Simulation of confidence ratings and RTs in race confidence models
Source:R/simulateRM.R
simulateRM.RdSimulates the decision responses, reaction times and state of the loosing accumulator
together with a discrete confidence judgment in the independent and partially anti-correlated
race model (IRM and PCRM) (Hellmann et al., 2023), given specific parameter constellations.
See RaceModels for more information about
parameters. Also computes the Gamma rank correlation between the confidence
ratings and condition (task difficulty), reaction times and accuracy in the
simulated output. Basically, this function is a wrapper for rIRM
and rPCRM for application in confidence experiments with
manipulation of specific parameters.
rRM_Kiani simulates a different version of race models, presented in
Kiani et al. (2014), but without a confidence measure.
Usage
simulateRM(paramDf, n = 10000, model = "IRM", time_scaled = FALSE,
gamma = FALSE, agg_simus = FALSE, stimulus = c(1, 2), delta = 0.01,
maxrt = 15, seed = NULL)
rRM_Kiani(paramDf, n = 10000, time_scaled = FALSE, gamma = FALSE,
agg_simus = FALSE, stimulus = c(1, 2), delta = 0.01, maxrt = 15,
seed = NULL)Arguments
- paramDf
a list or data frame with one row. Column names should match the names of RaceModels parameter names (only
mu1andmu2are not used in this context but replaced by the parameterv). For different stimulus quality/mean drift rates, names should bev1,v2,v3,.... Differentsparameters are possible withs1,s2,s3,... with equally many steps as for drift rates. Additionally, the confidence thresholds should be given by names withthetaUpper1,thetaUpper2,...,thetaLower1,... or, for symmetric thresholds only bytheta1,theta2,....- n
integer. The number of samples (per condition and stimulus direction) generated. Total number of samples is
n*nConditions*length(stimulus).- model
character scalar. One of "IRM" or "PCRM". ("IRMt" and "PCRMt" will also be accepted. In that case, time_scaled is set to TRUE.)
- time_scaled
logical. Whether a time_scaled transformation for the confidence measure should be used.
- gamma
logical. If TRUE, the gamma correlation between confidence ratings, rt and accuracy is computed.
- agg_simus
logical. Simulation is done on a trial basis with RTs outcome. If TRUE, the simulations will be aggregated over RTs to return only the distribution of response and confidence ratings. Default: FALSE.
- stimulus
numeric vector. Either 1, 2 or c(1, 2) (default). Together with condition represents the experimental situation. In a binary decision task the presented stimulus belongs to one of two categories. In the default setting trials with both categories presented are simulated but one can choose to simulate only trials with the stimulus coming from one category (each associated with positive drift in one of two accumulators).
- delta
numerical. Size of steps for the discretized simulation (see details).
- maxrt
numerical. Maximum reaction time to be simulated (see details). Default: 15.
- seed
numerical. Seeding for non-random data generation. (Also possible outside of the function.)
Value
Depending on gamma and agg_simus.
If gamma is FALSE, returns a data.frame with columns: condition,
stimulus, response, correct, rt, conf (the continuous confidence
measure) and rating (the discrete confidence rating) or
(if agg_simus=TRUE): condition, stimulus,response, correct,
rating and p (for the probability of a response and rating, given
the condition and stimulus).
If gamma is TRUE, returns a list with elements:
simus (the simulated data frame) and gamma, which is again a list with elements
condition, rt and correct, each a tibble with two columns (see details for more
information).
Details
The simulation is done by simulating normal variables in discretized steps until
one process reaches the boundary. If no boundary is met within the maximum time, response is
set to 0. The output of the fitting function fitRTConf with the respective model
fits the argument paramDf for simulation. The Gamma coefficients are computed separately for
correct/incorrect responses for the correlation of confidence ratings with condition and rt
and separately for conditions for the correlation of accuracy and confidence. The resulting
data frames in the output thus have two columns. One for the grouping variable and one for the
Gamma coefficient.
Note
Different parameters for different conditions are only allowed for drift rate, v,
and process variability, s. All other parameters are used for all conditions.
References
Hellmann, S., Zehetleitner, M., & Rausch, M. (2023). Simultaneous modeling of choice, confidence and response time in visual perception. Psychological Review 2023 Mar 13. doi: 10.1037/rev0000411. Epub ahead of print. PMID: 36913292.
Kiani, R., Corthell, L., & Shadlen, M.N. (2014) Choice certainty is informed by both evidence and decision time. Neuron, 84(6), 1329-1342. doi:10.1016/j.neuron.2014.12.015
Examples
# Examples for "PCRM" model (equivalent applicable for "IRM" model)
# 1. Define some parameter set in a data.frame
paramDf <- data.frame(a=2,b=2, v1=0.5, v2=1, t0=0.1,st0=0,
wx=0.6, wint=0.2, wrt=0.2,
theta1=4)
# 2. Simulate trials for both stimulus categories and all conditions (2)
simus <- simulateRM(paramDf, n=30,model="PCRM", time_scaled=TRUE)
head(simus)
#> condition stimulus response correct rt xj conf rating
#> 1 1 1 1 1 0.80 -0.7593297 2.554249 1
#> 2 1 1 1 1 1.31 -1.5730149 2.975266 1
