Slope-difference testing of three-way interactions in longitudinal multilevel models across five statistical packages

Although multilevel modeling is widely used, clear guidance on probing higher-order interactions remains scarce. This paper offers a concise, practitioner-friendly 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 M plus ). 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.