Diffusion-model data analyses are based on the assumption that information is accumulated continuously until one of two thresholds is hit. With a diffusion-model data analysis it is possible to analyze data from fast binary decision tasks. The analysis is based on the distributions of both correct and erroneous responses. From these distributions a set of parameters is estimated that allows to draw conclusions about the underlying cognitive processes. For more information, see Voss, Rothermund, & Voss (2004) or Voss, Nagler, & Lerche (2013) (Password is VOSS).
Parameters estimated by fast-dm
| Parameter | Typical Range |
Description | Notes |
|---|---|---|---|
| Threshold Separation (a) |
0.5 < a < 2 | Amount of information that is considered for a decision. Large values indicate a conservative decisional style. | |
| Relative Starting Point (zr) |
0.3 < zr < 0.7 | Indicator of an a priori bias in decision making. When the relative starting point zr deviates from 0.5, the amount of information necessary for a decision differs between response alternatives. | In earlier versions of fast-dm the absolute starting point z was estimated. In recent versions, fast-dm uses zr = z/a, which is scaled from 0 to 1 with zr = 0.5 indicating the absence of a decisional bias. |
| Drift (v) | -5 < v < 5 | Average slope of the information accumulation process. The drift gives information about the speed and direction of the accumulation of information. Large (absolute) values of drift indicate a good performance. If received information supports the response linked to the upper threshold the sign will be positive and vice versa. | |
| Response Time Constant (t0) |
0.1 < t0 < 0.5 | Average duration of all non-decisional processes (encoding and response execution). | Duration is given in seconds by fast-dm. |
| Differences in Speed of Response Execution (d) |
-0.1 < d < 0.1 | Positive values indicate that response execution is faster for responses linked to the upper threshold (coded as 1 in fast-dm) than for responses linked to the lower threshold. | Differences are given in seconds by fast-dm. |
| Inter-Trial-Variability of (Relative) Starting Point (szr) |
0 < szr < 0.5 | Range of a uniform distribution with mean zr describing the distribution of actual starting points from specific trials. | Minimal impact on the RT distributions. Can be fixed to 0 in most applications. |
| Inter-Trial-Variability of Drift (sv) |
0 < sv < 2 | Standard deviation of a normal distribution with mean v describing the distribution of actual drift rates from specific trials. | Minimal impact on the RT distributions. Can be fixed to 0 in most applications. |
| Inter-Trial-Variability of Non-Decisional Components (st0) |
0 < st0 < 0.2 | Range of a uniform distribution with mean t0 describing the distribution of actual t0 values across trials. | Accounts for response times below t0. Reduces skew of predicted RT distributions. |
| Percentage of Contaminants (p) |
0 < p < 1 | Contaminated RTs are modeled as a uniform distribution form the fastest to the slowest RT (Ratcliff & Tuerlinckx, 2004). p is an estimate for the relative amount of contaminated trials. | Very large trial numbers are needed to estmate p. Should be fixed to 0 in most applications. Implemented in fast-dm-30.2 |
Estimation Procedures implemented in fast-dm
| Method | Recommended Trial Number (Minimum) | Robustness | Speed of Estimation |
|---|---|---|---|
| Maximum Likelihood | Low (n>40) | Low (strict outlier analysis necessary) | Low (if inter-trial-variability parameters are included) |
| Kolmogorov-Smirnov | Medium (n>100) | High | Medium (dependent on trial numbers) |
| Chi-Square | High (n>500) | High | High (independent of trial numbers) |