Two-Level Random Effects in Multivariate Linear Mixed Model for Longitudinal Data.

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Bibliographic Details
Title:	Two-Level Random Effects in Multivariate Linear Mixed Model for Longitudinal Data.
Authors:	Santi, Vera Maya¹ vmsanti@unj.ac.id, Notodiputro, Khairil Anwar² khairil@apps.ipb.ac.id, Indahwati³ indahwati@apps.ipb.ac.id, Sartono, Bagus⁴ bagusco@apps.ipb.ac.id, Susetyo, Budi⁴ budisu@apps.ipb.ac.id, Kurnia, Anang⁵ anangk@apps.ipb.ac.id
Source:	Engineering Letters. Jan2026, Vol. 34 Issue 1, p368-379. 12p.
Subjects:	Multilevel models, Random effects model, Multivariate analysis, Simulation methods & models, Longitudinal method, Parameter estimation
Abstract:	This research is motivated by complex data problems such as longitudinal data structures, multivariate response variables, and hierarchical random effects. These problems must be addressed to answer substantive questions regarding the interrelated change problem between the measurement time and the variance at each level. A random effect is more problematic when a random hierarchical impact has some fixed effects. The basic model was introduced, i.e., a multivariate linear mixed model for longitudinal data, while a multilevel performance model was introduced for hierarchical data structures. This study proposes to develop a MLMM with two-level random effects on the nested data structure, namely the multilevel multivariate linear mixed model (MMLMM). The initial stage of this research involves deriving an analytical formula for parameter estimation within the model. The performance of the model is examined through the RMSEp, bias, and the consistency of the parameter coefficients. To evaluate the effectiveness of the proposed model, a simulationbased analysis was conducted. For an empirical study, MMLMM was applied to the average natural sciences major of high school national exam in West Java Province, Indonesia. Applying the proposed model to actual data shows that the standard error of the national exam average predicted score tends to be smaller when compared to the standard model. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	This research is motivated by complex data problems such as longitudinal data structures, multivariate response variables, and hierarchical random effects. These problems must be addressed to answer substantive questions regarding the interrelated change problem between the measurement time and the variance at each level. A random effect is more problematic when a random hierarchical impact has some fixed effects. The basic model was introduced, i.e., a multivariate linear mixed model for longitudinal data, while a multilevel performance model was introduced for hierarchical data structures. This study proposes to develop a MLMM with two-level random effects on the nested data structure, namely the multilevel multivariate linear mixed model (MMLMM). The initial stage of this research involves deriving an analytical formula for parameter estimation within the model. The performance of the model is examined through the RMSEp, bias, and the consistency of the parameter coefficients. To evaluate the effectiveness of the proposed model, a simulationbased analysis was conducted. For an empirical study, MMLMM was applied to the average natural sciences major of high school national exam in West Java Province, Indonesia. Applying the proposed model to actual data shows that the standard error of the national exam average predicted score tends to be smaller when compared to the standard model. [ABSTRACT FROM AUTHOR]
ISSN:	1816093X