DDM for All Control Data

Parse all control data to a single CSV, then check if subject data can fit a hierarchical drift decision model for different stimuli types

Experimental stimuli are as follows:

  • Condition 1: Same stimuli (see cat / hear cat) -- SS
  • Condition 2: Phonologically congruent (see cat / hear hat) -- CP
  • Condition 3: Semantically congruent (see cat / hear dog) -- CS
  • Condition 4: Unrelated stimuli (see house / hear cat) -- US

Parse all subject data to single csv

Generate a single csv for all data, using subject_idx as a unique patient identifier. Also give conditions (stim) a 2-character descriptive instead of a number.

CSV fields are as follows:

  • subj_idx: Unique subject identifier
  • rt: Reaction time
  • stim: Stimulus (SS/CP/CS/US)
  • response: Response to stimulus (True(1)/False(0))

In [1]:
def parse_condition(stim_num):
    if stim_num == '1':
        return 'SS'
    if stim_num == '2':
        return 'CP'
    if stim_num == '3':
        return 'CS'
    if stim_num == '4':
        return 'US'

In [2]:
import csv
import glob 


csv_dir = '../data/pilot_subjects/'
subjects = []

for csv_file in glob.glob(csv_dir + 'data*.csv'):
    subject = []
    subj_idx = csv_file[-9:-4]  # Use id from filename
    with open(csv_file, 'r') as f:
        reader = csv.DictReader(f)
        for trial in reader:
            trial['subj_idx'] = subj_idx
            trial['stim'] = parse_condition(trial['stim'])
            subject.append(trial)
    subjects.append(subject)
    
keys = subject[0].keys()

with open('../data/controls.csv', 'w') as out:
        writer = csv.DictWriter(out, keys)
        writer.writeheader()
        for subj in subjects:
            writer.writerows(subj)

First stab at hddm model fit


In [57]:
import hddm

data = hddm.load_csv('../data/all_subjects_clean.csv')

model = hddm.HDDM(data, depends_on={'v': 'stim'})
model.find_starting_values()
model.sample(6000, burn=20)


/Users/celefthe/anaconda/envs/lang-dec/lib/python3.5/site-packages/scipy/optimize/optimize.py:1850: RuntimeWarning: invalid value encountered in double_scalars
  tmp2 = (x - v) * (fx - fw)
/Users/celefthe/anaconda/envs/lang-dec/lib/python3.5/site-packages/scipy/optimize/optimize.py:1851: RuntimeWarning: invalid value encountered in double_scalars
  p = (x - v) * tmp2 - (x - w) * tmp1
/Users/celefthe/anaconda/envs/lang-dec/lib/python3.5/site-packages/pymc/Node.py:403: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
  self.__name__ = input['__name__']
 [-----------------100%-----------------] 6000 of 6000 complete in 262.5 sec
/Users/celefthe/anaconda/envs/lang-dec/lib/python3.5/site-packages/numpy/core/fromnumeric.py:224: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
  return reshape(newshape, order=order)
Out[57]:
<pymc.MCMC.MCMC at 0x11d3a6eb8>

In [4]:
model.print_stats()


