In experimental psychology and neuroscience the classical approach when comparing different models that make quantitative predictions about the behavior of participants is to aggregate the predictive ability of the model (e.g. as quantified by Akaike Information criterion) across participants, and then see which one provide on average the best performance. Although correct, this approach neglect the possibility that different participants might use different strategies that are best described by alternative, competing models.
Photo ©Roxie and Lee Carroll, www.akidsphoto.com.
In my previous lab I was known for promoting the use of multilevel, or mixed-effects model among my colleagues. (The slides on the /misc section of this website are part of this effort.) Multilevel models should be the standard approach in fields like experimental psychology and neuroscience, where the data is naturally grouped according to “observational units”, i.e. individual participants. I agree with Richard McElreath when he writes that “multilevel regression deserves to be the default form of regression” (see here, section 1.
Brief intro to the mathematical formalism used to describe rotations of the eyes in 3D (including the torsional component). The shape of the human eye is approximately a sphere with a diameter of 23 mm, and mechanically it behaves like a ball in a ball and socket joint. Because there is a functional distinguished axis - the visual axis, that is the line of gaze or more precisely the imaginary straight line passing through both the center of the pupil and the center of the fovea - the movements of the eyes are usually divided in gaze direction and cyclotorsion (or simply torsion): while gaze direction refers to the direction of the visual axis, the torsion indicates the rotation of the eyeball about the visual axis.