#> 3 1 1 2 0 2.24 -1.4555232 2.682460 1
#> 4 1 1 2 0 1.74 -0.7622289 2.244899 1
#> 5 1 1 1 1 2.75 0.3581217 1.309706 1
#> 6 1 1 1 1 0.58 -0.8454800 2.817382 1
# equivalent:
simus <- simulateRM(paramDf, model="PCRMt")
# \donttest{
library(ggplot2)
simus <- simus[simus$response!=0,]
simus$rating <- factor(simus$rating, labels=c("unsure", "sure"))
ggplot(simus, aes(x=rt, group=interaction(correct, rating),
color=as.factor(correct), linetype=rating))+
geom_density(linewidth=1.2)+
facet_grid(rows=vars(condition), labeller = "label_both")
# }
# automatically aggregate simulation distribution
# to get only accuracy x confidence rating distribution for
# all conditions
agg_simus <- simulateRM(paramDf, n = 20, model="PCRMt", agg_simus = TRUE)
head(agg_simus)
#> # A tibble: 6 × 4
#> # Groups: rating, correct [4]
#> rating correct condition p
#> <dbl> <dbl> <int> <dbl>
#> 1 1 0 1 0.075
#> 2 1 0 2 0.025
#> 3 1 1 1 0.8
#> 4 1 1 2 0.925
#> 5 2 0 1 0.025
#> 6 2 1 1 0.1
# \donttest{
agg_simus$rating <- factor(agg_simus$rating, labels=c("unsure", "sure"))
library(ggplot2)
ggplot(agg_simus, aes(x=rating, group=correct, fill=as.factor(correct), y=p))+
geom_bar(stat="identity", position="dodge")+
facet_grid(cols=vars(condition), labeller = "label_both")
# }
# \donttest{
# Compute Gamma correlation coefficients between
# confidence and other behavioral measures
# output will be a list
simu_list <- simulateRM(paramDf, model="IRMt", gamma=TRUE, n=200)
simu_list
#> $simus
#> condition stimulus response correct rt xj conf rating
#> 1 1 1 2 0 0.98 1.596153042 0.5416094 1
#> 2 1 1 1 1 0.96 0.529857451 1.4148102 1
#> 3 1 1 1 1 5.27 -5.798453657 5.4529833 2
#> 4 1 1 1 1 1.65 -0.344161027 1.9437156 1
#> 5 1 1 1 1 1.72 -0.580046540 2.1105780 1
#> 6 1 1 1 1 0.94 -0.290008022 2.0919434 1
#> 7 1 1 1 1 1.21 0.435663947 1.4253936 1
#> 8 1 1 1 1 4.39 -3.027220619 3.5983263 1
#> 9 1 1 1 1 4.84 -5.618981904 5.3631550 2
#> 10 1 1 1 1 2.00 -3.010691329 3.8785376 1
#> 11 1 1 1 1 3.53 -4.338630357 4.5956758 2
#> 12 1 1 1 1 2.46 0.035347044 1.5647567 1
#> 13 1 1 1 1 3.01 -0.762917676 2.0989229 1
#> 14 1 1 1 1 4.62 -4.148632162 4.3616660 2
#> 15 1 1 1 1 12.90 -8.039106871 6.6405690 2
#> 16 1 1 1 1 10.02 -0.914476485 1.9972554 1
#> 17 1 1 0 0 15.11 -6.062558626 5.3053678 1
#> 18 1 1 1 1 3.90 -0.798775859 2.0690117 1
#> 19 1 1 1 1 7.06 -5.057870650 4.8455880 2
#> 20 1 1 1 1 2.90 -1.070637964 2.3289171 1
#> 21 1 1 1 1 1.84 -0.731403875 2.2045963 1
#> 22 1 1 1 1 5.53 -3.575389984 3.9095880 1
#> 23 1 1 1 1 6.06 -1.374427644 2.3830237 1
#> 24 1 1 1 1 9.68 -6.984990202 6.0361949 2
#> 25 1 1 1 1 1.69 -3.028981376 3.9736475 1
#> 26 1 1 1 1 4.06 -0.438339760 1.8085700 1
#> 27 1 1 2 0 11.75 0.145521267 1.2799479 1
#> 28 1 1 1 1 3.48 -3.071064253 3.7030833 1
#> 29 1 1 1 1 2.20 -1.015319111 2.3633582 1
#> 30 1 1 1 1 6.74 0.853003808 0.8548369 1
#> 31 1 1 1 1 1.04 -0.692867087 2.3775006 1
#> 32 1 1 2 0 0.95 -0.843211709 2.5396367 1
#> 33 1 1 2 0 0.82 0.441536766 1.5381135 1
#> 34 1 1 1 1 1.05 -0.143457850 1.9310987 1
#> 35 1 1 1 1 8.60 -4.558277180 4.4534598 2
#> 36 1 1 1 1 1.61 -2.116508509 3.3026562 1
#> 37 1 1 1 1 6.78 -2.032305810 2.8087950 1
#> 38 1 1 1 1 2.16 0.748877622 1.0643597 1
#> 39 1 1 2 0 1.44 -1.380550653 2.7851743 1
#> 40 1 1 1 1 1.97 -0.920522780 2.3257077 1
#> 41 1 1 1 1 7.21 -5.231150514 4.9560748 2
#> 42 1 1 1 1 8.25 -5.056520481 4.7983275 2
#> 43 1 1 1 1 3.43 -3.223790970 3.8163979 1
#> 44 1 1 1 1 10.76 -6.633241189 5.7700423 2
#> 45 1 1 1 1 0.73 -0.298493697 2.2102385 1
#> 46 1 1 1 1 0.69 -0.183018501 2.1385985 1
#> 47 1 1 1 1 1.47 -0.684766026 2.2404812 1
#> 48 1 1 1 1 2.21 -1.471308824 2.6984205 1
#> 49 1 1 1 1 0.83 -2.482033523 3.9724671 1
#> 50 1 1 1 1 3.51 -0.600385554 1.9501750 1
#> 51 1 1 1 1 2.12 -1.958091717 3.0725553 1
#> 52 1 1 1 1 12.36 -17.025366548 12.5590598 2
#> 53 1 1 1 1 2.60 0.638646513 1.1155023 1
#> 54 1 1 1 1 9.91 -5.533255101 5.0648448 2
#> 55 1 1 1 1 3.14 0.155110152 1.4332652 1
#> 56 1 1 1 1 3.16 -2.304156487 3.1889308 1
#> 57 1 1 1 1 1.50 1.244349911 0.7501491 1
#> 58 1 1 1 1 8.23 -7.951911578 6.7393476 2
#> 59 1 1 1 1 10.56 -1.034368649 2.0701035 1
#> 60 1 1 1 1 1.15 -0.284428392 2.0117118 1
#> 61 1 1 1 1 1.68 -2.726476596 3.7470340 1
#> 62 1 1 1 1 1.96 -1.036903302 2.4141422 1
#> 63 1 1 1 1 2.62 -5.044871263 5.2404813 2
#> 64 1 1 1 1 2.16 1.244498133 0.6979243 1
#> 65 1 1 1 1 11.48 -6.289266586 5.5242919 2
#> 66 1 1 1 1 4.54 0.492293753 1.1426447 1
#> 67 1 1 1 1 3.33 -2.457807995 3.2820459 1
#> 68 1 1 1 1 2.32 -1.853460922 2.9635625 1
#> 69 1 1 1 1 5.47 -4.670310189 4.6641827 2
#> 70 1 1 1 1 4.06 -2.756668373 3.4325680 1
#> 71 1 1 1 1 0.99 -0.863893932 2.5374802 1
#> 72 1 1 1 1 0.81 -1.680173718 3.3189731 1
#> 73 1 1 1 1 3.77 -0.380120570 1.7809541 1
#> 74 1 1 1 1 7.33 -5.337950538 5.0229538 2
#> 75 1 1 1 1 4.34 -2.258084464 3.0655610 1
#> 76 1 1 1 1 4.00 0.435359944 1.1985152 1
#> 77 1 1 1 1 4.77 -3.519714318 3.9152214 1
#> 78 1 1 1 1 0.97 -0.293658692 2.0824298 1
#> 79 1 1 0 0 15.11 -9.316739681 7.4258656 1
#> 80 1 1 1 1 9.91 -6.356647322 5.6114579 2
#> 81 1 1 1 1 8.51 -4.922801417 4.7000809 2
#> 82 1 1 1 1 6.72 -1.633376469 2.5401885 1
#> 83 1 1 1 1 1.48 -0.292703897 1.9362095 1
#> 84 1 1 0 0 15.11 -8.593029305 6.9542796 1
#> 85 1 1 1 1 2.89 -4.125908181 4.5287788 2
#> 86 1 1 1 1 4.93 -0.200891305 1.6118260 1
#> 87 1 1 1 1 1.79 -1.484379452 2.7805322 1
#> 88 1 1 1 1 5.28 -2.251199872 3.0121689 1