/Users/celefthe/anaconda/envs/lang-dec/lib/python3.5/site-packages/numpy/core/fromnumeric.py:224: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
  return reshape(newshape, order=order)
                       mean        std       2.5q        25q        50q        75q      97.5q       mc err
a                   2.39576   0.152745    2.11016    2.29443    2.38941    2.49211    2.70333   0.00293055
a_std              0.569545   0.131783   0.370306   0.476155   0.552084   0.638271   0.876005   0.00298082
a_subj.17991        3.52977   0.241075    3.07717    3.36491    3.52228    3.68512    4.02475   0.00614853
a_subj.18288        2.38022   0.166946    2.07213     2.2667    2.37259     2.4832    2.72905    0.0044411
a_subj.18325        2.78442   0.257057    2.34213    2.60079    2.76479    2.94589    3.33576   0.00919474
a_subj.18333        2.28053   0.158222    1.98841    2.16915    2.27378    2.38402    2.60762   0.00441611
a_subj.18334        2.41955   0.240204    2.01519    2.25344     2.4054    2.56443    2.94104    0.0108646
a_subj.18350        1.62973   0.126326    1.40939    1.54025    1.62021    1.71136    1.89883   0.00414609
a_subj.18547        1.74868    0.11504    1.54181    1.66815     1.7398    1.82082    1.99447   0.00356107
a_subj.18619        2.59714   0.208432    2.21818    2.45366    2.58706    2.72622    3.03906   0.00655081
a_subj.18864        2.03522   0.152122    1.75923    1.92989    2.02427    2.13155    2.35875    0.0037835
a_subj.18919        2.35172   0.172002    2.02855    2.23207    2.34584     2.4655    2.70489   0.00508694
a_subj.18977        3.22412    0.20251    2.83277    3.08795    3.22097    3.35817    3.62853   0.00499172
a_subj.18978        2.20726   0.161037    1.92335    2.09558     2.1987    2.30881     2.5533   0.00525424
a_subj.18979        2.27812   0.189622    1.93533    2.14561    2.26924    2.40328    2.66544   0.00686928
a_subj.18988        2.65009   0.182688    2.30851     2.5228     2.6441    2.76728    3.02325   0.00460464
a_subj.19686        1.80616    0.13336     1.5714     1.7129    1.79831    1.89002    2.09735   0.00366935
a_subj.19687        2.48681   0.173869    2.17321    2.36483    2.47496    2.59959     2.8562   0.00456439
v(CP)               1.47559   0.102163    1.27916    1.40811    1.47431    1.54248    1.67828   0.00238597
v(CS)               1.95786   0.106418    1.75526    1.88599    1.95705    2.02747    2.17096   0.00262015
v(SS)               2.37192   0.112286    2.15409    2.29607    2.37199    2.44635    2.59636   0.00302127
v(US)               2.28449    0.10903    2.07393    2.21078    2.28264    2.35692    2.50229   0.00222824
v_std              0.316414  0.0603179   0.203449   0.275188   0.314504   0.354284   0.443224   0.00232312
v_subj(CP).17991    1.82967   0.191281    1.45724    1.69811    1.82795    1.96147     2.2004   0.00390881
v_subj(CP).18288    1.61922   0.207433    1.22307    1.47785    1.61443    1.75909    2.03768   0.00361467
v_subj(CP).18325    1.50641   0.179389    1.15983    1.38123    1.50812    1.63038    1.86118   0.00343361
v_subj(CP).18333    1.18237   0.186733   0.807938    1.06095    1.18373    1.31001    1.53634   0.00284106
v_subj(CP).18334    1.75333   0.215976    1.34317    1.60488    1.74799    1.89604    2.18607   0.00623666
v_subj(CP).18350    1.74649   0.240024    1.28824    1.58448    1.73801    1.91108    2.22665    0.0052998
v_subj(CP).18547    1.59607   0.216309    1.18437    1.44911    1.59084    1.74139    2.02493   0.00418742
v_subj(CP).18619    1.66288   0.196999    1.28527    1.53118    1.66197    1.79329    2.05041   0.00396026
v_subj(CP).18864    1.38517   0.197442    1.00098    1.25426    1.38403    1.51584    1.77609   0.00285255
v_subj(CP).18919    1.28781   0.179815   0.925007    1.16893    1.28905    1.40811    1.63436    0.0027996
v_subj(CP).18977    1.20678   0.173698   0.860854    1.09077    1.20989    1.32576    1.54706    0.0029068
v_subj(CP).18978    1.48524   0.192222    1.09911    1.36108    1.48724    1.61318    1.85979   0.00262691
v_subj(CP).18979    1.40412   0.180757    1.05249    1.28303    1.40686     1.5242    1.75899   0.00328325
v_subj(CP).18988    1.37952   0.183751     1.0204    1.25498    1.37984    1.50654    1.73486   0.00296729
v_subj(CP).19686    1.35855   0.201108   0.961949    1.22434    1.36102    1.49665    1.73683   0.00295636
v_subj(CP).19687    1.20286    0.18771   0.829306    1.07857    1.20572    1.33295    1.56144    0.0030637
v_subj(CS).17991    1.78797   0.182485    1.42977    1.66711    1.78937    1.90721    2.15108   0.00351197
v_subj(CS).18288    1.61342   0.187058    1.24736     1.4897    1.61521    1.73531    1.97526   0.00326267
v_subj(CS).18325    1.86654   0.190389    1.48837    1.74127    1.86635    1.99509    2.23904    0.0031599
v_subj(CS).18333    2.05416   0.210939    1.64235    1.91343    2.05569     2.1924    2.47733   0.00366685
v_subj(CS).18334     2.0989   0.219453    1.67184     1.9516    2.09367    2.24405     2.5381   0.00538247
v_subj(CS).18350    2.41435   0.282431    1.90327    2.21923    2.39935    2.59547    3.01567   0.00757248
v_subj(CS).18547    2.24709   0.245223    1.78535     2.0802    2.24226    2.40739    2.76105   0.00472545
v_subj(CS).18619    2.02537   0.204295    1.62539    1.88635     2.0271    2.16079    2.43134   0.00328405
v_subj(CS).18864    2.27909    0.24288    1.81565    2.11216    2.27446    2.44037    2.77111   0.00503581
v_subj(CS).18919    1.82018   0.204644    1.41094    1.68413    1.81794    1.95685    2.22314   0.00328023
v_subj(CS).18977    1.77046   0.181664    1.41474     1.6461    1.77177    1.89772    2.11892   0.00345327
v_subj(CS).18978     1.9441   0.206616    1.54305    1.80589    1.94417    2.08102    2.35422   0.00407739
v_subj(CS).18979    1.88583   0.204875    1.48806    1.74587    1.88391    2.02379    2.29308   0.00368429
v_subj(CS).18988    2.04384   0.199603    1.65558    1.90892    2.04038      2.177    2.43664   0.00357149
v_subj(CS).19686    1.84308   0.213248    1.41936    1.70146    1.84699    1.98624    2.27199   0.00331986
v_subj(CS).19687    1.61405   0.186211    1.24259     1.4898    1.61686    1.74316    1.96726   0.00360396
v_subj(SS).17991    2.17769   0.197264    1.78188    2.05059    2.18102    2.30726    2.56555   0.00371243
v_subj(SS).18288    2.56455   0.237031    2.10612    2.40527    2.56013    2.72008    3.04078   0.00489691
v_subj(SS).18325    2.25187   0.206891     1.8361    2.11315    2.25263    2.39079    2.65699   0.00374844
v_subj(SS).18333    2.67815   0.244651     2.2108    2.51292    2.67292     2.8375    3.17162   0.00553818
v_subj(SS).18334    2.81613   0.273756    2.30633    2.62947    2.80649     2.9893     3.3837   0.00812044
v_subj(SS).18350    2.78256   0.294729    2.23811    2.57622    2.76785    2.97653    3.39029   0.00775567
v_subj(SS).18547    2.14181   0.228931    1.68473    1.98897    2.14471    2.29557    2.59068   0.00346139
v_subj(SS).18619    2.00368   0.200253    1.59935    1.87131    2.00535    2.13773    2.39142   0.00412447
v_subj(SS).18864    2.49857   0.240455      2.048     2.3313    2.49333    2.65762      2.985   0.00438289
v_subj(SS).18919    2.02655   0.204372    1.61614    1.88802    2.03087    2.16572    2.40777   0.00358609
v_subj(SS).18977    1.97871   0.194627    1.58998    1.84477    1.98117    2.11082    2.34968   0.00391752
v_subj(SS).18978    2.05298   0.212036    1.63023    1.90996    2.05647    2.19507    2.46043   0.00375696
v_subj(SS).18979    2.43218   0.218007    2.00288    2.28765    2.43634    2.57318    2.86238   0.00367921
v_subj(SS).18988    2.46364   0.220766     2.0358    2.31685    2.45798    2.61027    2.90902   0.00424169
v_subj(SS).19686    2.58056   0.247569    2.11749    2.41461    2.57268    2.74042    3.09483    0.0050791
v_subj(SS).19687    2.52751   0.222819    2.10013    2.37856    2.52567    2.67461    2.97556   0.00427013
v_subj(US).17991    1.88831   0.184579    1.50866      1.768    1.89022    2.01207    2.25254   0.00354874
v_subj(US).18288    2.18663   0.206416    1.78183    2.05052    2.18657    2.32331    2.58928   0.00327386
v_subj(US).18325    2.14204   0.200401    1.74648    2.00891    2.14229    2.27598    2.53656   0.00351179
v_subj(US).18333    2.11505   0.201816    1.71753    1.97823    2.11519    2.25555    2.50247   0.00331561
v_subj(US).18334    2.55973    0.24664     2.0993    2.38966    2.55173    2.72073    3.06135   0.00647595
v_subj(US).18350    2.41986   0.244647    1.94594    2.25691    2.41875    2.57679    2.92198   0.00486468
v_subj(US).18547    2.38589   0.239808    1.91804    2.22694    2.38103    2.54368    2.86395   0.00419037
v_subj(US).18619     2.2115   0.203537    1.81391    2.07711    2.21149     2.3467    2.60945   0.00326021
v_subj(US).18864    2.73597    0.27663    2.21876    2.54498    2.72447    2.91639    3.31264    0.0065436
v_subj(US).18919    2.34436   0.217938    1.91041    2.19718    2.34356    2.49486    2.77368   0.00311133
v_subj(US).18977    2.08269   0.192819    1.69444    1.95279    2.08756    2.21369    2.45648   0.00338199
v_subj(US).18978    2.47411   0.232837    2.03801    2.31304    2.46961     2.6247    2.94408   0.00410308
v_subj(US).18979    2.41175   0.223207    1.98634    2.26258    2.40394    2.56004    2.86947   0.00440996
v_subj(US).18988    2.21645   0.208962    1.80057    2.07684    2.21906     2.3566    2.62867   0.00309159
v_subj(US).19686      2.304   0.230152    1.85753    2.14439    2.30465    2.45948    2.75085   0.00357543
v_subj(US).19687    2.06503   0.199584    1.67125    1.93698    2.06524    2.19964    2.45448   0.00331237
t                  0.576694  0.0797848   0.439339   0.521476   0.569778   0.624137   0.750406    0.0016466
t_std              0.337239  0.0825176   0.219187   0.278977   0.322942   0.378319   0.542652   0.00186254
t_subj.17991       0.193722    0.02484   0.137124   0.178509    0.19635   0.211471   0.235384  0.000532409
t_subj.18288       0.930123  0.0205667    0.88417   0.918043   0.932162   0.944763   0.963782  0.000514349
t_subj.18325       0.403409  0.0372177   0.321339   0.381106   0.406466    0.43036   0.465624   0.00127401
t_subj.18333       0.765438  0.0196946    0.72218   0.753257   0.767365    0.77957   0.797983  0.000494932
t_subj.18334       0.698793  0.0277976   0.637547   0.682357   0.701425   0.718522   0.744055   0.00114162
t_subj.18350       0.568706  0.0116495   0.542234   0.561863   0.570048   0.577017   0.587707  0.000319061
t_subj.18547       0.511359  0.0139041   0.479115   0.503406    0.51305   0.521221   0.533811  0.000375196
t_subj.18619       0.526001  0.0282933   0.461564   0.509172   0.528751   0.546067   0.573426  0.000807675
t_subj.18864       0.612742  0.0161527   0.577337   0.603405   0.614837   0.624207   0.638053  0.000363368
t_subj.18919       0.656597  0.0255529   0.602255   0.640905   0.658287    0.67452   0.701326  0.000743849
t_subj.18977      0.0526934  0.0153614  0.0203982  0.0426712  0.0537789  0.0636223  0.0796674  0.000298214
t_subj.18978       0.537071  0.0220068   0.487499   0.523601   0.539586    0.55266   0.574065    0.0006978
t_subj.18979       0.651014  0.0276998   0.591695   0.633581   0.653426   0.670877   0.699733  0.000934922
t_subj.18988       0.545161  0.0200159   0.500701   0.533375   0.547149    0.55971   0.577419  0.000445273
t_subj.19686       0.776009   0.018551   0.735441   0.764838   0.777654   0.789168   0.807307   0.00050541
t_subj.19687       0.825191  0.0231113   0.773127    0.81145    0.82762   0.841637   0.862817   0.00055305
DIC: 885.860554
deviance: 817.159195
pD: 68.701359
Parameters of Interest
  • Mean of a = 2.39576 (std = 0.152745)
  • Mean of t = 0.576694 s
  • Dift rate (v) mean values:
    • CP = 1.47559
    • CS = 1.95786
    • SS = 2.37192
    • US = 2.28449

