfó, Marco

Abstract

Mixed hidden Markov models represent an interesting tool for the analysis of longitudinal data. They allow to account for both time-constant and time-varying sources of unobserved heterogeneity, which are frequent in this kind of studies. Individual-specific latent features, which may be either constant or varying over time, are included in the linear predictor and lead to a general form of dependence between individual measurements. When a parametric (continuous) distribution is associated to time-constant random parameters, the estimation process requires the calculation of (multiple) integrals. These, generally, have not a closed form and should be numerically approximated. The aim is to compare the standard, the adaptive and the pseudo-adaptive Gaussian quadrature approximations by means of a large scale simulation study, where continuous and discrete responses with (conditional) density in the exponential family are considered. Simulation results show that the approximation error is often substantially reduced when the adaptive quadrature rules are considered in place of the standard one. Such an improvement comes at the cost of a higher computational complexity when the fully adaptive scheme is applied. It is shown that, when a sufficient number of repeated measurements per unit is available, the pseudo-adaptive quadrature represents a convenient compromise between quality of results and computational complexity.

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  • 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.
  • Handle: RePEc:eee:csdana:v:94:y:2016:i:c:p:193-209
    DOI: 10.1016/j.csda.2015.07.016
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    2. Antonello Maruotti & Jan Bulla & Tanya Mark, 2019. "Assessing the influence of marketing activities on customer behaviors: a dynamic clustering approach," METRON, Springer;Sapienza Università di Roma, vol. 77(1), pages 19-42, April.
    3. Catania, Leopoldo & Di Mari, Roberto, 2021. "Hierarchical Markov-switching models for multivariate integer-valued time-series," Journal of Econometrics, Elsevier, vol. 221(1), pages 118-137.
    4. Giorgio Eduardo Montanari & Marco Doretti & Maria Francesca Marino, 2022. "Model-based two-way clustering of second-level units in ordinal multilevel latent Markov models," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(2), pages 457-485, June.

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