The Role of Entropy in Construct Specification Equations (CSE) to Improve the Validity of Memory Tests

Abstract

Commonly used rating scales and tests have been found lacking reliability and validity, for example in neurodegenerative diseases studies, owing to not making recourse to the inherent ordinality of human responses, nor acknowledging the separability of person ability and item difficulty parameters according to the well-known Rasch model. Here, we adopt an information theory approach, particularly extending deployment of the classic Brillouin entropy expression when explaining the difficulty of recalling non-verbal sequences in memory tests (i.e., Corsi Block Test and Digit Span Test): a more ordered task, of less entropy, will generally be easier to perform. Construct specification equations (CSEs) as a part of a methodological development, with entropy-based variables dominating, are found experimentally to explain (r=R2 = 0.98) and predict the construct of task difficulty for short-term memory tests using data from the NeuroMET (n = 88) and Gothenburg MCI (n = 257) studies. We propose entropy-based equivalence criteria, whereby different tasks (in the form of items) from different tests can be combined, enabling new memory tests to be formed by choosing a bespoke selection of items, leading to more efficient testing, improved reliability (reduced uncertainties) and validity. This provides opportunities for more practical and accurate measurement in clinical practice, research and trials.

Keywords

• entropy
• information
• metrology
• measurement system analysis
• Rasch
• cognition