Plot posteriors


In [5]:
%matplotlib inline
model.plot_posteriors()


Plotting a
Plotting a_std
Plotting v(CP)
Plotting v(CS)
Plotting v(SS)
Plotting v(US)
Plotting v_std
Plotting t
Plotting t_std

Plot posterior of drift rate for group means


In [6]:
v_SS, v_CP, v_CS, v_US = model.nodes_db.node[['v(SS)', 'v(CP)', 'v(CS)', 'v(US)']]

hddm.analyze.plot_posterior_nodes([v_SS, v_CP, v_CS, v_US])


Calculate the proportion of the posteriors in which the drift rate for one condition is greater than the other


In [7]:
print('P(SS > US) = ' + str((v_SS.trace() > v_US.trace()).mean()))
print('P(CP > SS) = ' + str((v_CP.trace() > v_SS.trace()).mean()))
print('P(CS > SS) = ' + str((v_CS.trace() > v_SS.trace()).mean()))
print('P(CP > CS) = ' + str((v_CP.trace() > v_CS.trace()).mean()))


P(SS > US) = 0.732775919732
P(CP > SS) = 0.0
P(CS > SS) = 0.00317725752508
P(CP > CS) = 0.000334448160535

Therefore:

  • The drift rate for CP is significantly lower than all other conditions
  • The drift rate for CS is significantly lower than SS and US, but significantly higher than CP
  • The drift rates for SS and US are not significantly different

Check for model convergence


In [8]:
models = []
for i in range(5):
    m = hddm.HDDM(data, depends_on={'v': 'stim'})
    m.find_starting_values()
    m.sample(6000, burn=20)
    models.append(m)

hddm.analyze.gelman_rubin(models)


