Different Forms of Variability Could Explain a Difference Between Human and Rat Decision Making

Abstract

When observers make rapid, difficult perceptual decisions, their response time is highly variable from trial to trial. In a visual motion discrimination task, it has been reported that human accuracy declines with increasing response time, whereas rat accuracy increases with response time. This is of interest because different mathematical theories of decision-making differ in their predictions regarding the correlation of accuracy with response time. On the premise that perceptual decision-making mechanisms are likely to be conserved among mammals, we seek to unify the rodent and primate results in a common theoretical framework. We show that a bounded drift diffusion model (DDM) can explain both effects with variable parameters: trial-to-trial variability in the starting point of the diffusion process produces the pattern typically observed in rats, whereas variability in the drift rate produces the pattern typically observed in humans. We further show that the same effects can be produced by deterministic biases, even in the absence of parameter stochasticity or parameter change within a trial.

Keywords: bias; comparative decision making; context; drift diffusion; speed accuracy tradeoff.

FIGURE 1

The basic drift diffusion model is incompatible with data from rats or humans. (A) Simulated evidence accumulation in a basic drift diffusion model, for six example trials that terminated in correct decisions (green shades, solid symbols) and six that terminated in error decisions (red shades, open symbols). Although an equal number of traces are shown, in the condition illustrated 80% of the traces terminated by crossing the correct boundary. (B) Response time distributions for errors (red, dashed) vs. correct trials (green, solid) of 10⁴ trials like those simulated as in (A). (C) Cumulatives of the distributions shown in (B). (D,E) Distributions in (B,C) normalized to the number of trials. (F) Cumulative probability distribution of response time for errors and correct trials for an example experiment in a rat, a fixed-coherence experiment with 65% coherence, for which the rat was 82% correct. The null hypothesis that the distributions are the same can be rejected with P = 2.91e-171 (N = 8851,1913) by two-tailed Kolmogorov–Smirnov (KS) test. (G–I). Analysis of an example rat psychometric experiment. (G) Accuracy increased with coherence. (H) Mean response time decreased with coherence. (I) On average, the response time of a correct trial is greater than that of a temporally nearby error trial of the same coherence. (J) Like (F), for an example experiment in a human, a fixed-coherence experiment with 10% coherence for which the subject was 83% correct; P = 4.69e-05 (N = 745,153) by KS test. Errors are later than correct trials, unlike either the DDM model (E) or rats (F). (K–M) Like (G–I), for an example human psychometric experiment. (M) Error trials are longer than correct trials on average, unlike rats, and also incompatible with DDM. Data from Shevinsky and Reinagel (2019) and Reinagel and Shevinsky (2020).

FIGURE 2

Addition of variability to the parameters of the drift diffusion model. (A) Definition of parameters. The parameter a is the distance between the error and correct thresholds. The starting point of evidence accumulation is given by z. The average drift rate v depends on the stimulus strength. The observable outcomes are response time (RT) and decision (correct or error). The non-decision-time t reflects both sensory latency and motor latency, but is drawn at left for graphical simplicity. Parameters t, z, and v vary from trial to trial according to the variability parameters σ_t, σ_z, and σ_v, respectively. Drift rate variability was simulated by a normal distribution around the mean parameter. Starting point variability and non-decision time variability were simulated by uniform distributions centered on the mean parameter. Diagram after (Ratcliff and McKoon, 2008). (B–E) Analysis of trials simulated with parameters that produce qualitatively rat-like behavior: a = 1.84, t = 0.74, σ_v = 0.1, σ_z = 1.5, σ_t = 0.2, and v = −0.5c² + 2.5c, where c is coherence (motion stimulus strength). (B) Cumulative probability distributions of correct vs. error trial response times, for c = 0.8. (C) Psychometric curve. (D) Chronometric curve. (E) Difference between mean response times of errors and correct trials. (F–I) Like panels (B–E) but with parameters that produce qualitatively human-like behavior: a = 2.0, t = 0.5, σ_v = 1.5, σ_z = 0.3, σ_t = 0.03, and v = −80c² + 80c. (F) Cumulative RT probability distributions for c = 0.03. For all these simulations, the mean starting point z=0, timestep τ = 0.001, diffusion noise σ_n=1, N = 10⁵ trials per coherence. Open symbols show results obtained after setting σ_z = 0 and σ_v = 0. Note that in conditions with 100% accuracy the ⟨RT_c⟩−⟨RT_e⟩ difference is undefined.

