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Within behavioral science, it is common for data to be paradigmatically collected through repeated measurement of behavior (e.g., on each of 400 trials a human presses one of two buttons to indicate which of two possible stimuli they saw). Typical analytic tools used alongside such designs, such as ANOVA, linear regression, or T tests, implicitly assume that the data arises from distributions that are stationary across the repeated individual measurements (i.e., that every trial is independently and identically sampled from the same distribution, or iid, conditional on experimentally manipulated or observed variables). Interestingly, the use of such analytic tools is common even in those areas of behavioral science that are inherently concerned with time-evolving changes in behavior such as learning, memory, priming, adaptation, vigilance, cognitive control. For instance, in learning research it is common for researchers to first divide the repeated measurements into temporal bins (e.g., trials 1-100; 101-200; 201-300). They then calculate means within those bins, before applying the analysis tools above. Such an analytic method is explicitly modelling a process where performance can change between, but not within, bins. That is, conditional stationarity is assumed within the temporal bins. Beyond these fields, research methods in many others (e.g., attention, development, neuroscience, perception) attempt to by-pass the problem of non-stationarity by utilizing practice trials prior to collecting behavioral data. Practice trials are intended to give participants enough practice with the task that they reach a stable level of performance. However, whether this assumption is true is rarely tested. Our previous work has demonstrated, across several different experimental contexts, that by-trial modeling of performance provides estimates of the full timecourse of behavioral change. In doing so, these models of nonlinear monotonic trend stationarity provide both better estimates of behavior, as well as allowing for deeper inferences regarding the underlying processes at work, than statistical methods that assume that behavioral data remains unconditionally stationary over the course of a set of measurements (Kattner, Cochrane, & Green, 2017).

TEfits: Nonlinear regression for time-evolving indices