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 (evidence accumulation rate; can be positive or negative for below-chance performance).
- 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] -46.8172
# 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] -46.8172 -39.4188
# 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] -50.34562
# 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 0.6330928 0.06509706 99 100
#> 2 0.6067023 0.06068551 92 100
#> 3 0.6596245 0.05716099 96 100
#> 4 0.6479363 0.05988609 94 100
#> 5 0.6611418 0.05647038 95 100
#> 6 0.6548820 0.06455131 97 100
#> 7 0.6233123 0.07035881 99 100
#> 8 0.6439417 0.06313122 96 100
#> 9 0.5968648 0.04974145 95 100
#> 10 0.6504479 0.04801153 100 100
#> 11 0.6633062 0.06073794 94 100
#> 12 0.6215323 0.04175730 98 100
#> 13 0.5904859 0.05249843 92 100
#> 14 0.6004784 0.06541772 98 100
#> 15 0.6147015 0.04934332 95 100
#> 16 0.6723269 0.07028122 97 100
#> 17 0.6395157 0.06394442 95 100
#> 18 0.6136843 0.04325469 91 100
#> 19 0.6522689 0.05339963 94 100
#> 20 0.5884555 0.05451280 96 100
#> 21 0.6338096 0.05172390 95 100
#> 22 0.6675348 0.06379048 94 100
#> 23 0.6313025 0.05655082 96 100
#> 24 0.6710650 0.05873389 97 100
#> 25 0.6844724 0.06295105 95 100
#> 26 0.6143413 0.04614352 94 100
#> 27 0.6154903 0.04315498 94 100
#> 28 0.6186963 0.05139616 93 100
#> 29 0.6519301 0.05591479 96 100
#> 30 0.6558019 0.03844764 93 100
#> 31 0.6702752 0.06508662 96 100
#> 32 0.6694440 0.05335587 94 100
#> 33 0.6651431 0.05714546 97 100
#> 34 0.6623062 0.05926317 91 100
#> 35 0.6430432 0.04897622 97 100
#> 36 0.6159375 0.06995371 97 100
#> 37 0.6205665 0.06746362 95 100
#> 38 0.6479533 0.04375136 94 100
#> 39 0.6772545 0.05048432 92 100
#> 40 0.6804858 0.05792318 94 100
#> 41 0.5964190 0.04985665 97 100
#> 42 0.6180135 0.06592803 97 100
#> 43 0.6759123 0.06609616 96 100
#> 44 0.6115841 0.06846590 93 100
#> 45 0.6039356 0.04838173 97 100
#> 46 0.6534479 0.05463676 94 100
#> 47 0.6827265 0.06242710 93 100
#> 48 0.6838587 0.05275144 94 100
#> 49 0.6525391 0.06055379 96 100
#> 50 0.6568689 0.05873476 93 100
#> 51 0.6532560 0.06095689 95 100
#> 52 0.6390410 0.04568487 96 100
#> 53 0.5611998 0.05382874 95 100
#> 54 0.6560465 0.04772817 94 100
#> 55 0.6303716 0.05358205 97 100
#> 56 0.6612855 0.04684440 96 100
#> 57 0.6241090 0.05969555 96 100
#> 58 0.6025333 0.05094580 95 100
#> 59 0.6701058 0.06069475 96 100
#> 60 0.6435707 0.05217649 88 100
#> 61 0.7188638 0.05164959 94 100
#> 62 0.6604356 0.05264590 97 100
#> 63 0.6683303 0.07598606 98 100
#> 64 0.6569278 0.05249242 94 100
#> 65 0.6236264 0.06857890 98 100
#> 66 0.6303252 0.06038180 88 100
#> 67 0.6661014 0.06334310 94 100
#> 68 0.6632287 0.05088585 96 100
#> 69 0.6549883 0.07124614 97 100
#> 70 0.6158234 0.05724333 91 100
#> 71 0.6788709 0.05482040 97 100
#> 72 0.6050748 0.06316697 98 100
#> 73 0.6296946 0.05047677 95 100
#> 74 0.6986730 0.06492939 94 100
#> 75 0.6527223 0.06434130 96 100
#> 76 0.6595372 0.04291456 97 100
#> 77 0.6503535 0.08400249 91 100
#> 78 0.6136431 0.06702841 98 100
#> 79 0.6251914 0.05677260 95 100
#> 80 0.6435316 0.06167719 97 100
#> 81 0.5748085 0.04868985 95 100
