Parsimony vs. Complexity: A Comparison of Two-Level, Three-Level, and Cross- Classified Models Using Add Health and AHAA Data

Multilevel modeling has become a common analytic technique across a variety of disciplines including education and other social and behavioral sciences. Such models are often used when researchers examine relationships between school and/or neighborhood characteristics and some individual-level outcome (e.g., academic achievement, high school completion). Although many samples are theoretically cross-classified between multiple level-2 units, the application of cross-classified random effects models is rare in such research. This paper compares model fit and parameter estimates from five different PROC MIXED multilevel modeling approaches—(a) a two-level model with students nested in schools and neighborhood variables included as contextual variables at Level 1, (b) a two-level model with students nested in neighborhoods and school variables included as contextual variables at Level 1, (c) a three-level model with students nested in schools nested in neighborhoods, (d) a three-level model with students nested in neighborhoods nested in schools, and (e) a cross-classified random effects model with students cross-nested in schools and neighborhoods. Example SAS ® code for each of the modeling approaches is also included