Modeling Within-Item Dependencies in Parallel Data on Test Responses and Brain Activation

In this paper, we propose a joint modeling approach to analyze dependency in parallel response data. We define two types of dependency: higher-level dependency and within-item conditional dependency. While higher-level dependency can be estimated with common latent variable modeling approaches, within-item conditional dependency is a unique kind of information that is often not captured with extant methods, despite its potential to shed new insights into the relationship between the two types of response data. We differentiate three ways of modeling within-item conditional dependency by conditioning on raw values, expected values, or residual values of the response data, which have different implications in terms of response processes. The proposed approach is illustrated with the example of analyzing parallel data on response accuracy and brain activations from a Theory of Mind assessment. The consequence of ignoring within-item conditional dependency is investigated with empirical and simulation studies in comparison to conventional dependency analysis that focuses exclusively on relationships between latent variables.