/Users/celefthe/anaconda/envs/lang-dec/lib/python3.5/site-packages/scipy/optimize/optimize.py:1850: RuntimeWarning: invalid value encountered in double_scalars
  tmp2 = (x - v) * (fx - fw)
/Users/celefthe/anaconda/envs/lang-dec/lib/python3.5/site-packages/scipy/optimize/optimize.py:1851: RuntimeWarning: invalid value encountered in double_scalars
  p = (x - v) * tmp2 - (x - w) * tmp1
/Users/celefthe/anaconda/envs/lang-dec/lib/python3.5/site-packages/pymc/Node.py:403: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
  self.__name__ = input['__name__']
 [-----------------100%-----------------] 6000 of 6000 complete in 282.5 sec
/Users/celefthe/anaconda/envs/lang-dec/lib/python3.5/site-packages/numpy/core/fromnumeric.py:224: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
  return reshape(newshape, order=order)
 [-----------------100%-----------------] 6000 of 6000 complete in 288.0 sec
Out[8]:
{'a': 1.0004683770473366,
 'a_std': 1.0002930367583327,
 'a_subj.17991': 1.001475241554985,
 'a_subj.18288': 1.00092312622369,
 'a_subj.18325': 1.0000252899656865,
 'a_subj.18333': 1.0007237292037425,
 'a_subj.18334': 1.00202574301105,
 'a_subj.18350': 1.0015561857856901,
 'a_subj.18547': 1.0010168368145353,
 'a_subj.18619': 1.0023487766454109,
 'a_subj.18864': 1.0012664896806938,
 'a_subj.18919': 1.0010460888207739,
 'a_subj.18977': 1.0001279858651633,
 'a_subj.18978': 1.0009727221719167,
 'a_subj.18979': 1.0016689381274646,
 'a_subj.18988': 1.0006127559993909,
 'a_subj.19686': 1.0013119973689844,
 'a_subj.19687': 1.0004030368439716,
 't': 1.0001107976800878,
 't_std': 1.0003376375312927,
 't_subj.17991': 1.0014506128897218,
 't_subj.18288': 1.0008179323041115,
 't_subj.18325': 0.99992223288578996,
 't_subj.18333': 1.0002265422954852,
 't_subj.18334': 1.0011238707268417,
 't_subj.18350': 1.0006157710018271,
 't_subj.18547': 1.0005955706915415,
 't_subj.18619': 1.0023289887817504,
 't_subj.18864': 1.0008794293018699,
 't_subj.18919': 1.0010651502040682,
 't_subj.18977': 1.0002432208706404,
 't_subj.18978': 1.0012924587531327,
 't_subj.18979': 1.0020193497213641,
 't_subj.18988': 1.0004064120768033,
 't_subj.19686': 1.001161589042221,
 't_subj.19687': 1.0006468510259401,
 'v(CP)': 1.000609246460759,
 'v(CS)': 1.0021248860789154,
 'v(SS)': 1.0007671793680484,
 'v(US)': 1.0012008733675597,
 'v_std': 1.0021797852019303,
 'v_subj(CP).17991': 1.0009534690798896,
 'v_subj(CP).18288': 1.0001477177728142,
 'v_subj(CP).18325': 0.99994587739412288,
 'v_subj(CP).18333': 1.0000126852010109,
 'v_subj(CP).18334': 1.0013658415436231,
 'v_subj(CP).18350': 1.0003251971288205,
 'v_subj(CP).18547': 1.0003359009096913,
 'v_subj(CP).18619': 1.0005411502600929,
 'v_subj(CP).18864': 0.99988274207368988,
 'v_subj(CP).18919': 0.99992450645399999,
 'v_subj(CP).18977': 1.0002045575616929,
 'v_subj(CP).18978': 0.99995639304751649,
 'v_subj(CP).18979': 0.99991777856414277,
 'v_subj(CP).18988': 1.0000920699531337,
 'v_subj(CP).19686': 1.0004032667578737,
 'v_subj(CP).19687': 1.0000755009540161,
 'v_subj(CS).17991': 1.000253109797308,
 'v_subj(CS).18288': 1.0002166640278392,
 'v_subj(CS).18325': 0.99998898543186276,
 'v_subj(CS).18333': 1.0003820616038648,
 'v_subj(CS).18334': 1.0025235214890684,
 'v_subj(CS).18350': 1.0014747122279837,
 'v_subj(CS).18547': 1.0003675926555373,
 'v_subj(CS).18619': 1.0008341695727814,
 'v_subj(CS).18864': 1.000431746823311,
 'v_subj(CS).18919': 1.0000398072180072,
 'v_subj(CS).18977': 1.0005264669872997,
 'v_subj(CS).18978': 0.99995823894068792,
 'v_subj(CS).18979': 1.000912458740143,
 'v_subj(CS).18988': 1.0003689159385081,
 'v_subj(CS).19686': 0.99999820046745269,
 'v_subj(CS).19687': 1.0003280520635685,
 'v_subj(SS).17991': 1.0002360292717434,
 'v_subj(SS).18288': 1.0003733284877505,
 'v_subj(SS).18325': 0.99994989016068347,
 'v_subj(SS).18333': 1.0004963009244776,
 'v_subj(SS).18334': 1.0008297706090032,
 'v_subj(SS).18350': 1.0009591116552756,
 'v_subj(SS).18547': 1.000095994319536,
 'v_subj(SS).18619': 1.0000730821520862,
 'v_subj(SS).18864': 1.0005433865443407,
 'v_subj(SS).18919': 0.99988711850886014,
 'v_subj(SS).18977': 0.99986029280752386,
 'v_subj(SS).18978': 0.99994992956383089,
 'v_subj(SS).18979': 0.99992926968909679,
 'v_subj(SS).18988': 1.000580848686647,
 'v_subj(SS).19686': 1.0004841854317708,
 'v_subj(SS).19687': 1.0008335879711487,
 'v_subj(US).17991': 1.0001084754518739,
 'v_subj(US).18288': 1.0002734777931364,
 'v_subj(US).18325': 1.0001699243038449,
 'v_subj(US).18333': 1.0002756340119854,
 'v_subj(US).18334': 1.0013055213069293,
 'v_subj(US).18350': 1.000655217746022,
 'v_subj(US).18547': 1.000069838415798,
 'v_subj(US).18619': 1.0001338967138862,
 'v_subj(US).18864': 1.0012042225121585,
 'v_subj(US).18919': 1.0003687796376879,
 'v_subj(US).18977': 0.99996484797148355,
 'v_subj(US).18978': 1.0001101591078292,
 'v_subj(US).18979': 1.0001775425039627,
 'v_subj(US).18988': 1.0003342983549273,
 'v_subj(US).19686': 1.0000253981228666,
 'v_subj(US).19687': 1.0006723206877925}

Models converge!

