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Latent class models for time series analysis

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  • Suzanne Winsberg
  • Geert De Soete

Abstract

Latent class analysis of $N$ time series designed to classify and compare sets of series is discussed. For a particular time series $n$ in latent class $s(s=1,\;\ldots,\;S)$ the data $y_{n}$ are independently normally distributed with a vector of means, $\mu=(\mu_{1}(t),\;\ldots,\;\mu_{s}(t))'$ and common variance $\sigma^{2}$, that is, $y_{n}\sim{\cal N}(\mu_{s},\sigma^{2}I)$. The function of time, $\mu_{s}(t)$, can be represented by a linear combination of low‐order splines (piecewise polynomials). The probability density function for the data of a time series is posited to be a finite mixture of spherical multivariate normal densities. The maximum‐likelihood function is optimized by means of an EM algorithm. The stability of the estimates is investigated using a bootstrap procedure. Examples of real and artificial data are presented. Copyright © 1999 John Wiley & Sons, Ltd.

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  • Suzanne Winsberg & Geert De Soete, 1999. "Latent class models for time series analysis," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 15(3), pages 183-194, July.
    • Handle: RePEc:wly:apsmbi:v:15:y:1999:i:3:p:183-194
    DOI: 10.1002/(SICI)1526-4025(199907/09)15:33.0.CO;2-T
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    Cited by:

    1. Kerby Shedden & Robert Zucker, 2008. "Regularized Finite Mixture Models for Probability Trajectories," Psychometrika, Springer;The Psychometric Society, vol. 73(4), pages 625-646, December.

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