Harmonizing Healthy Aging Metrics: Comparing IRT and Equipercentile Equating for HRS Physical Activity Scales

Background: The Health and Retirement Study (HRS) administers three core physical activity (PA) items to all respondents and two additional items to a subsample. Because the two sets of items have different category response structures, they are difficult to use in a single combined scale. Purpose: This study aimed to harmonize these measures by developing and validating a crosswalk linking the three core items to an expanded five-item scale using Item Response Theory (IRT) and equipercentile (EP) equating. Methods: The 2022 HRS dataset was first partitioned into training (N = 14,856) and independent holdout (N = 1,000) samples. Both samples were subsequently reduced by restricting analyses to respondents with valid Psychosocial Leave-Behind survey weights (N = 2,820 and N = 831, respectively). A single-group nested scales equating design was employed. Following category and scale optimization, both IRT true-score and EP equating frameworks were employed followed by cross-validation and conditional error analysis. Results: The response formats for all five PA items were collapsed into a common three-category structure, which demonstrated improved category functioning and model fit. Expansion of the scale from three to five items increased total test information by 20.69%. A Graded Response Model produced a true-score equating crosswalk with acceptable predictive accuracy (MAE = 1.194; RMSE = 1.388; R² = 0.755). A parallel EP model applied log-linear smoothing to weighted empirical distributions and generated a raw-score translation table that demonstrated superior predictive performance (MAE = 0.837; RMSE = 1.089; R² = 0.766). Conclusion: Overall, IRT provided essential psychometric justification for the optimized three-category scale, whereas EP equating yielded the most accurate score conversions with lower prediction error. The validated crosswalk enables researchers to extend the expanded five-item physical activity metric to the broader HRS cohort, increasing analytic sample size while preserving behavioral information and improving the precision of epidemiological modeling.