title: Parallel but not equivalent: challenges and solutions for repeated assessment of cognition over time.
abstract: OBJECTIVE
  Analyses of individual differences in change may be unintentionally biased when versions of a neuropsychological test used at different follow-ups are not of equivalent difficulty. This study's objective was to compare mean, linear, and equipercentile equating methods and demonstrate their utility in longitudinal research.
  
  
  METHODS
  The Advanced Cognitive Training for Independent and Vital Elderly (ACTIVE, N = 1,401) study is a longitudinal randomized trial of cognitive training. The Alzheimer's Disease Neuroimaging Initiative (ADNI, n = 819) is an observational cohort study. Nonequivalent alternate versions of the Auditory Verbal Learning Test (AVLT) were administered in both studies.
  
  
  RESULTS
  Using visual displays, raw and mean-equated AVLT scores in both studies showed obvious nonlinear trajectories in reference groups that should show minimal change and poor equivalence over time (ps ≤ .001), and raw scores demonstrated poor fits in models of within-person change (root mean square errors of approximation, RMSEAs > 0.12). Linear and equipercentile equating produced more similar means in reference groups (ps ≥ .09) and performed better in growth models (RMSEAs < 0.05).
  
  
  CONCLUSIONS
  Equipercentile equating is the preferred equating method because it accommodates tests more difficult than a reference test at different percentiles of performance and performs well in models of within-person trajectory. The method has broad applications in both clinical and research settings to enhance the ability to use nonequivalent test forms.
authors.affiliation: Department of Mental Health, Johns Hopkins Bloomberg School of Public Health, Baltimore, MD, USA. aldengross@hsl.harvard.edu
authors.forename: Alden L
authors.initials: AL
authors.lastname: Gross
authors.forename: Sharon K
authors.initials: SK
authors.lastname: Inouye
authors.forename: George W
authors.initials: GW
authors.lastname: Rebok
authors.forename: Jason
authors.initials: J
authors.lastname: Brandt
authors.forename: Paul K
authors.initials: PK
authors.lastname: Crane
authors.forename: Jeanine M
authors.initials: JM
authors.lastname: Parisi
authors.forename: Doug
authors.initials: D
authors.lastname: Tommet
authors.forename: Karen
authors.initials: K
authors.lastname: Bandeen-Roche
authors.forename: Michelle C
authors.initials: MC
authors.lastname: Carlson
authors.forename: Richard N
authors.initials: RN
authors.lastname: Jones
mesh_terms: D000368:Aged; D000369:Aged, 80 and over; D003071:Cognition; D003072:Cognition Disorders / Q000175:diagnosis* / Q000523:psychology; D005260:Female; D006801:Humans; D007206:Individuality; D008137:Longitudinal Studies; D008297:Male; D009483:Neuropsychological Tests; D014706:Verbal Learning