Explore Bias


In [65]:
model_bias = hddm.HDDM(data, depends_on={'v': 'stim', 'z': 'stim'}, bias=True)
model_bias.find_starting_values()
model_bias.sample(6000, burn=20)


/Users/celefthe/anaconda/envs/lang-dec/lib/python3.5/site-packages/scipy/optimize/optimize.py:1850: RuntimeWarning: invalid value encountered in double_scalars
  tmp2 = (x - v) * (fx - fw)
/Users/celefthe/anaconda/envs/lang-dec/lib/python3.5/site-packages/scipy/optimize/optimize.py:1851: RuntimeWarning: invalid value encountered in double_scalars
  p = (x - v) * tmp2 - (x - w) * tmp1
/Users/celefthe/anaconda/envs/lang-dec/lib/python3.5/site-packages/pymc/Node.py:403: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
  self.__name__ = input['__name__']
 [-----------------100%-----------------] 6000 of 6000 complete in 411.5 sec
/Users/celefthe/anaconda/envs/lang-dec/lib/python3.5/site-packages/numpy/core/fromnumeric.py:224: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
  return reshape(newshape, order=order)
Out[65]:
<pymc.MCMC.MCMC at 0x12197ef60>

In [67]:
model_bias.plot_posteriors()


Plotting a
Plotting a_std
Plotting v(CP)
Plotting v(CS)
Plotting v(SS)
Plotting v(US)
Plotting v_std
Plotting t
Plotting t_std
Plotting z(CP)
Plotting z(CS)
Plotting z(SS)
Plotting z(US)
Plotting z_std

In [66]:
model_bias.print_stats()


