Density and random generation functions for the EZ-Diffusion Model. The model operates on aggregated data: mean reaction time, variance of reaction time, and number of responses to the upper boundary.
Arguments
- mean_rt
Observed mean reaction time(s) in seconds. For version "3par", a numeric vector or single value. For version "4par", either a vector of length 2 (c(mean_rt_upper, mean_rt_lower)) for single observation, or a matrix with 2 columns for multiple observations.
- var_rt
Observed variance of reaction times in seconds^2. For version "3par", a numeric vector or single value. For version "4par", either a vector of length 2 (c(var_rt_upper, var_rt_lower)) for single observation, or a matrix with 2 columns for multiple observations.
- n_upper
Number of responses to the upper boundary
- n_trials
Total number of trials
- drift
Drift rate (positive, evidence accumulation rate).
- bound
Boundary separation (distance between decision thresholds).
- ndt
Non-decision time (seconds).
- zr
Relative starting point (0 to 1). Only used for version "4par".
- s
Diffusion constant (standard deviation of noise), default = 1.
- version
Character; either "3par" (default) or "4par"
- log
Logical; if
TRUE, values are returned on the log scale.- n
Number of samples to generate
Value
dezdm gives the log-density of the observed summary statistics
under the EZDM, and rezdm generates random summary statistics from the
implied sampling distributions.
References
Wagenmakers, E.-J., Van Der Maas, H. L. J., & Grasman, R. P. P. P. (2007). An EZ-diffusion model for response time and accuracy. Psychonomic Bulletin & Review, 14(1), 3-22.
Chávez De la Peña, A. F., & Vandekerckhove, J. (2025). An EZ Bayesian hierarchical drift diffusion model for response time and accuracy. Psychonomic Bulletin & Review.
Examples
# 3-parameter version (single observation)
dezdm(
mean_rt = 0.5, var_rt = 0.02, n_upper = 80, n_trials = 100,
drift = 2, bound = 1.5, ndt = 0.3
)
#> [1] -46.81829
# 3-parameter version (vectorized)
dezdm(
mean_rt = c(0.5, 0.55), var_rt = c(0.02, 0.025),
n_upper = c(80, 75), n_trials = c(100, 100),
drift = 2, bound = 1.5, ndt = 0.3
)
#> [1] -46.81829 -39.41976
# 4-parameter version (single observation)
dezdm(
mean_rt = c(0.45, 0.55), var_rt = c(0.018, 0.025),
n_upper = 80, n_trials = 100,
drift = 2, bound = 1.5, ndt = 0.3, zr = 0.55, version = "4par"
)
#> [1] -50.34668
# generate random summary statistics
rezdm(n = 100, n_trials = 100, drift = 2, bound = 1.5, ndt = 0.3)
#> mean_rt var_rt n_upper n_trials
#> 1 0.6052179 0.06050207 95 100
#> 2 0.6254183 0.05563988 96 100
#> 3 0.6980983 0.06228497 89 100
#> 4 0.6111334 0.05344788 98 100
#> 5 0.6342018 0.06654405 98 100
#> 6 0.6472026 0.06436166 94 100
#> 7 0.6184780 0.06344055 93 100
#> 8 0.6445478 0.05849705 96 100
#> 9 0.6258324 0.06742749 97 100
#> 10 0.6238227 0.06413316 98 100
#> 11 0.6781039 0.07351276 92 100