#> 89 1 1 1 1 2.56 -3.352268719 4.0213730 2
#> 90 1 1 1 1 1.92 -1.512301538 2.7763290 1
#> 91 1 1 1 1 4.40 -5.869527644 5.5771698 2
#> 92 1 1 1 1 8.88 -9.169470164 7.5230815 2
#> 93 1 1 1 1 9.17 -5.325303081 4.9480562 2
#> 94 1 1 1 1 3.35 -2.154141466 3.0642855 1
#> 95 1 1 1 1 5.73 -3.140931202 3.6021775 1
#> 96 1 1 1 1 1.80 -2.462470258 3.5153868 1
#> 97 1 1 1 1 4.44 -0.330077879 1.7177444 1
#> 98 1 1 1 1 2.07 -1.943519077 3.0705337 1
#> 99 1 1 1 1 2.33 -1.259476940 2.5261575 1
#> 100 1 1 1 1 6.02 -2.160045862 2.9201807 1
#> 101 1 1 1 1 2.23 -0.726667130 2.1466943 1
#> 102 1 1 1 1 1.69 0.670068083 1.1675104 1
#> 103 1 1 2 0 1.38 0.721986135 1.1695081 1
#> 104 1 1 1 1 2.05 -2.297955740 3.3375624 1
#> 105 1 1 1 1 12.90 -2.142483083 2.7729634 1
#> 106 1 1 1 1 4.69 -1.241051110 2.3405413 1
#> 107 1 1 0 0 15.11 -15.365286186 11.3672350 1
#> 108 1 1 1 1 3.93 -2.165566696 3.0272363 1
#> 109 1 1 1 1 2.74 -1.405581581 2.5856386 1
#> 110 1 1 1 1 1.25 0.131304686 1.6562316 1
#> 111 1 1 2 0 3.71 -4.200469005 4.4782255 2
#> 112 1 1 1 1 1.66 -1.032787520 2.4654353 1
#> 113 1 1 1 1 3.37 -2.296713553 3.1638460 1
#> 114 1 1 1 1 8.94 -6.616335049 5.8166657 2
#> 115 1 1 1 1 6.45 -2.874698561 3.3910797 1
#> 116 1 1 1 1 3.02 -1.529818895 2.6480665 1
#> 117 1 1 1 1 1.75 -0.753086554 2.2362067 1
#> 118 1 1 1 1 2.29 -1.388259676 2.6260180 1
#> 119 1 1 1 1 7.25 -2.389655674 3.0369168 1
#> 120 1 1 1 1 4.68 -2.234170674 3.0296559 1
#> 121 1 1 1 1 2.47 -1.704477909 2.8338641 1
#> 122 1 1 1 1 3.04 1.308272556 0.6123636 1
#> 123 1 1 1 1 7.07 0.117473195 1.3478831 1
#> 124 1 1 2 0 1.10 1.084729667 0.9322163 1
#> 125 1 1 1 1 2.72 -1.271248073 2.4905060 1
#> 126 1 1 1 1 1.21 -0.761401090 2.3708734 1
#> 127 1 1 1 1 1.50 1.655134981 0.4342427 1
#> 128 1 1 1 1 5.01 -2.478542703 3.1816120 1
#> 129 1 1 1 1 12.62 -4.170542893 4.1076288 2
#> 130 1 1 1 1 3.14 -3.498729898 4.0446934 2
#> 131 1 1 1 1 8.98 -4.112414593 4.1448028 2
#> 132 1 1 1 1 2.24 -1.025252075 2.3654724 1
#> 133 1 1 1 1 3.34 -0.607755665 1.9655151 1
#> 134 1 1 1 1 1.88 -1.302527809 2.6264929 1
#> 135 1 1 1 1 3.86 -2.115080766 2.9966288 1
#> 136 1 1 1 1 5.56 -2.549152565 3.2044552 1
#> 137 1 1 1 1 6.02 -3.589400204 3.8952855 1
#> 138 1 1 1 1 1.99 -0.696905164 2.1559637 1
#> 139 1 1 1 1 1.99 1.028653771 0.8695964 1
#> 140 1 1 1 1 3.49 -1.320856509 2.4618673 1
#> 141 1 1 1 1 0.89 -0.432529110 2.2318969 1
#> 142 1 1 1 1 2.14 -1.719832246 2.8928081 1
#> 143 1 1 1 1 1.36 -0.476014942 2.1049450 1
#> 144 1 1 1 1 0.78 -0.139804337 2.0453970 1
#> 145 1 1 1 1 1.15 -1.437045488 2.9282499 1
#> 146 1 1 0 0 15.11 -0.851539687 1.9097502 1
#> 147 1 1 1 1 1.44 -1.977517338 3.2464944 1
#> 148 1 1 1 1 3.86 -1.288740408 2.4155940 1
#> 149 1 1 2 0 1.29 -0.122561093 1.8460261 1
#> 150 1 1 1 1 5.24 -4.654244937 4.6677755 2
#> 151 1 1 1 1 1.26 -0.167155196 1.8884191 1
#> 152 1 1 1 1 9.11 -4.316312108 4.2772707 2
#> 153 1 1 1 1 5.52 -4.220628090 4.3526819 2
#> 154 1 1 1 1 3.48 -2.147724653 3.0486334 1
#> 155 1 1 1 1 7.37 -3.946008761 4.0828317 2
#> 156 1 1 0 0 15.11 -10.246109715 8.0314641 1
#> 157 1 1 1 1 2.25 0.799001105 1.0208131 1
#> 158 1 1 1 1 1.03 1.028806322 0.9915227 1
#> 159 1 1 1 1 4.14 -4.684735315 4.7755009 2
#> 160 1 1 1 1 4.17 -6.525443060 6.0595832 2
#> 161 1 1 1 1 1.55 0.012980922 1.6883283 1
#> 162 1 1 1 1 1.29 1.452308651 0.6123681 1
#> 163 1 1 1 1 4.40 -2.574536928 3.2823782 1
#> 164 1 1 1 1 2.42 -3.536908425 4.1804832 2
#> 165 1 1 1 1 2.94 -0.748041621 2.0936357 1
#> 166 1 1 1 1 4.00 -1.427689143 2.5050230 1
#> 167 1 1 1 1 1.28 0.038018046 1.7225343 1
#> 168 1 1 1 1 4.96 -4.785845344 4.7778534 2
#> 169 1 1 1 1 1.92 -1.841971281 3.0230043 1
#> 170 1 1 1 1 2.37 0.076304183 1.5423225 1
#> 171 1 1 1 1 5.39 -5.083131804 4.9527601 2
#> 172 1 1 1 1 2.28 -0.380677245 1.8863431 1
#> 173 1 1 1 1 3.01 0.850364154 0.9418093 1
#> 174 1 1 1 1 4.03 -2.442360162 3.2144776 1
#> 175 1 1 1 1 10.16 -4.273462101 4.2227175 2
#> 176 1 1 1 1 6.79 -5.831942962 5.3820911 2
#> 177 1 1 1 1 8.17 -2.496393473 3.0848005 1
#> 178 1 1 1 1 1.64 -2.172104612 3.3368229 1
#> 179 1 1 1 1 4.04 -4.233901953 4.4692186 2
#> 180 1 1 1 1 1.10 -0.918103666 2.5344829 1
#> 181 1 1 1 1 5.24 -1.437690084 2.4540903 1
#> 182 1 1 1 1 0.46 0.768330496 1.4828915 1
#> 183 1 1 1 1 1.72 -1.550399710 2.8452662 1
#> 184 1 1 1 1 0.65 -0.453677051 2.4035937 1
#> 185 1 1 1 1 0.61 -0.312597710 2.3152715 1
#> 186 1 1 1 1 7.43 -5.750121569 5.2964592 2
#> 187 1 1 1 1 2.53 -0.292717807 1.7980866 1
#> 188 1 1 1 1 10.13 -11.190132376 8.8101990 2
#> 189 1 1 1 1 1.12 -0.458137385 2.1596957 1
#> 190 1 1 0 0 15.11 -4.473929554 4.2701812 1
#> 191 1 1 1 1 2.11 -2.433712829 3.4267568 1
#> 192 1 1 0 0 15.11 -10.737052133 8.3513733 1
#> 193 1 1 1 1 1.85 1.676248577 0.3943833 1
#> 194 1 1 1 1 6.48 -1.676331952 2.5760747 1
#> 195 1 1 1 1 2.20 -0.440053880 1.9388049 1
#> 196 1 1 1 1 2.50 -3.682825763 4.2724446 2
#> 197 1 1 1 1 9.38 -6.110854195 5.4646694 2
#> 198 1 1 1 1 8.32 0.106052512 1.3382445 1
#> 199 1 1 1 1 1.55 -1.432049075 2.7953527 1
#> 200 1 1 1 1 1.09 -0.301042762 2.0441602 1
#> 201 2 1 1 1 3.22 -3.159675494 3.7932512 1
#> 202 2 1 1 1 6.89 -5.938040398 5.4488453 2
#> 203 2 1 1 1 2.68 -4.784361144 5.0398830 2
#> 204 2 1 1 1 1.52 -1.101506756 2.5492857 1
#> 205 2 1 1 1 4.62 -3.276734480 3.7565062 1
#> 206 2 1 1 1 1.51 -2.248576270 3.4331655 1
#> 207 2 1 1 1 1.60 -1.798780099 3.0629056 1
#> 208 2 1 1 1 1.26 -0.559940562 2.1970287 1
#> 209 2 1 1 1 0.99 -2.331641913 3.7292910 1
