Diffusion Decision Modeling: A Deep Dive into the Four Main Parameters

In this blog, I explain the behavioral impacts of the four principal parameters of the Diffusion Decision Model (DDM; Ratcliff, 1978). Note that this blog is supposed to give you a general idea of how each of these parameters exert distinct behavioral effects. However, the specific interpretation of each parameter must always be contextualized according to the details of the task at hand (for more details, see Ging-Jehli et al., 2021). Moreover, for an introduction to these parameters and their psychological interpretations, please see my earlier blog, “Decoding Decision-Making.” All graphical illustrations were generated using the RTdist package in R, and the code for conducting your own simulations is available on my GitHub. At the conclusion of this post, you'll find a list of selected references that offer further insights.

Behavioral effect of changes in drift rate (v)

Imagine the upper boundary represents correct responses and the lower boundary errors. Higher drift rates lead to more accurate and faster mean RTs of associated correct responses. This is illustrated by the blue versus red distributions in the figure (Ratcliff, 1978; Ratcliff et al., 2016; Smith & Ratcliff, 2004). Moreover, the impact of drift rate changes is more pronounced in the tails (slowest responses) than in the leading edge (fastest responses) of the RT distributions. Typically, variations in drift rate reflect differences in task difficulty or stimulus discrimination (Ging-Jehli et al., 2021, 2024; Ging-Jehli & Ratcliff, 2020; Ratcliff et al., 2016). Though, note that the specific interpretation of each parameter must be contextualized according to the details of the task at hand (for more details, see Ging-Jehli et al., 2021).

Behavioral effect of changes in boundary separation (a)

Let’s again assume that the upper and lower boundaries represent correct and error responses, respectively. An increase in boundary separation indicates a shift towards a more cautious response strategy, prioritizing accuracy over speed. This results in higher accuracy but slower average RTs. The effects on RTs, particularly in the tails compared to the leading edges, show a roughly 1:2 ratio (Ratcliff et al., 2016; Smith & Ratcliff, 2004). Notably, changes in boundary separation have a greater impact on RTs than variations in drift rate. Changes in boundary separation are often influenced by modifications in task instructions, feedback, proactive difficulty or conflict, and stress.

Behavioral effect of changes in starting points (z)

The upper and lower boundaries now represent response options rather than correct or incorrect responses. This is to avoid the unreasonable assumption that people can predict the “accurate” outcome before a stimulus is presented. Therefore, models should typically set the starting point equidistant from both boundaries if the upper and lower boundaries represent corrects and errors, respectively. Variations in the starting point can bias responses towards the upper (A) or lower (B) options, with significant effects on the leading edge and asymmetric impacts on responses A versus B. Changes in starting points are often induced by influencing the frequency of the different stimulus occurrence or reward structures that change prior expectations about stimuli.

Behavioral effect of changes in nondecision time (Ter)

The nondecision time parameter accounts for the time taken by processes unrelated to the decision itself, such as stimulus encoding and motor response execution. Increases in nondecision time shift the entire reaction time (RT) distribution, impacting both correct and error responses. This parameter is influenced by various factors, including task-switching (Ging-Jehli & Ratcliff, 2020), sensory modality (Ging-Jehli et al., 2022), and the complexity of the stimulus features (Ging-Jehli et al., 2021; Smith & Ratcliff, 2004). Essentially, as nondecision time increases, it generally leads to slower overall response times, reflecting delays in these non-decision processes.

Summary

Take-home messages

• Above is a summary of the four main DDM parameters and how they produce distinct effects on the relative frequency of response options and their associated RT distributions.

• It’s important to note that model parameters can sometimes trade-off and how much they do so will depend on the task specifics, among others. I will explore this topic in depth in a future blog post, so stay tuned.

• If you examine the correct and error responses at a specific drift rate value in the first figure above, you’ll notice that they typically occur at similar speeds (i.e., similar mean RTs of corrects and errors). This uniformity results from excluding variability parameters in these simulations.

I will elaborate on the DDM variability parameters in my next blog post.

Selected References

Ging-Jehli, N. R., Arnold, L. E., Roley-Roberts, M. E., & deBeus, R. (2022). Characterizing Underlying Cognitive Components of ADHD Presentations and Co-morbid Diagnoses: A Diffusion Decision Model Analysis. Journal of Attention Disorders, 26(5), 706–722. https://doi.org/10.1177/10870547211020087

Ging-Jehli, N. R., Kuhn, M., Blank, J. M., Chanthrakumar, P., Steinberger, D. C., Yu, Z., Herrington, T. M., Dillon, D. G., Pizzagalli, D. A., & Frank, M. J. (2024). Cognitive signatures of depressive and anhedonic symptoms, and affective states, using computational modeling and neurocognitive testing. Biological Psychiatry: Cognitive Neuroscience and Neuroimaging. https://doi.org/10.1016/j.bpsc.2024.02.005

Ging-Jehli, N. R., & Ratcliff, R. (2020). Effects of aging in a task-switch paradigm with the diffusion decision model. Psychology and Aging, 35(6), 850–865. https://doi.org/10.1037/pag0000562

Ging-Jehli, N. R., Ratcliff, R., & Arnold, L. E. (2021). Improving neurocognitive testing using computational psychiatry—A systematic review for ADHD. Psychological Bulletin, 147(2), 169–231. https://doi.org/10.1037/bul0000319

Ratcliff, R. (1978). A theory of memory retrieval. Psychological Review, 85(2), 59–108. https://doi.org/10.1037/0033-295X.85.2.59

Ratcliff, R., Smith, P. L., Brown, S. D., & McKoon, G. (2016). Diffusion Decision Model: Current Issues and History. Trends in Cognitive Sciences, 20(4), 260–281. https://doi.org/10.1016/j.tics.2016.01.007

Smith, P. L., & Ratcliff, R. (2004). Psychology and neurobiology of simple decisions. Trends in Neurosciences, 27(3), 161–168. https://doi.org/10.1016/j.tins.2004.01.006