/Users/celefthe/anaconda/envs/lang-dec/lib/python3.5/site-packages/numpy/core/fromnumeric.py:224: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
  return reshape(newshape, order=order)
                      mean        std       2.5q        25q        50q        75q     97.5q       mc err
a                  2.33775   0.140992     2.0755    2.24308    2.33155     2.4236   2.64166   0.00300188
a_std             0.519316   0.121337    0.33484   0.435395   0.500567   0.582782  0.813579    0.0028198
a_subj.17991       3.22999   0.220317    2.82623    3.07389    3.22144    3.37386   3.67497   0.00629581
a_subj.18288       2.33037   0.160563    2.03794    2.21719    2.32306    2.43105   2.66471   0.00469429
a_subj.18325       2.77405   0.249531    2.33017     2.5988    2.75544    2.93424   3.31491   0.00990998
a_subj.18333       2.23933   0.152266    1.95872     2.1342    2.23458    2.33865    2.5627   0.00405877
a_subj.18334       2.33158   0.206306    1.96268    2.19038    2.31886    2.46151   2.77322   0.00755267
a_subj.18350       1.58352   0.119376    1.37997    1.49713     1.5748    1.65904   1.84513   0.00414128
a_subj.18547       1.68415   0.113893    1.47827    1.60479    1.67716    1.75769   1.91751   0.00331361
a_subj.18619       2.55774   0.202636     2.2008    2.41483    2.54501    2.68553   2.99587   0.00633095
a_subj.18864       1.96321   0.139891    1.72129    1.86468    1.95308    2.04989   2.26421   0.00456595
a_subj.18919       2.39904   0.181824    2.06935    2.27456     2.3884    2.51547   2.79044   0.00566148
a_subj.18977       2.99316   0.165889    2.67822    2.87882    2.98817    3.09967   3.33501   0.00484017
a_subj.18978       2.18738   0.151863    1.91775    2.08371    2.17546    2.28246   2.51864     0.005308
a_subj.18979       2.34246   0.195429    1.99902    2.20334    2.32694    2.46431   2.76466   0.00679365
a_subj.18988       2.53886   0.171272    2.22636    2.42088    2.53162    2.64557   2.89554   0.00496027
a_subj.19686       1.80724   0.130555    1.57088    1.71721    1.79814    1.88666   2.08649   0.00426846
a_subj.19687       2.46629   0.169955    2.15791     2.3477    2.45897    2.57784   2.82626   0.00522507
v(CP)              1.71065   0.113539    1.48509    1.63333    1.70825    1.78786   1.93615   0.00360825
v(CS)              2.13624   0.123272    1.90389     2.0511    2.13252    2.21677    2.3903   0.00471718
v(SS)              2.65944   0.138407    2.38892    2.56425    2.66204    2.75444   2.92293   0.00594386
v(US)               2.6037   0.138199    2.33691    2.51147    2.60375    2.69497   2.87581    0.0058896
v_std             0.296796  0.0703878   0.163715   0.249299   0.295934   0.340828  0.446858    0.0036655
v_subj(CP).17991   1.88959   0.206062     1.4977    1.75095    1.88535    2.02597    2.3015   0.00487744
v_subj(CP).18288   1.88243   0.215481    1.46728    1.73877     1.8786    2.02386   2.31288   0.00510464
v_subj(CP).18325   1.70193    0.20149    1.30282    1.56708     1.7017    1.83874   2.09761   0.00492046
v_subj(CP).18333   1.45607   0.203843    1.05268    1.31987    1.45659    1.58917   1.85561   0.00508924
v_subj(CP).18334   1.98139   0.229692    1.55763    1.82272    1.97244    2.13323   2.45162   0.00655873
v_subj(CP).18350   2.03443   0.270049    1.54262    1.84429    2.01826    2.21194   2.58175    0.0077642
v_subj(CP).18547   1.78277   0.224622    1.34726    1.62882    1.78055    1.93337   2.21911   0.00417821
v_subj(CP).18619   1.87575   0.211371    1.46212    1.73142    1.87376    2.01708   2.28694   0.00531059
v_subj(CP).18864     1.632   0.208436    1.22371    1.49335    1.62969    1.77293   2.04857   0.00420227
v_subj(CP).18919    1.5983   0.200256    1.19526     1.4641    1.60147    1.72806   1.99373   0.00451861
v_subj(CP).18977   1.51868    0.19607     1.1278    1.38804    1.51936    1.65184    1.9026   0.00469838
v_subj(CP).18978   1.72556   0.203379    1.33066    1.59001    1.72532    1.86179   2.13153   0.00455322
v_subj(CP).18979   1.52923   0.197912    1.13196    1.39786    1.52846    1.65985   1.91723    0.0044864
v_subj(CP).18988   1.67883    0.20508    1.27856     1.5422     1.6795    1.81658   2.07276   0.00465396
v_subj(CP).19686   1.62014   0.218177    1.19163    1.47061    1.62022    1.76933   2.04171   0.00484969
v_subj(CP).19687   1.46804   0.204552    1.05271    1.33046    1.47472    1.60927     1.855   0.00502746
v_subj(CS).17991   2.01646   0.199539    1.61871    1.88538    2.01954    2.15195   2.40214   0.00470397
v_subj(CS).18288   1.77236   0.201444    1.36725    1.63921    1.77594       1.91   2.15443   0.00505992
v_subj(CS).18325   1.97831   0.207566    1.55542    1.84275    1.97939    2.11905    2.3783   0.00524417
v_subj(CS).18333   2.27477   0.237529    1.82717     2.1149    2.26676     2.4279   2.77555    0.0062352
v_subj(CS).18334   2.30187   0.236519    1.85986    2.13765    2.29222    2.45663    2.7898   0.00702909
v_subj(CS).18350   2.58443   0.316281    2.01034    2.36119    2.56741    2.78849   3.26576    0.0115924
v_subj(CS).18547   2.43027    0.27155    1.93362    2.24166    2.41443    2.60544   2.99831   0.00898644
v_subj(CS).18619   2.16799   0.219201    1.73896    2.02627    2.16416    2.30911    2.6048   0.00577878
v_subj(CS).18864   2.40182   0.267633     1.9257    2.21358    2.38861     2.5798   2.94677   0.00890629
v_subj(CS).18919   1.95237   0.212393    1.52679    1.81338    1.95127     2.0924   2.36822   0.00507444
v_subj(CS).18977   2.05587   0.205412    1.65937    1.91626    2.05447    2.19172   2.45965   0.00477051
v_subj(CS).18978   2.04225   0.219256    1.60765    1.89834     2.0434    2.18558   2.48285   0.00593267
v_subj(CS).18979   2.03753   0.215036    1.60033    1.89578    2.03858    2.18477   2.46047   0.00545316
v_subj(CS).18988   2.23854   0.222252    1.81069    2.08725    2.23454    2.38737   2.67947   0.00624915
v_subj(CS).19686   2.07665   0.222049    1.63612    1.92933    2.07436    2.22471   2.50528   0.00470432
v_subj(CS).19687   1.84011   0.201263    1.44072    1.70381    1.84239    1.97433   2.22564   0.00454125
v_subj(SS).17991    2.5212    0.22913    2.07307    2.36797    2.52629    2.67651   2.97029   0.00710359
v_subj(SS).18288    2.8042   0.257249    2.30162     2.6268    2.79947    2.97723   3.31179   0.00783837
v_subj(SS).18325   2.55398   0.236337    2.08246    2.39574     2.5586    2.71143   3.01528   0.00724015
v_subj(SS).18333   2.79513   0.262191    2.28707    2.61858    2.78744    2.96754   3.32583   0.00832182
v_subj(SS).18334   2.98693   0.289485    2.46107    2.78714     2.9775    3.17835   3.57797    0.0108026
v_subj(SS).18350   2.94896   0.316233    2.37824    2.73409    2.92836    3.14871   3.61194    0.0114012
v_subj(SS).18547   2.48141    0.24919    1.97983    2.32111    2.48735    2.64928   2.97377   0.00678637
v_subj(SS).18619    2.3064   0.232647    1.83713    2.15172    2.31119    2.46402   2.74841   0.00693195
v_subj(SS).18864   2.82744   0.270738    2.32084    2.64598    2.81597    3.00333   3.39255    0.0078892
v_subj(SS).18919   2.31565   0.223842    1.87045    2.16552    2.31757     2.4695    2.7481   0.00695289
v_subj(SS).18977   2.58845   0.224135    2.14361    2.44319    2.59075    2.73704   3.02685   0.00660499
v_subj(SS).18978   2.38128   0.234641     1.9072    2.22235    2.38852    2.54215   2.83594   0.00640621
v_subj(SS).18979   2.75005   0.245127    2.28538    2.58667      2.743    2.90996   3.24749   0.00612384
v_subj(SS).18988   2.83274   0.252314    2.34808     2.6583    2.82951    3.00118   3.34681   0.00728314
v_subj(SS).19686   2.72373   0.265004    2.20659    2.54376    2.72285    2.89591   3.25117   0.00799773
v_subj(SS).19687   2.72441   0.245298    2.24013    2.56085    2.72294     2.8909   3.19724   0.00730216
v_subj(US).17991   2.20665   0.219956    1.76043    2.06096    2.21166    2.36071   2.62097   0.00665732
v_subj(US).18288   2.53797   0.232646    2.09033    2.38474    2.53887    2.69288   3.00238   0.00632924
v_subj(US).18325   2.40958   0.227217    1.95413    2.25416    2.41954     2.5646   2.84243   0.00613251
v_subj(US).18333   2.51646   0.227116    2.07248    2.36675    2.51791    2.66596   2.96117   0.00547049
v_subj(US).18334   2.77347   0.266618    2.27696    2.59223    2.76323    2.94426   3.32792   0.00919916
v_subj(US).18350   2.82724   0.280002     2.3083    2.64119    2.81523    2.99906   3.41122   0.00908353
v_subj(US).18547   2.68844   0.261132    2.18413    2.51024    2.68478    2.86116   3.22041   0.00724208
v_subj(US).18619   2.50219   0.227122    2.04374    2.34966    2.51053      2.651   2.94468   0.00563562
v_subj(US).18864   2.99552   0.302544    2.44592    2.78642    2.98048    3.19415   3.63066    0.0117702
v_subj(US).18919    2.6245   0.235264    2.15822    2.46905    2.62814    2.77997   3.09029   0.00663621
v_subj(US).18977   2.55012   0.221086       2.12    2.39726    2.55198    2.70015   2.97235   0.00613117
v_subj(US).18978   2.71782   0.257158    2.22297    2.54516    2.71372    2.88722   3.23582   0.00788448
v_subj(US).18979   2.70637   0.241524    2.24547    2.54415     2.7043    2.86766   3.18277   0.00711448
v_subj(US).18988   2.49139    0.23379     2.0243    2.33798    2.49456    2.64732   2.95772   0.00631707
v_subj(US).19686   2.64689   0.247381    2.16539    2.48374     2.6448    2.81131   3.15256   0.00640982
