Regression-based normative data in neuropsychology: Using raw scores as observed response variable outperforms...

Area of Science:

• Neuropsychology
• Biostatistics
• Psychometrics

Background:

• Regression-based normative data for neuropsychological variables are increasingly utilized.
• Existing methods often involve either raw data or transformed scores to address skewed response variables.
• The optimal approach for fitting linear models to these variables remains a subject of investigation.

Purpose of the Study:

• To compare the fit of linear regression models using raw scores versus transformed (scaled) scores for neuropsychological variables.
• To evaluate the accuracy of identifying individuals in the lowest 5% performance range under different modeling conditions.
• To assess the agreement between models using raw and scaled scores via Cohen's kappa statistic.

Main Methods:

• Real data from 163 healthy individuals were used to compare linear regression models for raw and scaled scores.
• A simulated population of 1,000,000 individuals was generated to test model performance across various sample sizes (n=100 to 10,000).
• Seven different scenarios were simulated, and the percentage of individuals scoring in the lowest 5% was analyzed.

Main Results:

• Linear models for raw and scaled scores showed similar performance when all covariates were included.
• Models using scaled scores with covariates from different regressions poorly identified low scores (Cohen's κ = 0.58), estimating near 0% in the lowest range.
• Models using raw scores accurately estimated the expected 5% of individuals in the lowest score range.

Conclusions:

• Raw scores are recommended over transformed scores when calculating normative data using linear regressions in neuropsychology.
• Transforming data solely for normality of the response variable is discouraged.
• If linear models do not fit well, consider nonlinear models rather than data transformation.