#> 12 0.6663506 0.05548701 92 100
#> 13 0.6091022 0.06164208 97 100
#> 14 0.6519874 0.07127367 95 100
#> 15 0.6107959 0.06618435 94 100
#> 16 0.6436366 0.05972240 96 100
#> 17 0.6409623 0.05643593 96 100
#> 18 0.6509810 0.05976457 94 100
#> 19 0.5970325 0.06306146 97 100
#> 20 0.6490920 0.06712302 94 100
#> 21 0.6489317 0.05774927 96 100
#> 22 0.6572365 0.04789838 97 100
#> 23 0.6433667 0.04871161 97 100
#> 24 0.6749454 0.05210940 94 100
#> 25 0.6791458 0.05591924 98 100
#> 26 0.6171466 0.04644418 93 100
#> 27 0.6542550 0.05155062 97 100
#> 28 0.6209785 0.07399368 95 100
#> 29 0.6438131 0.05926333 94 100
#> 30 0.6035100 0.04896390 92 100
#> 31 0.6396154 0.05401807 93 100
#> 32 0.7014167 0.06365506 97 100
#> 33 0.6476300 0.04953622 98 100
#> 34 0.6445773 0.04800872 93 100
#> 35 0.6406064 0.07377317 95 100
#> 36 0.6681105 0.04915244 93 100
#> 37 0.6621595 0.05108533 95 100
#> 38 0.6114874 0.05414572 98 100
#> 39 0.6025502 0.05883868 95 100
#> 40 0.6489919 0.06324619 98 100
#> 41 0.5942928 0.04972676 96 100
#> 42 0.6281111 0.05134011 94 100
#> 43 0.6613315 0.05530200 93 100
#> 44 0.6625984 0.05216417 94 100
#> 45 0.6638746 0.07744094 95 100
#> 46 0.6249537 0.06471903 96 100
#> 47 0.6497752 0.04674280 95 100
#> 48 0.6357006 0.05035930 95 100
#> 49 0.6722934 0.06993272 99 100
#> 50 0.6606856 0.07079888 97 100
#> 51 0.6300447 0.07485502 94 100
#> 52 0.6469153 0.07189078 97 100
#> 53 0.6029423 0.06650394 96 100
#> 54 0.6387738 0.05694117 93 100
#> 55 0.6690939 0.05254938 96 100
#> 56 0.6309338 0.04829231 98 100
#> 57 0.6854628 0.06324118 98 100
#> 58 0.5794162 0.08984538 97 100
#> 59 0.6536222 0.05298167 99 100
#> 60 0.5875901 0.06057551 97 100
#> 61 0.6214681 0.06209804 91 100
#> 62 0.6468571 0.06776517 96 100
#> 63 0.6481228 0.05878523 96 100
#> 64 0.6365232 0.04994417 97 100
#> 65 0.6358022 0.04496080 95 100
#> 66 0.6246808 0.04296971 96 100
#> 67 0.6411993 0.05358469 97 100
#> 68 0.6785620 0.05693912 90 100
#> 69 0.6461103 0.07417500 93 100
#> 70 0.6429481 0.05953882 97 100
#> 71 0.6406730 0.05909655 95 100
#> 72 0.6538638 0.05653600 99 100
#> 73 0.6586971 0.05190858 93 100
#> 74 0.6304437 0.04088859 97 100
#> 75 0.6421131 0.05756569 95 100
#> 76 0.6297958 0.05522054 93 100
#> 77 0.6508363 0.04957483 95 100
#> 78 0.6517144 0.05310660 97 100
#> 79 0.6746506 0.06238419 97 100
#> 80 0.6265239 0.07335301 97 100
#> 81 0.6839742 0.05887133 93 100
#> 82 0.6280588 0.03909572 95 100
#> 83 0.6047993 0.06138010 95 100
#> 84 0.6256696 0.05844426 93 100
#> 85 0.6845577 0.06272885 96 100
#> 86 0.6562022 0.05141454 94 100
#> 87 0.6182736 0.07102396 94 100
#> 88 0.6612252 0.07002556 90 100
#> 89 0.6590743 0.05809592 97 100
#> 90 0.6360479 0.04845979 95 100
#> 91 0.6250707 0.06098853 94 100
#> 92 0.6195319 0.05805368 95 100
#> 93 0.5935628 0.06454075 94 100
#> 94 0.6380651 0.06365892 94 100
#> 95 0.6626896 0.07446620 99 100
#> 96 0.6113765 0.05565502 97 100
