Identifying relationships between cognitive processes across tasks, contexts, and time
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It is commonly assumed that a specific testing occasion (task, design, procedure, etc.) provides insight into psychological phenomena that generalise to other, related testing occasions. However, this assumption is rarely tested in data. When it is tested, the two existing methods of comparison have one of the following two shortcomings: they either correlate summary statistics like mean response time or accuracy, which does not provide insight into relationships between latent psychological processes, or they first assume independence in cognitive processes across tasks and then, in a second step, test whether there is in fact a relationship. Our article develops a statistically principled method to directly estimate the correlation between latent components of cognitive processing across tasks, contexts, and time. Our method simultaneously estimates individual participant parameters of a cognitive model at each testing occasion, group-level parameters representing across-participant parameter averages and variances, and across-task covariances, i.e., correlations. The approach provides a natural way to "borrow" data across testing occasions, which increases the precision of parameter estimates across all testing occasions provided there is a non-zero relationship between some of the latent processes of the model. We illustrate the method in two applications in decision making contexts. The first assesses the effect of the neural scanning environment on model parameters, and the second assesses relationships between latent processes underlying performance of three different tasks. We conclude by highlighting the potential of the parameter-correlation method to provide an "assumption-light" tool for estimating the relatedness of cognitive processes across tasks, contexts, and time.
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