ABSTRACT
Introduction ......................................................................................................... 390 Data ...................................................................................................................... 391
PIRLS ................................................................................................................ 391 Plausible Value Outcomes ............................................................................. 392 Predictors ......................................................................................................... 394 Exploratory Data Analysis ............................................................................ 394 Missing Data ...................................................................................................400 Multiple Imputation ......................................................................................400
Multilevel Modeling ...........................................................................................405 Presentation of the Model .............................................................................405 Empty Model .................................................................................................. 407 Modeling Strategy ..........................................................................................408 Model Specification and Comparison .........................................................409 R2-Type Measures for Explained Variance ................................................. 412 Incorporating Design Weights ...................................................................... 414 Model Diagnostics .......................................................................................... 416 Interpretation of Results ................................................................................ 418
Discussion ............................................................................................................ 419 Other Multilevel Models ............................................................................... 419 Current and Future Research in Multilevel Analysis................................420
Acknowledgment ................................................................................................ 421 References .............................................................................................................422
Large-scale assessment data often exhibit a multilevel structure as a result of either sampling procedures, such as stratified sampling, or contextual factors, such as school settings where students are nested within schools, or cross-cultural settings where individuals are nested within countries. Observations within a cluster are likely to be correlated with one another and their dependency should be accounted for in the data analysis to permit valid statistical inferences. Moreover, relationships among variables may vary within clusters allowing for more detailed and informative study of contextual effects and their correlates.
