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Abstract:
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Disciplines have their favorite or conventional basis set. For example, polynomials are common in psychology, and Fourier transforms are often used in engineering and physics. There exists a vast set of possibilities for basis sets in generalized splines, which can be used to impose expected structure on a model via piecewise sums of any functions. The properties of basis set transformations can be leveraged in powerful ways, especially when they can give model parameters more natural, domain-relevant interpretations.
Here, we will show how Regression Spline Mixed Models (RSMM) can combine the nonparametric features of splines with a hierarchical random effects framework to explore EEG data at any of the many levels that are collected and of interest to researchers. We will then show how a verbalized hypothesis can be translated into a basis set for formal testing of interpretable model parameters. Having the ability to work at these levels in any time series biological context (EEG, fMRI, MEG, EKG, pupilometry, and others) is useful for recognizing outliers, learning about variance and statistical significance, and inspiring further analyses or future studies.
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