#> 82 0.6232061 0.03659991 97 100
#> 83 0.6589920 0.06001926 93 100
#> 84 0.6321231 0.05989998 96 100
#> 85 0.6333010 0.04666608 96 100
#> 86 0.6608460 0.06067553 97 100
#> 87 0.6260458 0.06043209 95 100
#> 88 0.6560523 0.06989989 95 100
#> 89 0.6036348 0.06332708 97 100
#> 90 0.6072784 0.06859433 94 100
#> 91 0.6015950 0.05107018 99 100
#> 92 0.6413772 0.05336061 97 100
#> 93 0.6343302 0.06115454 98 100
#> 94 0.6726708 0.05315609 95 100
#> 95 0.6383762 0.06332375 95 100
#> 96 0.6767997 0.07621064 99 100
#> 97 0.6874571 0.06096442 97 100
#> 98 0.6268826 0.06529676 95 100
#> 99 0.6495241 0.06756020 94 100
#> 100 0.6190468 0.05818894 95 100
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 0.6295673 0.8437794 0.07251529 6.594494e-02 95 100
#> 2 0.6320978 0.5114707 0.05050999 8.772947e-02 96 100
#> 3 0.5973184 0.6673136 0.06079219 1.404990e-04 98 100
#> 4 0.6151276 0.7629407 0.04919219 4.067938e-02 96 100
#> 5 0.6269469 0.6724622 0.05223744 8.286223e-04 98 100
#> 6 0.5769794 0.9552659 0.06613092 1.360440e-01 96 100
#> 7 0.6412830 0.9240977 0.04523218 1.451390e-01 96 100
#> 8 0.5862533 0.3736954 0.06312256 4.914088e-01 98 100
#> 9 0.6585223 0.7532250 0.06169105 7.491025e-02 97 100
#> 10 0.6116006 0.5878986 0.04948064 2.952359e-02 96 100
#> 11 0.5953911 0.6601617 0.05841401 1.273573e-03 96 100
#> 12 0.6481502 0.8012077 0.06609551 8.794254e-02 95 100
#> 13 0.6122368 0.6582434 0.05800952 1.207774e-01 97 100
#> 14 0.6496379 0.7677277 0.05427092 1.210271e-01 98 100
#> 15 0.5998191 0.7622475 0.05535902 2.570438e-02 98 100
#> 16 0.5979670 0.5571375 0.04750986 5.194862e-02 95 100
#> 17 0.6042490 0.5978987 0.05917475 4.281329e-02 97 100
#> 18 0.5811900 0.7509453 0.03992972 4.571999e-02 96 100
#> 19 0.6207346 0.6529731 0.05880500 1.139349e-01 93 100
#> 20 0.6053061 0.5714547 0.05450927 1.017138e-01 96 100
#> 21 0.5713753 0.6575810 0.05029375 5.842375e-02 97 100
#> 22 0.6232663 0.3655228 0.06297152 7.108647e-02 97 100
#> 23 0.6127105 NA 0.04976760 NA 99 100
#> 24 0.6136674 0.6094155 0.04544656 2.026951e-02 93 100
#> 25 0.6067371 0.6833750 0.06404082 2.179984e-02 98 100
#> 26 0.6040189 0.3671243 0.05657460 8.822396e-02 97 100
#> 27 0.5936968 NA 0.04667607 NA 99 100
#> 28 0.6294724 0.6667818 0.05879693 1.696963e-02 98 100
#> 29 0.6300068 0.7050965 0.06963457 8.973507e-02 98 100
#> 30 0.6355551 0.5300147 0.05710740 3.900999e-02 96 100
#> 31 0.5823655 NA 0.06665255 NA 99 100
#> 32 0.5885302 0.7730889 0.04407351 3.592315e-02 98 100
#> 33 0.6304477 NA 0.06660727 NA 100 100
#> 34 0.6324403 0.5647829 0.05122719 3.016586e-02 98 100
#> 35 0.5982677 0.6755132 0.05770518 1.102927e-02 95 100
#> 36 0.5916293 NA 0.04072482 NA 100 100
#> 37 0.6174610 0.4623220 0.06015877 1.122050e-01 95 100
#> 38 0.5819899 0.6601703 0.04833873 1.390548e-02 96 100
#> 39 0.6217734 0.8603251 0.05661979 8.924183e-02 97 100
#> 40 0.6542422 0.8217092 0.06806317 1.439070e-01 97 100
#> 41 0.5596505 0.4642255 0.05803406 1.400501e-01 98 100
#> 42 0.5939036 0.7901467 0.05931170 1.026820e-01 95 100
#> 43 0.6242977 1.0753507 0.04172722 7.093010e-02 98 100
#> 44 0.6432080 0.6652863 0.04920139 5.232873e-04 98 100