#> 210 2 1 1 1 0.92 -0.751565598 2.4795216 1
#> 211 2 1 1 1 4.01 -3.405865958 3.8914367 1
#> 212 2 1 1 1 1.87 -0.314431152 1.8869145 1
#> 213 2 1 1 1 1.36 -1.016512402 2.5255462 1
#> 214 2 1 1 1 1.62 -0.600827707 2.1446280 1
#> 215 2 1 1 1 1.01 -0.273186131 2.0501580 1
#> 216 2 1 1 1 3.65 -2.192303366 3.0665397 1
#> 217 2 1 1 1 4.18 -3.035659320 3.6190149 1
#> 218 2 1 1 1 0.97 -1.819233177 3.3248920 1
#> 219 2 1 1 1 2.73 -1.381190731 2.5690260 1
#> 220 2 1 1 1 1.60 -2.591429915 3.6679346 1
#> 221 2 1 1 1 3.19 -3.456503088 4.0084971 2
#> 222 2 1 1 1 1.22 -1.500133594 2.9505255 1
#> 223 2 1 1 1 0.73 -2.025360307 3.6814880 1
#> 224 2 1 1 1 0.63 -0.518575573 2.4777724 1
#> 225 2 1 1 1 1.75 -0.326634038 1.9139366 1
#> 226 2 1 1 1 0.73 -0.397138831 2.2942818 1
#> 227 2 1 1 1 1.03 0.400578198 1.4987480 1
#> 228 2 1 1 1 3.99 -9.478476716 8.1524538 2
#> 229 2 1 1 1 0.88 -0.603771847 2.3783567 1
#> 230 2 1 1 1 8.05 -12.741715720 9.9616317 2
#> 231 2 1 1 1 2.24 -1.459257086 2.6852113 1
#> 232 2 1 1 1 1.32 -1.023662280 2.5427679 1
#> 233 2 1 1 1 10.71 -12.810100693 9.8568094 2
#> 234 2 1 1 1 2.53 -6.218322731 6.1137050 2
#> 235 2 1 1 1 1.28 -1.685822807 3.0742236 1
#> 236 2 1 1 1 1.86 -3.170771224 4.0327415 2
#> 237 2 1 1 1 1.03 -0.101219400 1.9038946 1
#> 238 2 1 1 1 1.08 -2.811224363 4.0607792 2
#> 239 2 1 1 1 2.52 -3.694424683 4.2773226 2
#> 240 2 1 1 1 3.35 -2.633641002 3.4051810 1
#> 241 2 1 1 1 2.42 -3.017742770 3.8008140 1
#> 242 2 1 1 1 2.45 -3.154166475 3.8954070 1
#> 243 2 1 1 1 4.40 -2.214194064 3.0314180 1
#> 244 2 1 1 1 1.57 -1.957824980 3.1925240 1
#> 245 2 1 1 1 3.31 -3.517571579 4.0380937 2
#> 246 2 1 1 1 1.16 -0.868435184 2.4725324 1
#> 247 2 1 1 1 1.97 -3.036955823 3.9051054 1
#> 248 2 1 1 1 4.55 -6.662336298 6.1134791 2
#> 249 2 1 1 1 1.07 -0.948020004 2.5705334 1
#> 250 2 1 1 1 2.59 -2.939699361 3.7166459 1
#> 251 2 1 1 1 1.90 -2.437005824 3.4727045 1
#> 252 2 1 1 1 2.25 -1.309246079 2.5733239 1
#> 253 2 1 1 1 0.84 -0.916455313 2.6604306 1
#> 254 2 1 1 1 3.93 -0.235784811 1.6721526 1
#> 255 2 1 1 1 2.46 -2.921699722 3.7239595 1
#> 256 2 1 1 1 1.33 -2.968881731 4.0577209 2
#> 257 2 1 1 1 0.61 0.019649852 2.0228751 1
#> 258 2 1 1 1 1.86 -1.601793347 2.8548225 1
#> 259 2 1 1 1 0.90 -1.264041920 2.9118939 1
#> 260 2 1 1 1 0.75 -0.164857680 2.0840192 1
#> 261 2 1 1 1 1.34 0.828689665 1.0927650 1
#> 262 2 1 1 1 0.90 0.083196626 1.8022991 1
#> 263 2 1 1 1 1.51 0.053873966 1.6638928 1
#> 264 2 1 1 1 1.05 0.115061798 1.7229397 1
#> 265 2 1 1 1 1.07 -1.174806161 2.7526584 1
#> 266 2 1 1 1 1.59 -1.865502067 3.1164962 1
#> 267 2 1 1 1 2.04 0.607872681 1.1787659 1
#> 268 2 1 1 1 1.52 -1.059778272 2.5172450 1
#> 269 2 1 1 1 1.10 -0.781243260 2.4249946 1
#> 270 2 1 1 1 5.29 -4.364453180 4.4651991 2
#> 271 2 1 1 1 7.22 -9.050435002 7.5334793 2
#> 272 2 1 1 1 1.38 -1.108819174 2.5916350 1
#> 273 2 1 1 1 2.02 -1.479269293 2.7340884 1
#> 274 2 1 1 1 1.46 -0.962780530 2.4572796 1
#> 275 2 1 1 1 4.96 -3.443724456 3.8508212 1
#> 276 2 1 1 1 1.29 -1.007964189 2.5395975 1
#> 277 2 1 1 1 2.03 -3.159555592 3.9824824 1
#> 278 2 1 1 1 1.72 -1.146023571 2.5390989 1
#> 279 2 1 1 1 1.18 -2.027149119 3.3837648 1
#> 280 2 1 1 1 3.36 0.599482353 1.1062153 1
#> 281 2 1 1 1 0.79 -0.474090775 2.3209172 1
#> 282 2 1 1 1 1.16 -1.080104402 2.6406522 1
#> 283 2 1 1 1 1.69 -1.302513296 2.6639310 1
#> 284 2 1 1 1 2.89 -5.178880071 5.2866415 2
#> 285 2 1 1 1 2.20 -5.458083995 5.6421769 2
#> 286 2 1 1 1 0.55 0.186762292 1.9266881 1
#> 287 2 1 1 1 1.44 -2.826266547 3.9023855 1
#> 288 2 1 2 0 1.72 -0.607036038 2.1310127 1
#> 289 2 1 1 1 0.68 -0.388653712 2.3230963 1
#> 290 2 1 1 1 1.75 -3.753191281 4.5033852 2
#> 291 2 1 1 1 7.67 -8.729619743 7.2904124 2
#> 292 2 1 1 1 4.82 -5.984267776 5.6176296 2
#> 293 2 1 1 1 1.26 -0.439951548 2.1027539 1
#> 294 2 1 1 1 2.82 -4.752873596 4.9918982 2
#> 295 2 1 1 1 3.21 -4.720831468 4.9081153 2
#> 296 2 1 1 1 2.13 -3.122979145 3.9332853 1
#> 297 2 1 1 1 1.94 -0.872044542 2.2941285 1
#> 298 2 1 1 1 0.94 -0.968147002 2.6468089 1
#> 299 2 1 1 1 1.10 -1.054527157 2.6436217 1
#> 300 2 1 1 1 2.89 -3.698326298 4.2210324 2
#> 301 2 1 1 1 2.21 -4.902594094 5.2296305 2
#> 302 2 1 1 1 1.70 -1.338027866 2.6887191 1
#> 303 2 1 1 1 2.79 -4.967827217 5.1523103 2
#> 304 2 1 1 1 3.06 -2.735581575 3.5080968 1
#> 305 2 1 1 1 2.09 -2.264122569 3.3048011 1
#> 306 2 1 1 1 3.58 -3.527592949 4.0163872 2
#> 307 2 1 1 1 1.20 -3.129440078 4.2465024 2
#> 308 2 1 1 1 2.94 0.479560308 1.2113850 1
#> 309 2 1 1 1 1.97 -1.853399423 3.0218711 1
#> 310 2 1 1 1 2.96 -4.365111790 4.6900835 2
#> 311 2 1 1 1 1.03 -2.105916516 3.5224677 1
#> 312 2 1 1 1 2.88 -5.091660503 5.2256074 2
#> 313 2 1 1 1 2.49 -2.577464796 3.4680313 1
#> 314 2 1 1 1 1.64 -0.949552083 2.4062592 1
#> 315 2 1 1 1 1.26 -2.248402285 3.5236452 1
#> 316 2 1 1 1 2.40 -3.381387077 4.0703847 2
#> 317 2 1 1 1 0.83 -1.413665686 3.0813604 1
#> 318 2 1 1 1 6.63 -8.059071042 6.9009924 2
#> 319 2 1 1 1 0.49 -1.669036489 3.6967103 1
#> 320 2 1 1 1 0.82 -0.312543825 2.1683004 1
#> 321 2 1 1 1 1.35 -2.304197818 3.5313624 1
#> 322 2 1 1 1 2.34 -2.937074581 3.7556197 1
#> 323 2 1 1 1 2.00 -2.297415609 3.3470792 1
#> 324 2 1 1 1 2.28 -0.148337383 1.7154671 1
#> 325 2 1 1 1 3.06 -0.620729806 1.9933392 1
#> 326 2 1 1 1 1.60 -0.700199034 2.2243594 1
#> 327 2 1 1 1 1.28 -0.147634693 1.8681073 1
#> 328 2 1 1 1 0.94 -0.305942952 2.1049817 1
#> 329 2 1 1 1 1.43 -0.057099920 1.7644283 1
#> 330 2 1 1 1 1.81 -0.451868441 1.9990630 1
