Maximum likelihood estimation of discrete latent variable (DLV) models is usually performed by the expectation-maximization (EM) algorithm. A well-known drawback is related to the multimodality of the log-likelihood function so that the estimation algorithm can converge to a local maximum, not corresponding to the global one. We propose a tempered EM algorithm to explore the parameter space adequately for two main classes of DLV models, namely latent class and hidden Markov. We compare the proposal with the standard EM algorithm by an extensive Monte Carlo simulation study, evaluating both the ability to reach the global maximum and the computational time. We show the results of the analysis of discrete and continuous cross-sectional and longitudinal data referring to some applications of interest. All the results provide supporting evidence that the proposal outperforms the standard EM algorithm, and it significantly improves the chance to reach the global maximum. The advantage is relevant even considering the overall computing time.

Brusa, L., Bartolucci, F., Pennoni, F. (2023). Tempered expectation-maximization algorithm for the estimation of discrete latent variable models. COMPUTATIONAL STATISTICS, 38, 1391-1424 [10.1007/s00180-022-01276-7].

Tempered expectation-maximization algorithm for the estimation of discrete latent variable models

Brusa Luca
;
Pennoni Fulvia
2023

Abstract

Maximum likelihood estimation of discrete latent variable (DLV) models is usually performed by the expectation-maximization (EM) algorithm. A well-known drawback is related to the multimodality of the log-likelihood function so that the estimation algorithm can converge to a local maximum, not corresponding to the global one. We propose a tempered EM algorithm to explore the parameter space adequately for two main classes of DLV models, namely latent class and hidden Markov. We compare the proposal with the standard EM algorithm by an extensive Monte Carlo simulation study, evaluating both the ability to reach the global maximum and the computational time. We show the results of the analysis of discrete and continuous cross-sectional and longitudinal data referring to some applications of interest. All the results provide supporting evidence that the proposal outperforms the standard EM algorithm, and it significantly improves the chance to reach the global maximum. The advantage is relevant even considering the overall computing time.
Articolo in rivista - Articolo scientifico
Annealing; Global maximum; Hidden Markov model; Latent class model; Local maxima;
English
7-ott-2022
2023
38
1391
1424
open
Brusa, L., Bartolucci, F., Pennoni, F. (2023). Tempered expectation-maximization algorithm for the estimation of discrete latent variable models. COMPUTATIONAL STATISTICS, 38, 1391-1424 [10.1007/s00180-022-01276-7].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/393748
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