#> 45 0.6050643 0.8076987 0.04028089 5.379542e-02 96 100
#> 46 0.6115253 0.7366095 0.05727642 3.362359e-02 97 100
#> 47 0.6179933 0.6462888 0.06023504 3.251443e-02 96 100
#> 48 0.6368056 0.8382029 0.04460444 5.028376e-02 97 100
#> 49 0.6315243 0.4227948 0.05997528 4.178054e-02 96 100
#> 50 0.6012017 0.6580344 0.07255769 2.824223e-02 96 100
#> 51 0.5990354 0.9037728 0.06913628 1.024403e-01 97 100
#> 52 0.6161395 0.7721187 0.05687585 4.116261e-02 98 100
#> 53 0.5902118 0.7365785 0.05422370 3.609071e-02 96 100
#> 54 0.5664137 0.8747776 0.04823711 8.478922e-02 95 100
#> 55 0.5979981 0.6877169 0.04848923 1.471167e-01 96 100
#> 56 0.6159703 0.7497508 0.05364703 7.955427e-02 97 100
#> 57 0.6132035 0.7232543 0.05438193 2.199048e-02 96 100
#> 58 0.6068912 0.5883691 0.06100047 6.395670e-02 93 100
#> 59 0.5655012 0.7680331 0.07866987 8.015246e-02 96 100
#> 60 0.6125556 0.7565666 0.05671351 7.895931e-02 91 100
#> 61 0.6170409 0.6450699 0.07207494 1.059696e-02 93 100
#> 62 0.6595397 0.5026429 0.05743236 8.925177e-02 95 100
#> 63 0.5446846 0.6583564 0.07116811 3.564531e-03 98 100
#> 64 0.5853013 0.6741303 0.05570803 5.108503e-02 98 100
#> 65 0.6187329 0.5844177 0.07079873 1.007807e-01 94 100
#> 66 0.5790558 0.6494662 0.05819022 1.066147e-03 97 100
#> 67 0.6520117 0.7826483 0.05308372 8.720798e-02 97 100
#> 68 0.6388185 0.4267374 0.05236357 1.382534e-01 98 100
#> 69 0.6192317 0.6853107 0.05083846 1.156912e-02 97 100
#> 70 0.5932924 0.7126934 0.05373026 9.538665e-02 94 100
#> 71 0.6139888 0.7666147 0.05547828 2.370053e-02 97 100
#> 72 0.6117948 0.6664951 0.05682791 5.652457e-02 94 100
#> 73 0.6265021 0.3199878 0.05307565 8.876615e-02 97 100
#> 74 0.5989946 0.6762536 0.04200344 3.929702e-04 98 100
#> 75 0.6061053 NA 0.05899444 NA 100 100
#> 76 0.6201900 0.6491733 0.07102137 7.996064e-02 97 100
#> 77 0.6225243 1.0478376 0.04679312 1.704768e-01 97 100
#> 78 0.6026407 0.6686098 0.05838654 7.001612e-06 98 100
#> 79 0.5978713 0.3269993 0.05453544 1.267717e-01 97 100
#> 80 0.6314863 0.6794807 0.05312758 6.779086e-02 95 100
#> 81 0.6080299 NA 0.04890462 NA 99 100
#> 82 0.5871164 0.5229742 0.04363782 7.526974e-02 96 100
#> 83 0.5766547 0.5176090 0.05395927 2.132737e-02 96 100
#> 84 0.6311633 0.7354626 0.05273845 4.036989e-02 94 100
#> 85 0.6162625 0.3771659 0.04131055 4.475147e-02 98 100
#> 86 0.6181450 NA 0.06147180 NA 99 100
#> 87 0.6409817 0.8714495 0.06197870 9.396728e-02 94 100
#> 88 0.6435363 0.6177579 0.06175863 7.583563e-02 96 100
#> 89 0.6266914 0.6058099 0.05699086 3.882891e-02 96 100
#> 90 0.5620041 0.5206220 0.06772931 5.180630e-02 98 100
#> 91 0.6004314 1.1957896 0.04858873 1.235315e-01 98 100
#> 92 0.5656618 0.7274934 0.05800482 1.032673e-01 95 100
#> 93 0.6393932 0.6152189 0.06469085 3.746275e-03 96 100
#> 94 0.5917474 0.6847741 0.06400469 1.727901e-02 94 100
#> 95 0.5567018 0.5119306 0.04674984 8.988167e-02 96 100
#> 96 0.6041630 0.6956468 0.05798619 5.768874e-03 98 100
#> 97 0.5979620 0.7048022 0.05847856 1.246851e-02 95 100
#> 98 0.6318311 0.6927899 0.06266443 4.659150e-02 96 100
#> 99 0.5990506 0.4804478 0.06311816 2.490870e-02 97 100
#> 100 0.6483768 0.5589593 0.03766166 1.065355e-02 98 100