Children's Learning Institute, University of Texas Health Science Center at Houston, 7000 Fannin St., Suite 2373I, Houston, TX, 77030, USA.
Office of Institutional Research, National Central University, Taoyuan, Taiwan.
Behav Res Methods. 2018 Apr;50(2):786-803. doi: 10.3758/s13428-017-0905-7.
To prevent biased estimates of intraindividual growth and interindividual variability when working with clustered longitudinal data (e.g., repeated measures nested within students; students nested within schools), individual dependency should be considered. A Monte Carlo study was conducted to examine to what extent two model-based approaches (multilevel latent growth curve model - MLGCM, and maximum model - MM) and one design-based approach (design-based latent growth curve model - D-LGCM) could produce unbiased and efficient parameter estimates of intraindividual growth and interindividual variability given clustered longitudinal data. The solutions of a single-level latent growth curve model (SLGCM) were also provided to demonstrate the consequences of ignoring individual dependency. Design factors considered in the present simulation study were as follows: number of clusters (NC = 10, 30, 50, 100, 150, 200, and 500) and cluster size (CS = 5, 10, and 20). According to our results, when intraindividual growth is of interest, researchers are free to implement MLGCM, MM, or D-LGCM. With regard to interindividual variability, MLGCM and MM were capable of producing accurate parameter estimates and SEs. However, when D-LGCM and SLGCM were applied, parameter estimates of interindividual variability were not comprised exclusively of the variability in individual (e.g., students) growth but instead were the combined variability of individual and cluster (e.g., school) growth, which cannot be interpreted. The take-home message is that D-LGCM does not qualify as an alternative approach to analyzing clustered longitudinal data if interindividual variability is of interest.
为了防止在处理聚类纵向数据（例如，学生内部的重复测量；学生内部的学校）时对个体内增长和个体间变异性的有偏估计，应考虑个体依赖性。进行了一项蒙特卡罗研究，以检验基于模型的两种方法（多层次潜在增长曲线模型-MLGCM 和最大模型-MM）和一种基于设计的方法（基于设计的潜在增长曲线模型-D-LGCM）在给定聚类纵向数据的情况下，能够在多大程度上产生个体内增长和个体间变异性的无偏和有效的参数估计。还提供了单水平潜在增长曲线模型（SLGCM）的解，以说明忽略个体依赖性的后果。本模拟研究中考虑的设计因素如下：聚类数量（NC=10、30、50、100、150、200 和 500）和聚类大小（CS=5、10 和 20）。根据我们的结果，当个体内增长是研究重点时，研究人员可以自由实施 MLGCM、MM 或 D-LGCM。关于个体间变异性，MLGCM 和 MM 能够产生准确的参数估计值和 SE。然而，当应用 D-LGCM 和 SLGCM 时，个体间变异性的参数估计值不仅包括个体（例如，学生）增长的变异性，还包括个体和聚类（例如，学校）增长的组合变异性，这是无法解释的。重要的是，如果关注个体间变异性，则 D-LGCM 不符合分析聚类纵向数据的替代方法。
