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

Yenni Angraini*, Khairil Anwar Notodiputro*, Henk Folmer, Asep Saefuddin, Toni Toharudin

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

1 Citation (Scopus)
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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.

Original languageEnglish
Article number1286
Number of pages13
JournalSymmetry
Volume13
Issue number7
DOIs
Publication statusPublished - Jul-2021

Keywords

  • Expectation-maximization (EM) algorithm
  • Latent factor linear mixed model (LFLMM)
  • Longitudinal data analysis
  • Supplemented EM algorithm

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