Slope Difference Testing of Three Way Interactions in Longitudinal Multilevel Models Across Five Statistical Packages

• In Event: AERA Roundtable Session Wednesday 3:45 pm - Gold 3
  In Roundtable Session: Recent Developments in Multilevel Modeling: Model Estimation and Evaluation

Abstract

This paper offers a concise walkthrough of post-hoc probing of three-way cross-level interactions in longitudinal three-level MLMs across five leading statistical packages (R, HLM 8, SAS, Stata, and Mplus). Using the Early Childhood Longitudinal Study 2011 dataset (~17,000 students nested within 1,900 schools across nine waves), we show, step-by-step, how to compute simple slopes and six slope-difference contrasts for the Time × Approaches-to-Learning × School-Sector interaction in each program. All platforms yield virtually identical estimates; minor deviations in standard errors do not alter statistical conclusions. By collating syntax and interpretation in one place, the paper equips applied researchers to replicate and report rigorous three-way interaction probes irrespective of software choice.

Authors

• Peyton Perduyn, University of North Texas

• Yan Zhang, University of North Texas

• Qi Chen, University of North Texas