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