#> 331 2 1 1 1 1.58 -1.995801297 3.2187855 1
#> 332 2 1 1 1 1.55 -1.168780104 2.5936648 1
#> 333 2 1 1 1 8.87 -6.123135291 5.4900140 2
#> 334 2 1 1 1 4.13 -7.825895443 6.9740898 2
#> 335 2 1 1 1 1.43 -1.933417960 3.2156140 1
#> 336 2 1 1 1 2.39 -3.760413935 4.3497298 2
#> 337 2 1 1 1 3.09 -2.407062927 3.2696348 1
#> 338 2 1 1 1 2.79 0.967006388 0.8677038 1
#> 339 2 1 1 1 0.89 -0.746014249 2.4905276 1
#> 340 2 1 1 1 2.26 -1.672819594 2.8395820 1
#> 341 2 1 1 1 1.12 -1.170050659 2.7278235 1
#> 342 2 1 1 1 1.82 -0.916715150 2.3473226 1
#> 343 2 1 1 1 2.01 -3.814299789 4.4747107 2
#> 344 2 1 1 1 0.98 -0.423485840 2.1839811 1
#> 345 2 1 1 1 6.98 -5.903500225 5.4209857 2
#> 346 2 1 1 1 1.08 -0.963879719 2.5791525 1
#> 347 2 1 1 1 1.44 -3.663490362 4.5493700 2
#> 348 2 1 1 1 2.79 -2.267436281 3.2027843 1
#> 349 2 1 1 1 0.89 0.133996964 1.7645029 1
#> 350 2 1 1 1 0.81 -1.889738468 3.4944535 1
#> 351 2 1 1 1 3.20 -2.950592066 3.6462971 1
#> 352 2 1 1 1 0.61 -0.986562778 2.9083986 1
#> 353 2 1 1 1 1.42 -2.236243172 3.4532588 1
#> 354 2 1 1 1 1.31 -3.380259950 4.3882032 2
#> 355 2 1 1 1 1.28 0.675100366 1.2229885 1
#> 356 2 1 1 1 3.03 -2.200115709 3.1276574 1
#> 357 2 1 1 1 2.07 -2.997197955 3.8528841 1
#> 358 2 1 1 1 0.50 -0.790152761 2.8726432 1
#> 359 2 1 1 1 3.33 -5.453923671 5.4131320 2
#> 360 2 1 1 1 1.13 -3.169000083 4.3170993 2
#> 361 2 1 1 1 1.85 0.022153228 1.6369162 1
#> 362 2 1 1 1 0.65 0.134951325 1.8916754 1
#> 363 2 1 1 1 2.68 -3.048592913 3.7822936 1
#> 364 2 1 1 1 1.42 -2.747105439 3.8487059 1
#> 365 2 1 1 1 1.26 -1.016972934 2.5561169 1
#> 366 2 1 1 1 2.19 -4.222569892 4.7327331 2
#> 367 2 1 1 1 2.68 -1.589028805 2.7248182 1
#> 368 2 1 1 1 2.44 -0.563327974 2.0038809 1
#> 369 2 1 1 1 2.70 -3.807017135 4.3285168 2
#> 370 2 1 1 1 1.11 -2.295342368 3.6310179 1
#> 371 2 1 1 1 2.48 -0.298434982 1.8066726 1
#> 372 2 1 1 1 6.06 -4.577667869 4.5673875 2
#> 373 2 1 1 1 1.54 -2.493836851 3.6119416 1
#> 374 2 1 1 1 2.27 -1.858748372 2.9749157 1
#> 375 2 1 1 1 1.28 -0.621795078 2.2399036 1
#> 376 2 1 1 1 1.27 -0.423933632 2.0874457 1
#> 377 2 1 1 1 1.64 -3.053978917 4.0080744 2
#> 378 2 1 1 1 2.14 -3.646204097 4.3183772 2
#> 379 2 1 1 1 1.57 -1.825455543 3.0912671 1
#> 380 2 1 1 1 2.31 -4.652351640 5.0209167 2
#> 381 2 1 1 1 1.07 -2.016198750 3.4283549 1
#> 382 2 1 1 1 1.64 -4.029760751 4.7508050 2
#> 383 2 1 1 1 6.35 -3.838191847 4.0499705 2
#> 384 2 1 1 1 2.37 -1.722115281 2.8601048 1
#> 385 2 1 1 1 9.92 -10.953903072 8.6629157 2
#> 386 2 1 1 1 1.72 -0.139110670 1.7767301 1
#> 387 2 1 1 1 2.16 0.784193447 1.0382490 1
#> 388 2 1 1 1 2.39 -2.172924979 3.1874280 1
#> 389 2 1 1 1 1.70 -2.123250893 3.2840076 1
#> 390 2 1 1 1 2.54 -2.011538027 3.0485845 1
#> 391 2 1 1 1 3.01 -1.386070039 2.5458740 1
#> 392 2 1 1 1 0.62 -0.086559792 2.1079935 1
#> 393 2 1 1 1 1.43 0.584569092 1.2681474 1
#> 394 2 1 1 1 1.76 -0.764637380 2.2431675 1
#> 395 2 1 1 1 1.49 -1.592373726 2.9344643 1
#> 396 2 1 1 1 0.98 -1.274706606 2.8761945 1
#> 397 2 1 1 1 5.99 -6.254308584 5.7152194 2
#> 398 2 1 1 1 0.77 -0.008184399 1.9399271 1
#> 399 2 1 1 1 0.87 1.149939489 0.9317042 1
#> 400 2 1 1 1 0.98 -0.667708548 2.3825832 1
#> 401 1 2 2 1 1.72 -2.373681443 3.4686014 1
#> 402 1 2 2 1 1.12 -1.025479809 2.6124517 1
#> 403 1 2 2 1 2.34 -1.889876389 2.9873631 1
#> 404 1 2 2 1 1.20 1.454283896 0.6221862 1
#> 405 1 2 2 1 3.26 -2.919793676 3.6179050 1
#> 406 1 2 2 1 2.58 -3.478051641 4.1095444 2
#> 407 1 2 2 1 4.22 -1.410464275 2.4808545 1
#> 408 1 2 2 1 2.23 0.219113034 1.4496187 1
#> 409 1 2 1 0 3.02 -0.597765332 1.9797458 1
#> 410 1 2 2 1 1.79 -2.630486715 3.6445208 1
#> 411 1 2 2 1 4.28 -4.318294627 4.5068758 2
#> 412 1 2 2 1 8.61 -0.762474977 1.9154369 1
#> 413 1 2 2 1 11.61 -5.839543353 5.2248273 2
#> 414 1 2 2 1 3.34 -3.572503280 4.0737801 2
#> 415 1 2 2 1 1.02 0.476771024 1.4400670 1
#> 416 1 2 2 1 6.48 -0.876176237 2.0326243 1
#> 417 1 2 2 1 2.37 -1.242320926 2.5085380 1
#> 418 1 2 2 1 4.21 -1.903825571 2.8260711 1
#> 419 1 2 2 1 6.93 -1.264154331 2.2848193 1
#> 420 1 2 2 1 1.55 -1.478236614 2.8307366 1
#> 421 1 2 2 1 2.36 -1.355431768 2.5926971 1
#> 422 1 2 2 1 2.43 -0.502758705 1.9606019 1
#> 423 1 2 2 1 3.94 -2.217372218 3.0629192 1
#> 424 1 2 2 1 3.84 -1.374543966 2.4771309 1
#> 425 1 2 2 1 4.81 -5.831685893 5.5128967 2
#> 426 1 2 2 1 1.20 1.033596127 0.9548208 1
#> 427 1 2 2 1 1.02 0.246780507 1.6260176 1
#> 428 1 2 1 0 1.29 0.364405438 1.4645659 1
#> 429 1 2 2 1 4.45 -2.232655849 3.0413668 1
#> 430 1 2 2 1 6.52 -1.833334575 2.6815137 1
#> 431 1 2 2 1 3.54 -1.914668647 2.8787635 1
#> 432 1 2 2 1 5.45 -1.386615507 2.4112692 1
#> 433 1 2 2 1 0.88 -1.069338528 2.7631268 1
#> 434 1 2 2 1 5.09 -1.542063525 2.5318995 1
#> 435 1 2 2 1 2.03 -3.170379639 3.9905351 1
#> 436 1 2 2 1 0.68 -0.645019974 2.5442411 1
#> 437 1 2 2 1 9.94 -2.794593112 3.2462056 1
#> 438 1 2 1 0 1.26 -0.582885979 2.2150568 1
#> 439 1 2 2 1 3.91 -1.272647952 2.4013775 1
#> 440 1 2 2 1 0.97 0.431032395 1.4922250 1
#> 441 1 2 1 0 1.29 -1.042980404 2.5670271 1
#> 442 1 2 2 1 1.80 -2.313328207 3.4030243 1
#> 443 1 2 2 1 0.99 -0.746514272 2.4421680 1
#> 444 1 2 2 1 1.32 -1.388909313 2.8280519 1
#> 445 1 2 2 1 2.83 0.545213350 1.1700129 1
#> 446 1 2 2 1 6.48 -5.677854528 5.2938318 2
#> 447 1 2 0 0 15.11 -13.987756596 10.4696057 1
#> 448 1 2 2 1 1.51 0.935270931 0.9866006 1
#> 449 1 2 2 1 1.77 -1.921812590 3.1148101 1
#> 450 1 2 2 1 3.98 -1.656451606 2.6666620 1
#> 451 1 2 1 0 1.85 1.266559843 0.7021356 1
