Transformation of Rasch model logits for enhanced interpretability.

Area of Science:

• Psychometrics
• Health Outcomes Research
• Statistical Modeling

Background:

• Rasch model enables linear measurement from ordinal health outcome data.
• Log-odds units (logits) from Rasch models can be less intuitive for users.
• Transforming logits into user-friendly ranges preserves linear properties and enhances interpretability.

Purpose of the Study:

• To explore and illustrate logit transformations using the least measurable difference (LMD), standard error of measurement (SEM), and least significant difference (LSD).
• To evaluate the suitability of different user-defined ranges (e.g., 0-10, 0-100, 0-24) compared to LMD, SEM, and LSD transformations.
• To introduce a freely available Excel tool for performing these logit transformations.

Main Methods:

• Empirical illustration using 1053 responses to the Epworth Sleepiness Scale.
• Transformation of logit measures into LMD, SEM, LSD, and user-defined ranges (0-10, 0-100, 0-24).
• Utilized a custom-developed Excel tool for conducting the transformations.

Main Results:

• LMD, SEM, and LSD transformations resulted in ranges of 0-34, 0-17, and 0-12, respectively.
• The 0-10 range was narrower than LSD, indicating potential loss of information.
• The 0-100 range was wider than LMD, suggesting an overestimation of precision; the 0-24 range was deemed reasonable.

Conclusions:

• LMD, SEM, and LSD transformations are valuable for benchmarking when selecting appropriate ranges for transformed logit measures.
• These transformations aid in avoiding information loss or overestimation of precision in health outcome scales.
• The provided Excel tool facilitates these benchmarking and transformation processes.