v_subj(US).19687   2.45005   0.224068    1.99487     2.3059    2.45259    2.60102   2.88299   0.00546107
t                 0.559562  0.0737887   0.432199   0.509383   0.553196    0.60289   0.72089   0.00159028
t_std             0.299953  0.0733693   0.196967   0.249705   0.287335   0.335926  0.481177   0.00189391
t_subj.17991       0.18763  0.0278933   0.125159    0.17109   0.190634   0.207023  0.234143  0.000715253
t_subj.18288      0.904433  0.0265951   0.846545   0.887366   0.907051    0.92369  0.949502  0.000760754
t_subj.18325      0.357137  0.0462925   0.254439    0.32817   0.360585    0.38998  0.438519    0.0017939
t_subj.18333      0.752231   0.025329   0.697721   0.736162   0.754982   0.770555  0.794861  0.000901737
t_subj.18334      0.678471   0.031306   0.609486   0.659107   0.680988   0.700366  0.732563   0.00122884
t_subj.18350       0.56244   0.014953    0.52873   0.553166   0.564206   0.573434  0.586483  0.000556825
t_subj.18547      0.504669  0.0177686   0.464746   0.493753   0.506425   0.517672  0.533368  0.000514524
t_subj.18619      0.489185  0.0355394   0.406584   0.467466   0.493555   0.514917  0.547374    0.0011357
t_subj.18864       0.59905  0.0192933   0.554708   0.587133   0.601001   0.612842  0.630855  0.000583887
t_subj.18919       0.61712  0.0351947   0.539721   0.594783   0.619269   0.642337  0.678976   0.00119118
t_subj.18977      0.084703  0.0150397  0.0511263  0.0756192  0.0862754  0.0955538  0.109539  0.000374144
t_subj.18978      0.514866   0.028172    0.45171   0.498294   0.517934   0.534484  0.563011   0.00115065
t_subj.18979      0.608199  0.0364035   0.526177   0.585549   0.611962    0.63344  0.670947   0.00134155
t_subj.18988      0.522763  0.0252898   0.466667   0.507508   0.524929    0.54022  0.565664  0.000703955
t_subj.19686       0.76057  0.0242652   0.706548   0.746234   0.762389   0.777279  0.801691  0.000891568
t_subj.19687       0.79538  0.0304273   0.730387   0.775541   0.797982   0.817121   0.84757  0.000996644
z(CP)             0.404753  0.0222697     0.3625   0.389623   0.404394   0.419938  0.448922  0.000824511
z(CS)             0.423535  0.0238456   0.376358   0.407294   0.423823   0.439788  0.469242   0.00108747
z(SS)             0.404102  0.0249942   0.354682   0.388139   0.404036   0.420259   0.45234   0.00120698
z(US)             0.392763  0.0256483   0.341785   0.375622   0.392487   0.409838  0.444518   0.00125727
z_std              0.18778  0.0347632   0.118741   0.165585   0.188331   0.211014  0.255201   0.00193951
z_subj(CP).17991  0.448916  0.0451539   0.361516   0.418148   0.447767   0.479224  0.538765   0.00136952
z_subj(CP).18288  0.395648  0.0398017   0.320049   0.368345    0.39544   0.422886  0.474536  0.000972441
z_subj(CP).18325  0.414936  0.0416433   0.335527   0.386384   0.414499     0.4424  0.498501   0.00103862
z_subj(CP).18333  0.394726  0.0387848    0.31949   0.368214   0.394545    0.42079  0.471259  0.000890693
z_subj(CP).18334  0.394605  0.0407184   0.315222   0.367614   0.393904   0.421166  0.476584  0.000973507
z_subj(CP).18350  0.391459  0.0393695   0.314982   0.365033   0.390505   0.417992  0.470539  0.000797165
z_subj(CP).18547  0.426871  0.0409342   0.349145   0.399452   0.426163   0.453124  0.510882  0.000904334
z_subj(CP).18619  0.408834  0.0410421   0.329848   0.380145   0.408805   0.436085  0.491711   0.00110578
z_subj(CP).18864   0.39455  0.0399693   0.319227   0.367142    0.39395    0.42077   0.47657   0.00091318
z_subj(CP).18919  0.374092  0.0392918   0.296902   0.347661   0.373654   0.400107  0.451611  0.000871748
z_subj(CP).18977  0.384237  0.0401024   0.306313   0.357779   0.384228   0.410819  0.463572   0.00095542
z_subj(CP).18978  0.398306   0.039697   0.322372   0.371334    0.39782   0.424225  0.477426  0.000911307
z_subj(CP).18979   0.46316  0.0441344   0.381472   0.432789   0.461333   0.492242  0.555078   0.00141535
z_subj(CP).18988  0.375887   0.039412   0.297023   0.349746   0.376258   0.403036  0.452251  0.000942765
z_subj(CP).19686  0.409864  0.0389686   0.333348   0.383988   0.408992    0.43617  0.486778  0.000978993
z_subj(CP).19687  0.395797  0.0397259   0.318741   0.368828   0.396409   0.422287  0.474859  0.000870342
z_subj(CS).17991  0.381967  0.0404028   0.300443    0.35578   0.381775   0.408825  0.459209   0.00100757
z_subj(CS).18288  0.427981  0.0420771    0.34939   0.398937    0.42675   0.455608  0.511661   0.00113895
z_subj(CS).18325  0.445166  0.0422332   0.364759   0.416028   0.444659   0.472708  0.530449   0.00131887
z_subj(CS).18333  0.414033  0.0428276   0.330203   0.385221   0.413264   0.442596  0.500686    0.0011915
z_subj(CS).18334  0.403841  0.0407882   0.324209   0.376457   0.404093   0.430666  0.486445   0.00106837
z_subj(CS).18350  0.434974  0.0422605   0.354511   0.405845   0.434453   0.463738  0.518129   0.00124374
z_subj(CS).18547  0.423179  0.0412023   0.342271    0.39556   0.423416   0.450479  0.504094   0.00117256
z_subj(CS).18619  0.429985  0.0425836    0.34826   0.401072   0.429914   0.458578  0.516791   0.00128341
z_subj(CS).18864  0.444081  0.0434421   0.361915   0.414538   0.443427   0.473474  0.530677   0.00140746
z_subj(CS).18919  0.452268  0.0437623   0.366952   0.423155   0.451962   0.481733  0.536307   0.00140419
z_subj(CS).18977  0.389611  0.0409189   0.310486    0.36234   0.389691   0.416886  0.470592   0.00113113
z_subj(CS).18978  0.464003  0.0439947   0.378951   0.433948   0.462882   0.492437  0.552743   0.00165301
z_subj(CS).18979  0.441841  0.0438409   0.358507   0.411312   0.442091   0.471376  0.529439    0.0014361
z_subj(CS).18988  0.406265  0.0414726   0.324772   0.378523   0.406423     0.4338  0.485927   0.00126297
z_subj(CS).19686  0.411914  0.0413219   0.333846   0.383039   0.411427   0.439189  0.493718   0.00105854
z_subj(CS).19687  0.401819  0.0403084   0.324373   0.374161    0.40168   0.428168  0.483105   0.00102963
z_subj(SS).17991  0.360931  0.0417519   0.277622   0.332752   0.361649   0.389318  0.443284   0.00126161
z_subj(SS).18288  0.422839  0.0436685   0.341025   0.392839   0.421716    0.45149  0.511878   0.00144138
z_subj(SS).18325   0.38433  0.0424493   0.301723   0.355959   0.384446   0.412976  0.469643    0.0012415
z_subj(SS).18333  0.477513  0.0492818   0.383575   0.443316   0.477818   0.510447  0.573343   0.00216073
z_subj(SS).18334  0.438766  0.0454909   0.351767   0.406534   0.438208   0.469478  0.528622    0.0017473
z_subj(SS).18350  0.468852  0.0497332   0.372011   0.435267   0.468279   0.501393  0.567528   0.00215106
z_subj(SS).18547   0.39201  0.0379534   0.318136   0.365551   0.391486   0.417722  0.467734   0.00103663
z_subj(SS).18619  0.387762  0.0415533   0.308898   0.359584   0.386484   0.415175  0.473085   0.00121258
z_subj(SS).18864  0.391334   0.041118   0.312424   0.363289   0.390987   0.419056  0.474786   0.00117267
z_subj(SS).18919  0.403703  0.0418437   0.321679   0.375825    0.40272   0.430984   0.48884   0.00122847
z_subj(SS).18977  0.284174   0.039816   0.209654   0.256919   0.283397   0.311313  0.363658   0.00143538
z_subj(SS).18978  0.390133    0.03998   0.312436   0.363549   0.389155   0.416301  0.469474   0.00114045
z_subj(SS).18979  0.395964  0.0411568   0.316139   0.368843   0.394315   0.422905  0.478806   0.00125519
z_subj(SS).18988  0.361692  0.0411194   0.280655   0.333807   0.361513   0.389093  0.440974   0.00122469
z_subj(SS).19686  0.479797  0.0494407   0.385702   0.445111   0.478706   0.513105  0.576387   0.00207709
z_subj(SS).19687  0.435347  0.0461094   0.347101   0.404204   0.434645   0.465857  0.529747   0.00165154
z_subj(US).17991  0.363928  0.0423021   0.279386   0.335519   0.364211   0.392388  0.448779   0.00130405
z_subj(US).18288  0.371136  0.0409447   0.291311   0.343808   0.371441   0.398995  0.450356   0.00116546
z_subj(US).18325  0.402079  0.0439538   0.317694   0.372473   0.401034    0.43049   0.49127   0.00133537
z_subj(US).18333  0.360937   0.040252   0.282367   0.333678   0.359911   0.388353  0.439625   0.00115873
z_subj(US).18334   0.43008  0.0464512   0.341376   0.398219   0.429519    0.46143  0.521831   0.00159821
z_subj(US).18350  0.366526   0.040009   0.290691   0.338951   0.365991   0.393879  0.446564    0.0011289
z_subj(US).18547  0.409818  0.0424198   0.330103   0.380384   0.408868   0.438644  0.496496    0.0012783
z_subj(US).18619  0.394906  0.0430904   0.312967   0.365178   0.393965   0.423746  0.481198   0.00130201
z_subj(US).18864  0.421335  0.0452936   0.333328    0.39093   0.420558   0.450583  0.513507   0.00165044
z_subj(US).18919  0.411961  0.0452271   0.324218   0.380967   0.411842   0.442769  0.502233   0.00161131
z_subj(US).18977  0.345765  0.0414032   0.263604   0.317715   0.345875   0.374291  0.425697   0.00134172
z_subj(US).18978   0.43191  0.0470416   0.341187   0.400029   0.431063   0.463638   0.52583   0.00188955
z_subj(US).18979  0.407369  0.0436133   0.324149   0.376883   0.406621   0.436255  0.497258   0.00151197
z_subj(US).18988  0.403893  0.0427819   0.323586   0.375016   0.402961   0.431537  0.492488   0.00136715
z_subj(US).19686  0.399859  0.0421577   0.319097   0.370796   0.398809   0.427977  0.486289   0.00140767
z_subj(US).19687  0.362256  0.0403855   0.283779   0.335166   0.361668    0.38948   0.44198    0.0011899
DIC: 784.850834
deviance: 698.619830
pD: 86.231004

