Estimating the growth of discriminative information guiding perceptual decisions

Many different models of perceptual decision-making assume that sensory evidence is integrated over time up to a response criterion. Models in this class make different assumptions about the noise sources involved, the presence of leakage and competitive interactions, etc. Most models can account for the finding that the accuracy of decision-making improves with time, typically because there will be a source of internal noise that can be “integrated out". The response signal paradigm aims to interrogate the internal evidence at different points in time, essentially taking snapshots of the underlying dynamic process. This snapshot is then represented and analyzed in a signal detection framework. Visual psychophysics offers a rich toolbox that enables us to estimate this noisy internal representation.
We used the double-pass agreement method to estimate the internal signal-to-noise ratio at a number of different points in time. Observers performed a 4-AFC orientation discrimination task in Gaussian noise (σ_ext = 0:16). The target orientation was fixed for each individual (± 45°) and the three non-targets had the orthogonal orientation. The test display was presented briefly (80 ms). An auditory tone signaled to the observer that a response was required. The observer moved the mouse cursor towards the estimated target location. Only responses initiated within a 500 ms deadline from the signal-to-respond were considered. At each delay the contrast of all 4 patterns was varied to yield a full psychometric function. Each individual test display was presented twice.
The accuracy and consistency data were analyzed with an observer model that consisted of a non-linear transducer, additive and multiplicative internal noise (Lu & Dosher 2008). The signal-to-noise ratio is: d^’_int = (kc) ^y/ √(σ^2y_ext + σ²_int), where the internal noise consists of additive and multiplicative components: σ²_int = σ²_add + m² [σ^2y_ext + (kc)^2y]. The free parameters of the model are the gain of the filter, k, non-linearity, γ, additive internal noise, σ_add and multiplicative noise scalar, m. To test for the effect(s) of processing time, we fit the data from all 6 signal delays with a number of competing models that vary in what component(s) of the model are free to absorb the effect of time (number of free parameters in parentheses): 1. Saturated: different set of 4 parameters for each delay (24); 2. Additive: the additive noise is the only parameter allowed to vary with time (9); 3. Multiplicative: the multiplicative noise scalar is allowed to vary with time (9); 4. Guessing: the internal evidence remains constant, but it is the proportion of decisions guided by that evidence that varies with time (9, assuming m = 0). For each model we computed a Bayesian Information Criterion.

Descriptive psychometric function fits showed that the main effect of time is on asymptotic performance. Asymptotic performance well below ceiling is indicative of frequent guessing and/or multiplicative noise. Indeed, the guessing and multiplicative noise models were by far the most competitive. However, the guessing model was the clear winner. Nevertheless, if we construct a typical “speed-accuracy trade-off" (SAT) curve at a single contrast level from the descriptive psychometric function fits, it shows the typical exponential growth to asymptote reported in previous studies (e.g. Carrasco & McElree 2001). Our findings suggest that this pattern is not necessarily indicative of an improvement in the internal signal-to-noise. Rather, it may simply be that observers are guessing on a large number of trials, particularly at the early signal delays, in order to be able to meet the tight response deadline. As the delay increases, it becomes more likely that the internal evidence may be used to prepare and execute a response in time.

These results were replicated in a second experiment in which the stimulus was visible up to response initiation (rather than the fixed, brief viewing time used here). We have run several other experiments in which we varied the presentation time of the test display, but did not adopt the response signal ethodology (Ludwig & Evens, in preparation). This data was analyzed using the same model selection approach. Here we consistently obtained superior fits of a saturated observer model, suggesting a clear growth in evidence.

This work was supported by a grant from the UK Engineering and Physical Sciences Research Council EP/E054323/1 to CL