To Be Long or To Be Wide: How Data Format Influences Convergence and Estimation Accuracy in Multilevel Structural Equation Modeling

A two-level data set can be structured in either long format (LF) or wide format (WF), and both have corresponding SEM approaches for estimating multilevel models. Intuitively, one might expect these approaches to perform similarly. However, the two data formats yield data matrices with different numbers of columns and rows, and their cols:rows is related to the magnitude of eigenvalue bias in sample covariance matrices. Previous studies have shown similar performance for both approaches, but they were limited to settings where cols≪rows in both data formats. We conducted a Monte Carlo study to investigate whether varying cols:rows result in differing performances. Specifically, we examined the p:N (cols:rows) effect on convergence and estimation accuracy in multilevel settings. Our findings suggest that (1) the LF approach is more likely to achieve convergence, but for the models that converged in both, (2) the LF and WF approach yield similar estimation accuracy, which is related to (3) differential cols:rows effects in both approaches, and (4) smaller <i>ICC</i> values lead to less accurate between-group parameter estimates.

两水平数据集可采用长格式（LF）或宽格式（WF）进行构建，二者均配有适配的结构方程模型（Structural Equation Modeling, SEM）方法以开展多层模型估计。直观而言，人们或许会认为这两类方法的表现相近。然而，这两种数据格式所生成的数据矩阵的行列数量存在差异，且其列行数比与样本协方差矩阵的特征值偏差幅度相关。既往研究表明两类方法性能相近，但此类研究均局限于两种数据格式下列数远小于行数（cols≪rows）的场景。本研究通过开展蒙特卡洛研究，探究列行数比的变化是否会导致模型表现出现差异。具体而言，我们考察了p:N（即列行数比）对多层模型场景下模型收敛性与估计精度的影响。本研究结果显示：（1）长格式方法更易实现模型收敛；（2）在两种格式均成功收敛的模型中，长格式与宽格式方法的估计精度相近，这一结果与（3）两类方法所受列行数比的差异化影响有关；（4）更小的组内相关系数（Intraclass Correlation Coefficient, ICC）值会导致组间参数估计的精度更低。