FIGURE 3

Parameter sweep of the variable-parameter DDM. (A–C) Curves show the difference between correct and error mean response times, ⟨RT_correct⟩−⟨RT_error⟩, as a function of drift rate parameter v = [0.0, 0.1, 0.2, 0.3, 0.4, 0.5]. Colors indicate starting point variability σ_z = [0.0, 0.02, 0.07, 0.10], in spectral order from low (dark blue) to high (red). Line thickness indicates drift rate variability σ_v = [0.0, 0.08, 0.12, 0.16]. Black curve is for σ_v = 0, σ_z = 0. (A) Simulations with threshold separation a = 0.08. (B) Simulations with a = 0.11. (C) Simulations with a = 0.16. For all the simulations shown, z=0, t = 0.3, σ_t = 0.2, τ = 0.001, and σ_n = 0.1. (D) Distribution of threshold separation a from fits of this model to datasets from Reinagel and Shevinsky (2020). (E) Distribution of a among example psychometric experiments from unique unbiased subjects in those datasets (see section “Materials and Methods”). (F) Distribution of starting point variability, expressed as a fraction of threshold separation: σ_z/a. (G) Distribution of σ_z/a in the unbiased example sets. (H) Distribution of drift rate variability σ_v. (I) Distribution of σ_v in the unbiased example sets. (J) Average difference between correct and error response times ⟨RT_c−RT_e⟩ computed locally within coherence, averaged over coherences ≥ 0.4. Fixed coherence (light), psychometric with < 10% lapse (medium) or with ≥ 10% lapse (dark). Upward bars show the results from the rat dataset, as analyzed in Shevinsky and Reinagel (2019); N = 51 psychometric, N = 38 fixed-coherence experiments had sufficient trials for this analysis. Lower bars show results for trial data simulated by the models (N = 58 psychometric and N = 39 fixed). (K) Like (J), but for the rat unbiased example subset; N = 11 data or models. (L) Like (J) but for human dataset (N = 81 psychometric, N = 9 fixed) and models fit to human dataset (N = 93 psychometric, N = 9 fixed), averaged over coherences ≥ 0.04. (M) Like (L) but for the human unbiased example subset, N = 45 (data) or N = 51 (model). For descriptive statistics see Supplementary Materials. Because of the limitations of fitting, we refrain from making statistical claims about comparisons of human-to-rat or data-to-model distributions.

FIGURE 4

Bias is sufficient to produce either a rat-like or human-like effect within the basic DDM. Simulations were performed with σ_v = 0, σ_z = 0, σ_t = 0 (i.e., the basic model in Figure 1) but with different forms of bias added. Trials were simulated with 50% right response targets (rightward motion), with 5 × 10⁵ trials per coherence. (A–E) A right side bias was simulated by displacing the starting point z toward the correct boundary on right-target trials, or toward the error boundary for left-target trials, by the amount indicated by color key at right. Where coherence is signed, negative indicates leftward motion and positive, rightward motion. If a coherence axis is unsigned, the left and right motion trials are pooled. (A) Percent right responses, as a function of coherence (sensory stimulus strength), which determines the drift rate v. (B) Average accuracy of the response as a function of coherence. (C) Average response time as a function of coherence. (D) Difference between correct and error mean response times, ⟨RT_correct⟩−⟨RT_error⟩, as a function of coherence. (E) Difference between correct and error mean responses times when left-motion and right-motion trials are pooled. Compare to rat data (Figure 1I) or high σ_z model (thin red curves in Figures 3A–C). (F–J) Like (A–E), but here bias was simulated by increasing the drift rate v on R-target trials, or decreasing it on L-target trials, by the amount indicated in color key at right. Compare panel (J) to human data (Figure 1M) or high σ_v model (thick blue curves in Figures 3A–C). (K–O) Like (A–E) but here the starting point z was displaced toward the side that was rewarded in previous trial (if any). Same color key as (A–E). (P–T) Like (F–J) but here the drift rate v was increased if the target was on the side rewarded in previous trial, or decreased if the target was on the opposite side. Same color key as (F–J). For a similar analysis separated by behavioral choice instead, see Supplementary Figure 2 in Supplementary Materials.