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Symmetry
Volume 13
Issue 7
10.3390/sym13071286
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Article

Estimating the Variance of Estimator of the Latent Factor Linear Mixed Model Using Supplemented Expectation-Maximization Algorithm

by
Yenni Angraini
1,2,*,
Khairil Anwar Notodiputro
1,*,
Henk Folmer
2,
Asep Saefuddin
1 and
Toni Toharudin
3
1
Department of Statistics, IPB University, Bogor 16680, Indonesia
2
Faculty of Spatial Sciences, University of Groningen, 9747 Groningen, The Netherlands
3
Department of Statistics, University of Padjadjaran, Bandung 16426, Indonesia
*
Authors to whom correspondence should be addressed.
Symmetry 2021, 13(7), 1286; https://doi.org/10.3390/sym13071286
Submission received: 3 June 2021 / Revised: 1 July 2021 / Accepted: 15 July 2021 / Published: 17 July 2021
(This article belongs to the Special Issue Symmetry in Statistics and Data Science)
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Abstract

This paper deals with symmetrical data that can be modelled based on Gaussian distribution, such as linear mixed models for longitudinal data. The latent factor linear mixed model (LFLMM) is a method generally used for analysing changes in high-dimensional longitudinal data. It is usual that the model estimates are based on the expectation-maximization (EM) algorithm, but unfortunately, the algorithm does not produce the standard errors of the regression coefficients, which then hampers testing procedures. To fill in the gap, the Supplemented EM (SEM) algorithm for the case of fixed variables is proposed in this paper. The computational aspects of the SEM algorithm have been investigated by means of simulation. We also calculate the variance matrix of beta using the second moment as a benchmark to compare with the asymptotic variance matrix of beta of SEM. Both the second moment and SEM produce symmetrical results, the variance estimates of beta are getting smaller when number of subjects in the simulation increases. In addition, the practical usefulness of this work was illustrated using real data on political attitudes and behaviour in Flanders-Belgium.
Keywords: latent factor linear mixed model (LFLMM); expectation-maximization (EM) algorithm; supplemented EM algorithm; longitudinal data analysis latent factor linear mixed model (LFLMM); expectation-maximization (EM) algorithm; supplemented EM algorithm; longitudinal data analysis

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MDPI and ACS Style

Angraini, Y.; Notodiputro, K.A.; Folmer, H.; Saefuddin, A.; Toharudin, T. Estimating the Variance of Estimator of the Latent Factor Linear Mixed Model Using Supplemented Expectation-Maximization Algorithm. Symmetry 2021, 13, 1286. https://doi.org/10.3390/sym13071286

AMA Style

Angraini Y, Notodiputro KA, Folmer H, Saefuddin A, Toharudin T. Estimating the Variance of Estimator of the Latent Factor Linear Mixed Model Using Supplemented Expectation-Maximization Algorithm. Symmetry. 2021; 13(7):1286. https://doi.org/10.3390/sym13071286

Chicago/Turabian Style

Angraini, Yenni, Khairil Anwar Notodiputro, Henk Folmer, Asep Saefuddin, and Toni Toharudin. 2021. "Estimating the Variance of Estimator of the Latent Factor Linear Mixed Model Using Supplemented Expectation-Maximization Algorithm" Symmetry 13, no. 7: 1286. https://doi.org/10.3390/sym13071286

APA Style

Angraini, Y., Notodiputro, K. A., Folmer, H., Saefuddin, A., & Toharudin, T. (2021). Estimating the Variance of Estimator of the Latent Factor Linear Mixed Model Using Supplemented Expectation-Maximization Algorithm. Symmetry, 13(7), 1286. https://doi.org/10.3390/sym13071286

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