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.

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

“…Apart from this local communication, it is, of course, in many cases, also required to communicate measurement information as globally as needed, across distances and amongst different persons, according to what is meaningful for the quality assurance in each field of application [ 37 ]. The present work shares a background common with our previous paper [ 11 ], as can be briefly summarised as follows: The amount of “useful information” in a measurement system, analogous to a certain extent with the original entropy concept as a measure of “useful energy” in steam engines [ 40 ], can be described with the well-known conditional entropy expression: Expression (A1) states how the amount of information changes during transmission in a measurement system in terms of the entropy in the response ( Y ) of the system when observing a quantity ( Z ) attributed to the measurement object. At the start of the measurement process, there is an initial “deficit” in the entropy (i.e., “surplus” information) coming from prior knowledge (prior distribution, P ) of the measurand (attribute, Z , of the object entity, (A)).…”

“…Here, we complement these analyses with ab initio theoretical and quasi-theoretical causal estimates of the memory task difficulty, thus providing evidence for construct validity, item equivalence, and enabling metrological references based on causality and best understanding. Our previous work on recalling the simplest nonverbal items—taps and numbers [ 11 , 12 ]—gave first principle, ab initio explanations of the task difficulty in terms of entropy: less entropy means a more ordered task, which is thus easier to perform. This entropy-based explanatory theory, summarized in Appendix B , is extended here to include causal explanations of recall in the word learning list test RAVLT IR, including SPE such as primacy and recency.…”

“…Further studies remain to be done about how the diagnostic sensitivity correlates with the cognitive health of each cohort member, which may be expressed in terms of the explanatory variables (such as biomarkers) in the CSE for a person’s (instrument) ability [ 22 , 23 ]. Another approach—pursued in the final case study (below)—will address the evidence of (perceived) changes in the average task difficulty for different parts of the cohort grouped clinically according to the cognitive status and interpreted in terms of the apparent scale distortions, multidimensionality, and resultant changes (residuals) in response.…”

“…The overall aim of the present work is to highlight entropy-based explanations when developing metrological methods to word learning list tests, including a better definition and analysis of SPEs, by extending earlier simple syntax studies [ 11 , 12 ]. As recounted in Appendix A , the concept of entropy can be usefully deployed when explaining such effects throughout the measurement process.…”

Entropy in Brain Networks

“…Specifically, activation and interaction enthalpy parameters were associated with characteristic configuration variable values of the resulting pattern from free energy minimization of 2D CVM. The versatility of measures from information theory is also evident in the study carried out by Melin et al [ 6 ], in which entropy-based construct specification equations are used to improve validity of memory tests and to design novel combined tests. This new methodology can indeed contribute to obtain reliable diagnoses of neurological diseases, such as dementia, and to properly characterize cognitive processes generated by cerebral networks by providing accurate scoring.…”