#> 452 1 2 2 1 1.82 -1.203993668 2.5634992 1
#> 453 1 2 2 1 11.29 -4.351823302 4.2506457 2
#> 454 1 2 2 1 7.07 -3.599067049 3.8593552 1
#> 455 1 2 2 1 1.40 -0.080081602 1.7883310 1
#> 456 1 2 2 1 4.05 -1.582020728 2.6103054 1
#> 457 1 2 2 1 0.87 0.391489247 1.5596412 1
#> 458 1 2 2 1 2.74 -0.720488242 2.0902534 1
#> 459 1 2 2 1 5.14 -2.393491600 3.1165854 1
#> 460 1 2 2 1 2.67 0.184771679 1.4403552 1
#> 461 1 2 2 1 2.38 -1.303105857 2.5518238 1
#> 462 1 2 2 1 2.84 -2.532651867 3.3880706 1
#> 463 1 2 2 1 3.78 -4.442954503 4.6417544 2
#> 464 1 2 1 0 2.81 1.158204708 0.7288394 1
#> 465 1 2 2 1 1.63 -1.543737913 2.8609216 1
#> 466 1 2 2 1 4.43 -3.444411787 3.8860444 1
#> 467 1 2 2 1 2.39 -2.613757171 3.5101893 1
#> 468 1 2 2 1 1.04 -0.413400761 2.1521713 1
#> 469 1 2 2 1 1.27 -0.749185779 2.3427362 1
#> 470 1 2 2 1 1.05 -0.885417465 2.5285213 1
#> 471 1 2 2 1 2.28 -0.175596049 1.7355146 1
#> 472 1 2 2 1 5.63 -7.268116523 6.4341594 2
#> 473 1 2 2 1 2.04 -1.214173284 2.5336240 1
#> 474 1 2 2 1 3.05 -3.500572698 4.0572996 2
#> 475 1 2 2 1 3.65 -0.684036944 2.0014789 1
#> 476 1 2 2 1 7.24 -1.929671821 2.7267798 1
#> 477 1 2 2 1 3.77 -1.374649268 2.4814992 1
#> 478 1 2 2 1 2.91 -1.866608335 2.9006000 1
#> 479 1 2 2 1 4.00 -2.624841190 3.3445545 1
#> 480 1 2 0 0 15.11 -11.583714281 8.9030774 1
#> 481 1 2 2 1 11.70 -3.383990822 3.6052753 1
#> 482 1 2 2 1 4.12 -2.201915138 3.0400450 1
#> 483 1 2 2 1 14.03 -9.267505714 7.4178747 2
#> 484 1 2 2 1 2.78 -2.560134788 3.4153595 1
#> 485 1 2 2 1 2.44 -3.089320259 3.8497348 1
#> 486 1 2 2 1 2.15 -1.606873524 2.8076401 1
#> 487 1 2 2 1 1.40 0.088682693 1.6574692 1
#> 488 1 2 2 1 4.38 -6.381250409 5.9356700 2
#> 489 1 2 2 1 2.16 -0.413394577 1.9236817 1
#> 490 1 2 2 1 1.04 1.394078244 0.6948294 1
#> 491 1 2 2 1 7.61 -8.319792563 7.0180057 2
#> 492 1 2 2 1 2.63 -0.721268905 2.1006697 1
#> 493 1 2 2 1 2.20 -2.298802284 3.3105856 1
#> 494 1 2 0 0 15.11 -7.521232885 6.2558728 1
#> 495 1 2 2 1 1.15 -0.571013343 2.2395984 1
#> 496 1 2 2 1 2.01 -2.099877363 3.1979548 1
#> 497 1 2 2 1 2.15 -1.686343516 2.8664230 1
#> 498 1 2 1 0 1.89 -0.867709897 2.2987984 1
#> 499 1 2 2 1 2.01 -0.449682687 1.9690302 1
#> 500 1 2 2 1 8.37 -4.798699412 4.6215943 2
#> 501 1 2 2 1 2.89 -1.322726294 2.5112255 1
#> 502 1 2 2 1 5.02 0.592014015 1.0619124 1
#> 503 1 2 2 1 3.32 -2.762130436 3.4995002 1
#> 504 1 2 2 1 2.02 -1.555375756 2.7907373 1
#> 505 1 2 2 1 11.52 0.093056683 1.3162076 1
#> 506 1 2 2 1 11.28 -9.716372042 7.7904512 2
#> 507 1 2 2 1 2.38 -0.309400301 1.8239810 1
#> 508 1 2 2 1 3.42 -0.371709908 1.7931192 1
#> 509 1 2 2 1 6.80 -0.773097480 1.9553934 1
#> 510 1 2 2 1 2.30 1.014682026 0.8588910 1
#> 511 1 2 2 1 9.41 -5.011061164 4.7317405 2
#> 512 1 2 2 1 2.77 -0.782192434 2.1322483 1
#> 513 1 2 2 1 6.45 -4.155821874 4.2614334 2
#> 514 1 2 2 1 2.90 -1.715878224 2.7931822 1
#> 515 1 2 2 1 3.73 -1.528966533 2.5927981 1
#> 516 1 2 2 1 2.14 -3.076666977 3.8969038 1
#> 517 1 2 2 1 1.72 0.028614873 1.6497392 1
#> 518 1 2 2 1 5.75 -4.270192903 4.3738344 2
#> 519 1 2 2 1 4.36 -0.469441443 1.8178548 1
#> 520 1 2 2 1 3.18 -3.679427676 4.1688480 2
#> 521 1 2 2 1 9.48 -2.430835740 3.0131476 1
#> 522 1 2 2 1 2.09 -0.285659372 1.8372241 1
#> 523 1 2 2 1 5.40 -3.309025557 3.7335085 1
#> 524 1 2 1 0 1.64 0.392875238 1.3844511 1
#> 525 1 2 2 1 2.62 -3.047916661 3.7907159 1
#> 526 1 2 2 1 6.28 -4.260306062 4.3402883 2
#> 527 1 2 1 0 0.77 -0.764191624 2.5782534 1
#> 528 1 2 2 1 3.01 -1.395268643 2.5524716 1
#> 529 1 2 2 1 4.28 -0.788123741 2.0434406 1
#> 530 1 2 2 1 7.17 -3.945104483 4.0894578 2
#> 531 1 2 2 1 1.49 -0.641522411 2.2026532 1
#> 532 1 2 2 1 5.21 -4.509240644 4.5699229 2
#> 533 1 2 2 1 1.39 0.947816135 0.9926797 1
#> 534 1 2 2 1 8.10 -6.104813268 5.5066955 2
#> 535 1 2 2 1 0.86 -0.040777273 1.9220685 1
#> 536 1 2 2 1 2.46 -1.128817754 2.4148169 1
#> 537 1 2 1 0 8.23 -1.473917078 2.3981645 1
#> 538 1 2 1 0 3.87 0.325324080 1.2803112 1
#> 539 1 2 2 1 1.42 0.551897303 1.2950216 1
#> 540 1 2 2 1 2.14 -0.939446522 2.3153008 1
#> 541 1 2 2 1 10.23 -8.883017258 7.2765204 2
#> 542 1 2 2 1 3.93 -2.551260074 3.2980683 1
#> 543 1 2 1 0 0.49 0.675369419 1.5392560 1
#> 544 1 2 2 1 1.08 -0.770387688 2.4239660 1
#> 545 1 2 2 1 4.59 -3.002485303 3.5680408 1
#> 546 1 2 2 1 0.85 -0.223937198 2.0788987 1
#> 547 1 2 2 1 10.41 -3.713566068 3.8463107 1
#> 548 1 2 2 1 5.15 -0.856026633 2.0567978 1
#> 549 1 2 2 1 1.92 -1.087231460 2.4582704 1
#> 550 1 2 2 1 0.94 -0.432292174 2.2083629 1
#> 551 1 2 1 0 2.24 -0.817788887 2.2126307 1
#> 552 1 2 2 1 2.35 -1.547637309 2.7349340 1
#> 553 1 2 2 1 1.17 -0.728085726 2.3576667 1
#> 554 1 2 2 1 2.13 -0.946980247 2.3222356 1
#> 555 1 2 2 1 2.05 -1.055820585 2.4143790 1
#> 556 1 2 2 1 2.87 -3.877662918 4.3530752 2
#> 557 1 2 2 1 1.71 -0.461287555 2.0223479 1
#> 558 1 2 2 1 2.58 -1.447439346 2.6332890 1
#> 559 1 2 2 1 4.28 -4.593433384 4.6988740 2
#> 560 1 2 2 1 9.17 -5.318243612 4.9433517 2
#> 561 1 2 2 1 1.77 -1.675317902 2.9287647 1
#> 562 1 2 2 1 2.67 -1.582433295 2.7211486 1
#> 563 1 2 1 0 3.68 1.794686391 0.2505938 1
#> 564 1 2 2 1 2.05 -1.838277102 2.9959187 1
#> 565 1 2 2 1 0.97 -1.147327670 2.7776770 1
#> 566 1 2 2 1 4.51 -2.751716130 3.3988122 1
#> 567 1 2 2 1 4.68 -0.971161923 2.1538176 1
#> 568 1 2 2 1 3.33 -1.766832110 2.7905665 1
#> 569 1 2 2 1 3.09 0.966721840 0.8551419 1
#> 570 1 2 2 1 5.29 -2.695546295 3.3173412 1
#> 571 1 2 2 1 9.88 -8.438171817 6.9944079 2
#> 572 1 2 2 1 2.87 -0.482710201 1.9081377 1
