A Method for Imputing Misfit Ordinal Responses in a Guttman Scale

This study introduces a method for imputing misfitting ordinal responses at the intersection of misfit persons and misfit items within a Guttman-ordered dataset. The approach replaces each identified misfit response with the nearest integer to the average of its surrounding responses in a local 3×3 window. We apply this technique to a university student depression survey dataset (University Student Depression Inventory, USDI) to evaluate its effectiveness. Results indicate that the imputation method substantially reduces mean-square fit statistics for targeted misfitting items, improving their fit to the Rasch model while preserving the integrity of other item responses. Compared to traditional approaches that delete misfitting persons or items, the proposed method retains the full dataset and yields more stable item difficulty estimates and fit statistics. Statistical comparisons confirm that the imputation does not significantly distort non-misfitting item metrics or the overall measurement scale. This targeted imputation offers an effective alternative to row-wise or column-wise deletions, mitigating data loss and potential bias, and has important implications for psychometric measurement practice.