Functional Principal Components of the Capacity Coefficient

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The efficiency of an information processing system across changes in workload (i.e. number of items to be processed) is particularly important in cognitive science. The capacity coefficient (Townsend & Nozawa, 1996; Townsend & Wenger 2004) is an empirical measure of workload efficiency based on estimated reaction time distributions. The capacity coefficient is a function of time, so different values can be assessed for fast and slow responses. This level of description affords many possibilities for comparing among subjects or conditions, but can also lead to difficulty in interpreting the results. In this talk I describe how a functional extension of principal components analysis, which we call fPCA, can be applied to workload capacity analysis. I will demonstrate its use as a tool for dimensionality reduction, to obtain a finite set of values that maximally distinguish the functions. This reduced description, usually only a couple of factor loading values, can be used for purposes such as structural equations modeling or other approaches designed for a discrete number of dependent variables. I will also discuss how fPCA is an appropriate tool for studying the meaning of changes in capacity across time, an underexploited source of information inherent in the capacity coefficient. The applications of fPCA to workload efficiency in other research goals will also be highlighted.


Presented at the 45th Annual Meeting of the Society for Mathematical Psychology, Columbus, OH.