Linear and Nonlinear Effects of Spatial and Temporal Attention: Human Data and Drift Diffusion Model

Attention can be affected by expectations about where and when stimuli will appear. These two influences, spatial and temporal, may be present together and may interact with each other in unknown complex ways. To explore these possibilities, we used an attention paradigm that incorporated three variables known to produce effects on performance in a speeded reaction-time task: spatial cueing to indicate where a target stimulus is likely to appear, temporal statistics to indicate when the target is likely to appear, and preparation for a block of trials of similar length. When analyzing the data for linear trends, we found that each of these factors impacted performance but did not interact. When analyzing nonlinear trends in the data, we found an interaction between spatial and temporal attention that was modulated by preparation for a block of trials of similar length. We evaluated whether attentional effects across spatial, temporal, and preparatory domains could be explained by one unitary mechanism, rather than multiple modality-specific mechanisms, using an augmented drift diffusion model. In the model, attention is allocated according to an interplay between the costs and benefits of maintaining attention. The model successfully replicated the linear effects observed in the human data, and accounted for some but not all nonlinear features in the data, suggesting that many disparate features of attention can be parsimoniously explained by a cost-benefit framework, but some complexity in attention control remains to be understood.