TY - JOUR

T1 - Estimating the variance of estimator of the latent factor linear mixed model using supplemented expectation-maximization algorithm

AU - Angraini, Yenni

AU - Notodiputro, Khairil Anwar

AU - Folmer, Henk

AU - Saefuddin, Asep

AU - Toharudin, Toni

N1 - Funding Information:
Funding: This research was funded by RUG and IPB University.
Publisher Copyright:
© 2021 by the authors. Licensee MDPI, Basel, Switzerland.

PY - 2021/7

Y1 - 2021/7

N2 - 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.

AB - 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.

KW - Expectation-maximization (EM) algorithm

KW - Latent factor linear mixed model (LFLMM)

KW - Longitudinal data analysis

KW - Supplemented EM algorithm

UR - http://www.scopus.com/inward/record.url?scp=85111374704&partnerID=8YFLogxK

U2 - 10.3390/sym13071286

DO - 10.3390/sym13071286

M3 - Article

AN - SCOPUS:85111374704

SN - 2073-8994

VL - 13

JO - Symmetry

JF - Symmetry

IS - 7

M1 - 1286

ER -