Test equating sleep scales: applying the Leunbach's model

In most cases, the total scores from different instruments assessing the same construct are not directly comparable, but must be equated. In this study we aimed to illustrate a novel test equating methodology applied to sleep functions, a domain in which few score comparability studies exist.

Eight scales from two cross-sectional self-report studies were considered, and one scale was common to both studies. The International Classification of Functioning, Disability and Health (ICF) was used to establish content comparability. Direct (common persons) and indirect (common item) equating was assessed by means of Leunbach's model, which equates the scores of two scales depending on the same person parameter, taking into account several tests of fit and the Standard Error of Equating (SEE).

All items were linked to the body functions category b134 of the ICF, which corresponds to 'Sleep functions'. The scales were classified into three sleep aspects: four scales were assessing mainly sleep disturbance, one quality of sleep, and three impact of sleep on daily life. Of 16 direct equated pairs, 15 could be equated according to Leunbach's model, and of 12 indirect equated pairs, 8 could be equated. Raw score conversion tables between each of these 23 equated pairs are provided. The SEE was higher for indirect than for direct equating. Pairs measuring the same sleep aspect did not show better fit indices than pairs from different aspects. The instruments mapped to a higher order concept of sleep functions.

Leunbach's equating model has been successfully applied to a functioning domain little explored in test equating. This novel methodology, together with the ICF, enables comparison of clinical outcomes and research results, and facilitates communication among clinicians.