#> 573 1 2 2 1 2.93 -3.245947627 3.8901347 1
#> 574 1 2 2 1 1.13 -1.737362149 3.1759896 1
#> 575 1 2 2 1 4.19 0.167009551 1.3799590 1
#> 576 1 2 2 1 10.22 -5.713622702 5.1759944 2
#> 577 1 2 2 1 2.73 -2.634376113 3.4754867 1
#> 578 1 2 2 1 3.86 0.342200810 1.2688106 1
#> 579 1 2 1 0 1.12 -0.259973011 2.0015547 1
#> 580 1 2 2 1 3.94 -4.418104480 4.6079698 2
#> 581 1 2 2 1 5.06 -3.272081185 3.7264982 1
#> 582 1 2 2 1 1.90 -2.156296730 3.2624334 1
#> 583 1 2 1 0 1.56 1.116418938 0.8419212 1
#> 584 1 2 2 1 7.16 -5.388325270 5.0643927 2
#> 585 1 2 1 0 0.92 0.326433128 1.5946323 1
#> 586 1 2 2 1 2.35 -1.565574540 2.7480880 1
#> 587 1 2 2 1 3.49 -2.453293799 3.2643408 1
#> 588 1 2 2 1 1.69 1.011020098 0.9088607 1
#> 589 1 2 2 1 2.59 0.147207371 1.4732524 1
#> 590 1 2 2 1 6.21 -5.480756224 5.1746431 2
#> 591 1 2 2 1 3.38 -4.198534321 4.5140657 2
#> 592 1 2 2 1 3.16 -1.675871111 2.7401262 1
#> 593 1 2 2 1 1.40 0.921245583 1.0118903 1
#> 594 1 2 2 1 1.42 -1.523513046 2.9015504 1
#> 595 1 2 2 1 0.61 -0.333192737 2.3333963 1
#> 596 1 2 2 1 1.65 -0.174553734 1.8147048 1
#> 597 1 2 2 1 2.67 -0.430262909 1.8861056 1
#> 598 1 2 2 1 3.35 -1.137965364 2.3418453 1
#> 599 1 2 2 1 5.54 -5.195877585 5.0203173 2
#> 600 1 2 2 1 1.99 0.365544273 1.3639303 1
#> 601 2 2 2 1 2.23 -2.681900217 3.5877749 1
#> 602 2 2 2 1 1.70 -0.628450066 2.1507784 1
#> 603 2 2 2 1 1.31 -1.916201052 3.2435754 1
#> 604 2 2 2 1 1.26 -0.462908383 2.1207910 1
#> 605 2 2 2 1 1.93 -1.183575897 2.5286632 1
#> 606 2 2 2 1 1.46 -3.368126068 4.3130003 2
#> 607 2 2 2 1 2.07 -2.436906613 3.4368711 1
#> 608 2 2 2 1 1.33 -3.867225934 4.7587294 2
#> 609 2 2 2 1 1.29 -0.324396575 2.0041318 1
#> 610 2 2 2 1 1.65 -1.087828695 2.5093818 1
#> 611 2 2 2 1 2.49 -1.142522135 2.4214282 1
#> 612 2 2 2 1 3.06 -3.374433746 3.9656731 1
#> 613 2 2 2 1 3.27 -1.376968958 2.5178515 1
#> 614 2 2 2 1 1.87 -2.527018405 3.5470833 1
#> 615 2 2 2 1 3.55 -1.593620920 2.6507970 1
#> 616 2 2 2 1 4.98 -3.138419955 3.6387984 1
#> 617 2 2 2 1 3.33 -2.969469027 3.6459817 1
#> 618 2 2 2 1 1.95 -2.013489085 3.1452915 1
#> 619 2 2 2 1 1.06 -1.515396376 3.0309393 1
#> 620 2 2 2 1 1.69 -1.611417028 2.8982685 1
#> 621 2 2 2 1 2.36 -4.318907256 4.7650373 2
#> 622 2 2 2 1 1.91 -2.000923264 3.1439854 1
#> 623 2 2 2 1 2.66 -2.500249803 3.3876811 1
#> 624 2 2 2 1 1.62 0.567966630 1.2537479 1
#> 625 2 2 1 0 1.28 0.751519147 1.1630674 1
#> 626 2 2 2 1 2.99 -1.044955127 2.3028502 1
#> 627 2 2 2 1 2.20 -1.270551088 2.5517227 1
#> 628 2 2 2 1 1.18 -1.328744974 2.8303143 1
#> 629 2 2 2 1 2.61 -3.072397523 3.8100112 1
#> 630 2 2 2 1 1.76 -4.179069995 4.8218498 2
#> 631 2 2 2 1 1.89 -1.595580302 2.8443278 1
#> 632 2 2 2 1 1.52 -0.065928300 1.7541310 1
#> 633 2 2 2 1 3.36 -1.780665198 2.7979522 1
#> 634 2 2 2 1 1.32 -2.760648829 3.8994786 1
#> 635 2 2 2 1 1.90 -1.932916403 3.0951056 1
#> 636 2 2 2 1 3.59 -6.800090402 6.3292279 2
#> 637 2 2 2 1 1.89 -0.234354837 1.8241070 1
#> 638 2 2 2 1 1.73 -2.043155696 3.2159143 1
#> 639 2 2 2 1 4.31 -2.996287614 3.5822549 1
#> 640 2 2 2 1 2.41 -0.532878673 1.9846199 1
#> 641 2 2 2 1 2.25 0.479513530 1.2560834 1
#> 642 2 2 2 1 0.90 -0.136845927 1.9835276 1
#> 643 2 2 2 1 3.98 -4.155694354 4.4199673 2
#> 644 2 2 1 0 0.71 1.138807713 0.9933179 1
#> 645 2 2 2 1 2.73 -4.095563579 4.5324005 2
#> 646 2 2 2 1 2.74 -5.444103399 5.5058593 2
#> 647 2 2 2 1 1.84 -0.023026272 1.6721658 1
#> 648 2 2 2 1 0.53 0.309320952 1.8350568 1
#> 649 2 2 2 1 0.79 -2.279743410 3.8390589 1
#> 650 2 2 2 1 1.57 -2.253248178 3.4185101 1
#> 651 2 2 2 1 0.95 -1.845852550 3.3587245 1
#> 652 2 2 2 1 4.12 -3.198468983 3.7373845 1
#> 653 2 2 2 1 1.02 -1.411375789 2.9666609 1
#> 654 2 2 2 1 2.71 -1.931703337 2.9695515 1
#> 655 2 2 2 1 1.13 -1.125686497 2.6884438 1
#> 656 2 2 2 1 0.58 -1.587264766 3.4765881 1
#> 657 2 2 2 1 7.32 -6.426620743 5.7576174 2
#> 658 2 2 2 1 6.03 -8.671405122 7.3614174 2
#> 659 2 2 2 1 2.81 -4.849182311 5.0631171 2
#> 660 2 2 2 1 2.78 -1.866221319 2.9142363 1
#> 661 2 2 2 1 1.29 -0.897265743 2.4528830 1
#> 662 2 2 2 1 1.02 -1.033462308 2.6611124 1
#> 663 2 2 2 1 0.88 -1.211133617 2.8803141 1
#> 664 2 2 2 1 2.30 -0.269485679 1.8025488 1
#> 665 2 2 2 1 1.77 -0.735972396 2.2197799 1
#> 666 2 2 2 1 0.83 -0.914028314 2.6646217 1
#> 667 2 2 2 1 1.93 -4.656868641 5.1261452 2
#> 668 2 2 2 1 0.88 -2.312520224 3.7905611 1
#> 669 2 2 2 1 3.31 -4.385033435 4.6554048 2
#> 670 2 2 2 1 0.96 0.551028951 1.3975413 1
#> 671 2 2 2 1 1.69 -1.314557997 2.6730682 1
#> 672 2 2 2 1 0.90 -1.088540103 2.7673494 1
#> 673 2 2 2 1 1.33 0.726224409 1.1743042 1
#> 674 2 2 2 1 2.11 -1.265409970 2.5609636 1
#> 675 2 2 2 1 2.72 -0.584640055 1.9937036 1
#> 676 2 2 2 1 2.30 0.461356698 1.2654966 1
#> 677 2 2 2 1 3.47 -6.437517072 6.0906989 2
#> 678 2 2 2 1 0.99 -0.403279286 2.1634613 1
#> 679 2 2 2 1 0.72 -0.409925569 2.3120773 1
#> 680 2 2 2 1 1.36 0.341573883 1.4687185 1
#> 681 2 2 2 1 0.70 0.364138458 1.6620934 1
#> 682 2 2 2 1 2.56 -1.773934434 2.8731105 1
#> 683 2 2 2 1 2.06 -1.116996425 2.4583402 1
#> 684 2 2 2 1 2.13 -2.259528494 3.2940102 1
#> 685 2 2 2 1 4.21 -3.000735650 3.5924303 1
#> 686 2 2 2 1 2.38 -3.143637391 3.8999271 1
#> 687 2 2 2 1 1.61 0.321085447 1.4433627 1
#> 688 2 2 2 1 1.37 -2.181042693 3.4281120 1
#> 689 2 2 2 1 1.31 -1.220101155 2.6993518 1
#> 690 2 2 2 1 1.52 -0.610711341 2.1724351 1
#> 691 2 2 2 1 1.47 -0.785617018 2.3182244 1
#> 692 2 2 2 1 2.33 -3.148921325 3.9128773 1
#> 693 2 2 2 1 0.78 0.126700877 1.8208569 1