#> 97 0.5813777 0.05200712 93 100
#> 98 0.5854616 0.05035923 92 100
#> 99 0.6584005 0.06810745 93 100
#> 100 0.6651854 0.05783690 94 100
rezdm(
n = 100, n_trials = 100, drift = 2, bound = 1.5, ndt = 0.3,
zr = 0.55, version = "4par"
)
#> mean_rt_upper mean_rt_lower var_rt_upper var_rt_lower n_upper n_trials
#> 1 0.6502511 0.7649559 0.04989655 0.0566983804 95 100
#> 2 0.5885282 NA 0.07202299 NA 99 100
#> 3 0.5661361 0.7601864 0.06791018 0.0178861595 98 100
#> 4 0.5988479 NA 0.06136743 NA 100 100
#> 5 0.6650872 0.5876834 0.07303294 0.0361821900 97 100
#> 6 0.5934796 NA 0.05259932 NA 99 100
#> 7 0.6136431 NA 0.04519916 NA 99 100
#> 8 0.6078325 NA 0.05180133 NA 99 100
#> 9 0.6436044 NA 0.04781537 NA 100 100
#> 10 0.5879990 0.7411341 0.05455867 0.0492931339 96 100
#> 11 0.5898870 0.5701947 0.05068076 0.0175300817 96 100
#> 12 0.5975441 0.6987746 0.04965899 0.0006577261 98 100
#> 13 0.6074822 0.6684668 0.05773212 0.0162000056 97 100
#> 14 0.5941104 0.5207589 0.05287414 0.0615187804 95 100
#> 15 0.5967974 0.6289906 0.04844397 0.0178301824 97 100
#> 16 0.6464962 0.7071709 0.04560899 0.1019294204 97 100
#> 17 0.6711845 0.7453830 0.06244705 0.0592707432 96 100
#> 18 0.6393857 0.7939970 0.06400634 0.0687673939 95 100
#> 19 0.6441257 0.7588128 0.06055501 0.0110337500 94 100
#> 20 0.6097072 0.5430035 0.05157123 0.1042595383 96 100
#> 21 0.5880901 0.5604545 0.06843787 0.0192550108 98 100
#> 22 0.6119675 0.9670759 0.05459167 0.0618571499 98 100
#> 23 0.5880676 NA 0.05729573 NA 99 100
#> 24 0.5891970 0.7147013 0.06241311 0.0312805778 98 100
#> 25 0.6193063 0.6097477 0.06388925 0.0206531266 96 100
#> 26 0.5860630 0.7883369 0.04846007 0.0477973937 94 100
#> 27 0.5788661 0.3984580 0.05635381 0.0719746029 95 100
#> 28 0.6089412 0.6662716 0.04937643 0.0758691671 96 100
#> 29 0.5983654 0.8210196 0.06579482 0.1199972451 95 100
#> 30 0.6194269 0.6892982 0.06511848 0.0104190400 96 100
#> 31 0.6351105 0.4870586 0.05532864 0.0262685720 94 100
#> 32 0.6386732 0.7409576 0.06392190 0.0334840543 95 100
#> 33 0.5542522 0.7087651 0.04955178 0.0222317307 94 100
#> 34 0.6058988 0.6517884 0.04307826 0.0047805714 97 100
#> 35 0.5898270 0.6329341 0.06226155 0.0558343281 93 100
#> 36 0.5913624 NA 0.05749672 NA 99 100
#> 37 0.6197150 0.6894210 0.06513621 0.0037066232 98 100
#> 38 0.5923942 0.7621588 0.05190030 0.0342465501 96 100
#> 39 0.6162915 0.6684157 0.06784264 0.0059436739 96 100
#> 40 0.5854641 0.9358323 0.05739004 0.0649269577 96 100
#> 41 0.6373105 0.4309415 0.05339503 0.0843122914 98 100
#> 42 0.5894361 0.3687429 0.06714432 0.0531072177 98 100
#> 43 0.6386572 0.6545556 0.05994743 0.0233428060 95 100
#> 44 0.6445549 0.5961913 0.05775674 0.0526948705 98 100
#> 45 0.6379854 0.6164503 0.05240530 0.0720440336 96 100
#> 46 0.6421695 0.7224946 0.05480577 0.1168618796 95 100
#> 47 0.6513483 0.7100595 0.06083781 0.0371535815 95 100
#> 48 0.6086234 0.6608077 0.04542720 0.0199195948 96 100
