Evaluating three independent-channels models of temporal-order and simultaneity judgment

How do people judge the temporal order and simultaneity/successiveness of events? Three candidate models can explain the theoretically constraining shapes of the psychometric functions observed in tasks with more complex response formats. First, the response-error model allows that internal states generated by a triggered-moments process are misreported due to finger errors, requiring that psychometric functions are parallel after empirically accounting for finger errors (parallelism) and that successiveness perception is necessary for temporal-order perception (necessity). Second, the two-stage model posits that two independent and serial processes generate simultaneity/successiveness and temporal-order judgments, requiring that temporal-order judgment accuracy does not depend on simultaneity/successiveness judgment accuracy (independence) and that simultaneity responses are not slower than order responses (seriality). Third, the two-threshold model formalizes the idea that the order threshold can be higher than the successiveness threshold, requiring necessity and that the order threshold is not lower than the successiveness threshold (threshold inequality). Five experiments evaluated these model assumptions against precise individual data collected with audio-visual and visual stimuli in temporal-order judgment, simultaneity judgment, ternary-response, and dual-response tasks. The response-error model was invalidated by near-universal violations of parallelism in 63/64 tests, and the two-stage model by consistent violations of independence (20/20) and predominant violations of seriality (30/44). By contrast, the threshold inequality in the two-threshold model was satisfied in 39/40 tests, whereas necessity was violated in 10/20 tests. Joint model fits across the four tasks also revealed that the two-threshold model provides the best general account of temporal judgment. We conclude that the two-threshold model is the least inadequate of the three candidate models, and consider a generalized two-threshold model with fluctuating criteria to address violations of necessity.