Missing Data Treatment Of A Level 2 Variable In A 3 Level Hierarchical Linear Model
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Methodology for Multilevel Modeling in Educational Research
This edited volume documents attempts to conduct systematic and prodigious research using multilevel analysis in educational settings, and present their findings and identify future research directions. It showcases the versatility of multilevel analysis, and elucidates the unique advantages in examining complex and wide-ranging educational issues. This book brings together leading experts around the world to share their works in the field, highlighting recent advances, creative and unique approaches, and innovative methods using multilevel modeling and theoretical and practical aspects of multilevel analysis in culturally and linguistically-diverse educational contexts.
Missing Data Treatment of a Level-2 Variable in A 3-Level Hierarchical Linear Model
Data used in educational research often come with a hierarchical structure such as students nested in classrooms and classrooms nested in schools. Hierarchical linear model (HLM) analysis allows applied researchers to incorporate the hierarchical structure of the data into data analysis to examine effects of variables at each level. However, problems such as missing data pose analytical challenges of biased estimation. With missing data occurring in level-2 variables in a 3-level HLM analysis, the choice of the missing data treatment may affect parameter estimation at all levels. This Monte Carlo simulation study was designed to compare performance of six missing data treatment (MDT) methods--listwise deletion, mean substitution, restrictive Expectation-Maximization (EM), inclusive EM, restrictive multiple imputation (MI) and inclusive MI in generating unbiased estimates in a 3-level HLM model. An "intercept-only" 3-level HLM model was adopted. Missingness was generated as missing at random (MAR) for a level-2 predictor variable. The six MDTs were applied and the imputed datasets were analyzed using the same HLM model. Parameter estimates from the imputed datasets were compared to those obtained from the complete datasets. The comparisons focused on the accuracy and precision of parameter estimates of fixed and random effects in the HLM model. Results revealed that every MDT method produced more biases in the estimates with high proportion of missingness, and their performances improved as the level-sample size increased. Listwise deletion was a viable choice when level-2 sample size was small, it generated the most accurate but less precise estimates. With medium and large sample sizes, the restrictive EM method was effective in producing accurate and precise estimates for fixed effects parameters at all levels. The inclusive EM method outperformed all other methods in producing accurate and precise estimates for random effects. The two MI methods did not produce satisfactory estimates for level-2 fixed effects. However, the inclusive MI outperformed the restrictive MI on level-2 estimates of both fixed and random effects across the study conditions. This study provides statistical evidence and practical recommendations for researchers who must consider different MDT methods when they encounter missing data in hierarchical data structures.
Hierarchical Linear Modeling
This book provides a brief, easy-to-read guide to implementing hierarchical linear modeling using three leading software platforms, followed by a set of original how-to applications articles following a standardard instructional format. The "guide" portion consists of five chapters by the editor, providing an overview of HLM, discussion of methodological assumptions, and parallel worked model examples in SPSS, SAS, and HLM software. The "applications" portion consists of ten contributions in which authors provide step by step presentations of how HLM is implemented and reported for introductory to intermediate applications.