BFF: Bayesian, Fiducial, and Frequentist Analysis of Cognitive Engagement among Cognitively Impaired Older Adults.

Engagement in cognitively demanding activities is beneficial to preserving cognitive health. Our goal was to demonstrate the utility of frequentist, Bayesian, and fiducial statistical methods for evaluating the robustness of effects in identifying factors that contribute to cognitive engagement for older adults experiencing cognitive decline. We collected a total of 504 observations across two longitudinal waves of data from 28 cognitively impaired older adults. Participants' systolic blood pressure responsivity, an index of cognitive engagement, was continuously sampled during cognitive testing. Participants reported on physical and mental health challenges and provided hair samples to assess chronic stress at each wave. Using the three statistical paradigms, we compared results from six model testing levels and longitudinal changes in health and stress predicting changes in cognitive engagement. Findings were mostly consistent across the three paradigms, providing additional confidence in determining effects. We extend selective engagement theory to cognitive impairment, noting that health challenges and stress appear to be important moderators. Further, we emphasize the utility of the Bayesian and fiducial paradigms for use with relatively small sample sizes because they are not based on asymptotic distributions. In particular, the fiducial paradigm is a useful tool because it provides more information than values without the need to specify prior distributions, which may unduly influence the results based on a small sample. We provide the R code used to develop and implement all models.