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AEA 2013 #548: When People Move: Using Cross-Classified and Multiple Membership Growth Curve Modeling in Non-Hierarchical Multilevel Data Structures

This demonstration explains the concepts of multiple membership and cross-classification and demonstrates the use of a multilevel modeling software package (MLwiN) to account for these data structures in analyzing repeated measures data

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Focus Search - background Terms and Definitions Multilevel Data Units “nested” within units Examples: Students in classrooms Employees in job sites Measurement occasions in students in schools Outcomes within groups are likely correlated, so use multilevel modeling, not regression Unconditional HLM Growth Models The reading score at time t for student i who attended school j: At Level 1 (measurement time): Intercept (Starting Point) Slope (Annual Growth) Year has to start at 0 Unconditional HLM Growth Models The reading score at time t for student i who attended school j: At Level 2 (student): Intercept: Slope: Unconditional HLM Growth Models At Level 3 (school): Intercept: Slope: The reading score at time t for student i who attended school j: Hierarchical Usually multilevel = hierarchical Each unit belongs to one (and only one) higher-level unit When this isn’t true, we have non-hierarchical multilevel data Cross-Classification Lower-level units belong to more than 1 higher-level classification Examples: Students may attend the same school but live in different neighborhoods (e.g., Scotland Neighbourhood Study, Garner & Raudenbush, 1991) (Fielding & Goldstein, 2006) Cross-Classification Multiple Membership Lower-level units belong to more than 1 higher-level unit within the same classification Examples: Patients served by multiple nurses Doctors practicing in multiple hospitals Students taking multiple classes Students attending more than one high school Sch1 Sch2 Sch3 Sch4 Sch5 Sch6 Sch1 Subsequent Schools First Year Schools Sch2 Sch3 Sch4 Cross-classified Multiple Membership Growth Models With Mobility (Adapted from Grady & Beretvas, 2010, pp. 405-407) The reading score at time t for student i who attended (the set of) school(s) j1 in the first year and (the set of) school(s) j2 in subsequent years: At Level 1 (measurement time): Intercept (Starting Point) Slope (Annual Growth) Year has to start at 0 Growth Models With Mobility (Adapted from Grady & Beretvas, 2010, pp. 405-407) The reading score at time t for student i who attended (the set of) school(s) j1 in the first year and (the set of) school(s) j2 in subsequent years: At Level 2 (student): Intercept: Slope: Growth Models With Mobility (Adapted from Grady & Beretvas, 2010, pp. 405-407) At Level 3 (school): Intercept: Slope: Starting point takes into account all first-year schools Growth curve also takes into account all subsequent schools Can ignoring mobility change your study’s findings?