#> 694 2 2 2 1 5.17 -4.951053117 4.8768692 2
#> 695 2 2 2 1 1.35 1.051731282 0.9174781 1
#> 696 2 2 2 1 1.51 -0.958113821 2.4415349 1
#> 697 2 2 2 1 1.52 0.230382918 1.5266125 1
#> 698 2 2 2 1 1.50 -1.717454608 3.0278681 1
#> 699 2 2 2 1 1.10 -0.298571950 2.0388576 1
#> 700 2 2 2 1 2.60 -3.424952964 4.0676712 2
#> 701 2 2 2 1 2.89 -1.416504602 2.5787212 1
#> 702 2 2 2 1 3.69 -3.403565757 3.9180740 1
#> 703 2 2 1 0 0.65 0.805070410 1.3088862 1
#> 704 2 2 2 1 4.80 -2.448358318 3.1716430 1
#> 705 2 2 2 1 1.85 -2.067086599 3.2063234 1
#> 706 2 2 2 1 1.40 -3.988393370 4.8188813 2
#> 707 2 2 2 1 3.49 0.034625201 1.5013390 1
#> 708 2 2 2 1 2.41 -3.360087949 4.0529789 2
#> 709 2 2 2 1 2.41 -4.875967269 5.1619816 2
#> 710 2 2 2 1 2.46 -1.032928909 2.3448000 1
#> 711 2 2 2 1 2.21 -3.048150575 3.8616341 1
#> 712 2 2 2 1 1.68 -3.831418306 4.5858079 2
#> 713 2 2 2 1 1.83 -1.738015580 2.9632587 1
#> 714 2 2 2 1 6.35 -9.727395358 8.0546288 2
#> 715 2 2 2 1 2.62 -2.395572179 3.3171215 1
#> 716 2 2 2 1 3.54 -6.421738893 6.0690156 2
#> 717 2 2 2 1 0.74 0.009601181 1.9418390 1
#> 718 2 2 2 1 1.12 -0.865082398 2.4844498 1
#> 719 2 2 2 1 2.90 -2.733031491 3.5250472 1
#> 720 2 2 2 1 1.13 -0.057584675 1.8370963 1
#> 721 2 2 2 1 1.06 -1.681450210 3.1644671 1
#> 722 2 2 2 1 0.74 -0.034165144 1.9790404 1
#> 723 2 2 2 1 1.23 -1.624485108 3.0447610 1
#> 724 2 2 2 1 0.61 0.022845531 2.0200627 1
#> 725 2 2 2 1 1.08 -1.246097624 2.8054998 1
#> 726 2 2 2 1 1.19 -0.919236226 2.5023312 1
#> 727 2 2 2 1 3.09 -3.935774488 4.3636771 2
#> 728 2 2 2 1 0.99 -0.866746596 2.5397966 1
#> 729 2 2 2 1 1.09 -0.041665834 1.8363973 1
#> 730 2 2 2 1 1.59 -0.381809220 1.9831827 1
#> 731 2 2 2 1 1.96 -3.025069208 3.8986005 1
#> 732 2 2 2 1 2.97 -4.029527961 4.4475966 2
#> 733 2 2 2 1 1.54 -1.666648560 2.9777639 1
#> 734 2 2 2 1 1.67 -2.340766188 3.4569388 1
#> 735 2 2 2 1 1.45 -2.147467647 3.3745275 1
#> 736 2 2 2 1 1.67 -1.871817580 3.1007173 1
#> 737 2 2 2 1 1.80 -0.612656054 2.1217498 1
#> 738 2 2 2 1 3.87 -3.543865823 4.0003720 2
#> 739 2 2 2 1 1.59 -1.054389056 2.4969304 1
#> 740 2 2 2 1 0.98 -0.945399180 2.6084014 1
#> 741 2 2 2 1 2.32 -1.445218986 2.6638185 1
#> 742 2 2 2 1 4.02 -2.280499449 3.1017107 1
#> 743 2 2 2 1 3.30 -3.183110513 3.8011591 1
#> 744 2 2 2 1 0.88 -0.490922037 2.2850914 1
#> 745 2 2 2 1 2.81 -0.232277260 1.7320601 1
#> 746 2 2 2 1 0.76 0.320040739 1.6677359 1
#> 747 2 2 2 1 2.88 -0.617945243 2.0047470 1
#> 748 2 2 2 1 3.28 -0.797441834 2.1043650 1
#> 749 2 2 2 1 3.37 -1.574660718 2.6507551 1
#> 750 2 2 2 1 3.05 -1.865788056 2.8860671 1
#> 751 2 2 2 1 1.62 -0.595730723 2.1407430 1
#> 752 2 2 2 1 0.91 -0.646263850 2.3980392 1
#> 753 2 2 2 1 2.71 -2.986640281 3.7331116 1
#> 754 2 2 2 1 1.95 -4.088249116 4.6952263 2
#> 755 2 2 2 1 0.60 -0.327666326 2.3378060 1
#> 756 2 2 2 1 3.39 -2.212201938 3.1020372 1
#> 757 2 2 2 1 2.12 -1.704092587 2.8844132 1
#> 758 2 2 2 1 1.57 0.402580290 1.3869150 1
#> 759 2 2 2 1 2.10 0.736040305 1.0785481 1
#> 760 2 2 2 1 1.67 -1.753913183 3.0111551 1
#> 761 2 2 2 1 0.82 -1.158861937 2.8755703 1
#> 762 2 2 2 1 0.76 -1.442725986 3.1593591 1
#> 763 2 2 2 1 1.76 -3.459888216 4.2787021 2
#> 764 2 2 2 1 2.70 -5.256169646 5.3777536 2
#> 765 2 2 2 1 2.59 -2.501165468 3.3979437 1
#> 766 2 2 2 1 2.37 -2.235303658 3.2361408 1
#> 767 2 2 2 1 1.63 -3.127728363 4.0674320 2
#> 768 2 2 2 1 5.79 -5.470308317 5.1923726 2
#> 769 2 2 2 1 1.59 -2.508053238 3.6073065 1
#> 770 2 2 2 1 1.88 -1.495891311 2.7714974 1
#> 771 2 2 2 1 1.81 -3.263413252 4.1159983 2
#> 772 2 2 2 1 4.03 -6.172459794 5.8288547 2
#> 773 2 2 2 1 3.49 -1.123215911 2.3218142 1
#> 774 2 2 2 1 3.57 -3.544355345 4.0292520 2
#> 775 2 2 2 1 1.10 -1.145038977 2.7160312 1
#> 776 2 2 2 1 1.96 -3.766900559 4.4524868 2
#> 777 2 2 2 1 1.06 0.713992361 1.2382339 1
#> 778 2 2 2 1 4.97 -6.416531658 5.9033266 2
#> 779 2 2 2 1 3.19 -0.174776659 1.6660795 1
#> 780 2 2 2 1 3.09 -0.552598113 1.9424630 1
#> 781 2 2 2 1 0.97 -2.234737898 3.6632884 1
#> 782 2 2 2 1 2.06 0.685178100 1.1195820 1
#> 783 2 2 2 1 6.50 -10.352532121 8.4671296 2
#> 784 2 2 2 1 1.28 -2.269594164 3.5319674 1
#> 785 2 2 2 1 1.92 -0.957750601 2.3613863 1
#> 786 2 2 2 1 3.37 -6.515067441 6.1614093 2
#> 787 2 2 2 1 1.11 0.139489590 1.6855691 1
#> 788 2 2 2 1 1.18 -0.801080593 2.4121667 1
#> 789 2 2 2 1 0.92 -1.903813627 3.4253594 1
#> 790 2 2 2 1 8.65 -5.584788024 5.1380599 2
#> 791 2 2 2 1 0.87 -0.951533558 2.6715582 1
#> 792 2 2 2 1 1.66 0.024092845 1.6620708 1
#> 793 2 2 2 1 1.59 0.557401678 1.2657699 1
#> 794 2 2 2 1 1.35 -2.038174846 3.3241610 1
#> 795 2 2 2 1 2.31 0.271629180 1.4040827 1
#> 796 2 2 2 1 1.64 -0.341189968 1.9431955 1
#> 797 2 2 2 1 2.24 0.195846604 1.4658680 1
#> 798 2 2 2 1 0.92 -0.833661841 2.5469114 1
#> 799 2 2 2 1 1.41 -0.638347478 2.2187763 1
#> 800 2 2 2 1 2.85 -0.928666780 2.2310151 1
#>
#> $gamma
#> $gamma$condition
#> # A tibble: 2 × 2
#> correct Gamma
#> <dbl> <dbl>
#> 1 0 -1
#> 2 1 0.0134
#>
#> $gamma$rt
#> # A tibble: 2 × 2
#> correct Gamma
#> <dbl> <dbl>
#> 1 0 0.3
#> 2 1 0.622
#>
#> $gamma$correct
#> # A tibble: 2 × 2
#> condition Gamma
#> <int> <dbl>
#> 1 1 0.818
#> 2 2 1
#>
#> $gamma$rt_bycondition
#> # A tibble: 2 × 2
#> condition Gamma
#> <int> <dbl>
#> 1 1 0.690
#> 2 2 0.616
#>
#> $gamma$rt_byconditionbycorrect
#> # A tibble: 4 × 3
#> # Groups: condition [2]
#> condition correct Gamma
#> <int> <dbl> <dbl>
#> 1 1 0 0.222
#> 2 1 1 0.747
#> 3 2 0 NaN
#> 4 2 1 0.612
#>
#>
# }