#> 49 0.6154137 0.9753739 0.06454822 0.0484148033 97 100
#> 50 0.5940066 0.5962897 0.05927818 0.0880821475 96 100
#> 51 0.5936590 0.5761910 0.04909567 0.0294379339 97 100
#> 52 0.6322256 0.6109041 0.05072763 0.0272219765 96 100
#> 53 0.6084217 0.7008212 0.05292776 0.0324502753 95 100
#> 54 0.5640575 0.4305302 0.06215920 0.1042389484 97 100
#> 55 0.5888341 0.4441832 0.04880785 0.0520642157 96 100
#> 56 0.6157849 NA 0.03688014 NA 99 100
#> 57 0.6292686 0.7412298 0.05063281 0.0755898668 98 100
#> 58 0.6055325 0.5107231 0.05989304 0.0707868658 97 100
#> 59 0.6351687 0.6726005 0.04514480 0.0125345601 96 100
#> 60 0.6136025 0.5933774 0.05856345 0.0763960161 96 100
#> 61 0.6619773 0.4864303 0.07463913 0.0826458142 96 100
#> 62 0.5658197 0.6232584 0.05686281 0.0982514800 97 100
#> 63 0.5925006 0.4509459 0.05297950 0.0308991127 96 100
#> 64 0.6282330 NA 0.06070118 NA 100 100
#> 65 0.5973281 0.7117089 0.03607314 0.0440500718 98 100
#> 66 0.6281872 0.5874707 0.04779714 0.0096981018 98 100
#> 67 0.6656722 NA 0.05569766 NA 100 100
#> 68 0.6327527 0.7296523 0.04923677 0.0425230735 98 100
#> 69 0.6413402 0.6847073 0.05284246 0.0005693311 98 100
#> 70 0.5727004 0.6391576 0.05167510 0.0602124879 95 100
#> 71 0.6216509 0.6610914 0.04279558 0.0098159957 96 100
#> 72 0.5870782 0.6723137 0.04062062 0.0621615312 96 100
#> 73 0.6372833 NA 0.05249562 NA 99 100
#> 74 0.6148388 0.8798555 0.04790742 0.2230895276 98 100
#> 75 0.6242288 0.7936442 0.06513523 0.2211701707 97 100
#> 76 0.6232099 0.6671429 0.05250682 0.1707600700 98 100
#> 77 0.6093080 0.4400994 0.05327112 0.1146225998 95 100
#> 78 0.5965755 0.6912063 0.05060187 0.0473521824 93 100
#> 79 0.6144070 0.6808274 0.06130882 0.0646025957 94 100
#> 80 0.6185848 0.6624157 0.04723519 0.0007469715 98 100
#> 81 0.5516827 0.7661256 0.04898964 0.0764927619 95 100
#> 82 0.6152020 0.9666840 0.04893381 0.0612704692 98 100
#> 83 0.6201223 0.8300093 0.05389726 0.1202119850 98 100
#> 84 0.5865748 0.7254114 0.05576797 0.0314577898 98 100
#> 85 0.6117304 0.6038887 0.05546558 0.0621342152 97 100
#> 86 0.5631120 0.6500472 0.05527303 0.0168799620 95 100
#> 87 0.6379170 0.7102212 0.04730706 0.0118317114 96 100
#> 88 0.6260746 0.5494706 0.05920880 0.0774671028 96 100
#> 89 0.5704335 0.8525632 0.05775482 0.0631036836 94 100
#> 90 0.6459393 0.8691286 0.05470662 0.0406217110 97 100
#> 91 0.6137296 0.5882533 0.05583998 0.0894212880 96 100
#> 92 0.6207608 0.8247125 0.06283831 0.0136249756 98 100
#> 93 0.6496656 0.7042346 0.05973638 0.0012830829 98 100
#> 94 0.6204379 1.1354141 0.05652376 0.2383413666 98 100
#> 95 0.6267790 0.5910407 0.03783508 0.0771920198 97 100
#> 96 0.6221307 0.8589899 0.05960141 0.0717127501 95 100
#> 97 0.6329551 0.7022623 0.06000839 0.0318497299 97 100
#> 98 0.5966331 NA 0.04373281 NA 100 100
#> 99 0.6288519 0.5726042 0.06549926 0.1276221992 98 100
#> 100 0.6356014 0.5513523 0.06818854 0.0383397174 96 100