Diagnosing Ceiling Effects and Unstable Nonlinearity in Short Ordinal Scales: A TIMSS 2023 Application

Short ordinal self-report scales are widely used to study children's digital lives, yet their measurement properties can distort conclusions about nonlinear relationships. We introduced an integrated diagnostic workflow for such scales-covering range, structure, reliability, method variance and functional form-and applied it to the TIMSS 2023 Digital Self-Efficacy scale across all 63 Grade 4 and 47 Grade 8 education-system and benchmarking samples (source database N = 719,881 children; 630,461 with complete seven-item measurement data). The scale was endpoint-concentrated, markedly at Grade 8, losing 83% and 95% of its test information between the mean and two standard deviations above it; an exact marginal calculation from a testlet model gave 80% and 89%. The apparent multidimensionality was better represented as localized covariance among three similarly worded items than as a separable second dimension, and omega hierarchical of 0.79 and 0.83 supported using the total score. In a factorial simulation evaluating the population projection coefficient on the analysis scale, endpoint concentration raised rejection of no curvature from 5.4% to 16.7% with raw summed scores, while latent scoring returned it to 5.5% and raised power from 71% to 88%, whether the item parameters were known or, in a smaller supporting condition, estimated in the analysis sample. Applied to cybervictimization, the quadratic association was attenuated but did not reverse sign once covariates were matched, and its prediction interval included zero. The range and reliability diagnostics behaved similarly on a second scale from the same assessment; broader applicability of the full workflow is proposed on theoretical grounds rather than established here.