(untitled) (Journal of Educational Data Mining, 2020)
Affect dynamics, the investigation of how student affect transitions from one state to another, is a popular area of research in adaptive learning environments. Recently, the commonly used transition metric L has come under critical examination when applied to data that exclude self-transitions (i.e., transitions where a student remains in the same affective state on consecutive observations); in this situation, recent work has shown that L potentially overestimates the significance of certain transitions. In order to deal with the unintended side effects of removing self-transitions, a solution was proposed that shifts the chance value of L from zero to a positive value that varies based on the number of affective states in the study. Although this treatment compensates for the aforementioned issues, it could lead to misinterpretation of the results due to the counterintuitive nonzero chance value. Motivated by these issues, in this work we study a modified version of the L statistic, which we refer to as L*, with an aim to shift the chance value back to zero when self-transitions are removed. We begin by studying the mathematical and statistical properties of L*, and we also compare these properties to those of the L statistic. After analyzing the theoretical attributes of L*, we then evaluate its performance when applied to data. In our first evaluation, we compute L* values on simulated sequences of affective states, where the base rates of the states vary from being uniform to highly non-uniform. The results provide evidence that the L* values at chance are not sensitive to unequal base rates, as the computed values from our experiments are centered closely around zero. Our second evaluation applies L* to actual student data generated from students working in a digital learning environment; in this case, the use of L* seemingly gives a more coherent picture in comparison to the values returned by the L statistic. Finally, along with these analyses, we also outline a recommended procedure for applying L* to sequences of affective states.