In [70]:
model_bias.print_stats()


/Users/celefthe/anaconda/envs/lang-dec/lib/python3.5/site-packages/numpy/core/fromnumeric.py:224: VisibleDeprecationWarning: using a non-integer number instead of an integer will result in an error in the future
  return reshape(newshape, order=order)
                      mean        std       2.5q        25q        50q        75q     97.5q       mc err
a                  2.33775   0.140992     2.0755    2.24308    2.33155     2.4236   2.64166   0.00300188
a_std             0.519316   0.121337    0.33484   0.435395   0.500567   0.582782  0.813579    0.0028198
a_subj.17991       3.22999   0.220317    2.82623    3.07389    3.22144    3.37386   3.67497   0.00629581
a_subj.18288       2.33037   0.160563    2.03794    2.21719    2.32306    2.43105   2.66471   0.00469429
a_subj.18325       2.77405   0.249531    2.33017     2.5988    2.75544    2.93424   3.31491   0.00990998
a_subj.18333       2.23933   0.152266    1.95872     2.1342    2.23458    2.33865    2.5627   0.00405877
a_subj.18334       2.33158   0.206306    1.96268    2.19038    2.31886    2.46151   2.77322   0.00755267
a_subj.18350       1.58352   0.119376    1.37997    1.49713     1.5748    1.65904   1.84513   0.00414128
a_subj.18547       1.68415   0.113893    1.47827    1.60479    1.67716    1.75769   1.91751   0.00331361
a_subj.18619       2.55774   0.202636     2.2008    2.41483    2.54501    2.68553   2.99587   0.00633095
a_subj.18864       1.96321   0.139891    1.72129    1.86468    1.95308    2.04989   2.26421   0.00456595
a_subj.18919       2.39904   0.181824    2.06935    2.27456     2.3884    2.51547   2.79044   0.00566148
a_subj.18977       2.99316   0.165889    2.67822    2.87882    2.98817    3.09967   3.33501   0.00484017
a_subj.18978       2.18738   0.151863    1.91775    2.08371    2.17546    2.28246   2.51864     0.005308
a_subj.18979       2.34246   0.195429    1.99902    2.20334    2.32694    2.46431   2.76466   0.00679365
a_subj.18988       2.53886   0.171272    2.22636    2.42088    2.53162    2.64557   2.89554   0.00496027
a_subj.19686       1.80724   0.130555    1.57088    1.71721    1.79814    1.88666   2.08649   0.00426846
a_subj.19687       2.46629   0.169955    2.15791     2.3477    2.45897    2.57784   2.82626   0.00522507
v(CP)              1.71065   0.113539    1.48509    1.63333    1.70825    1.78786   1.93615   0.00360825
v(CS)              2.13624   0.123272    1.90389     2.0511    2.13252    2.21677    2.3903   0.00471718
v(SS)              2.65944   0.138407    2.38892    2.56425    2.66204    2.75444   2.92293   0.00594386
v(US)               2.6037   0.138199    2.33691    2.51147    2.60375    2.69497   2.87581    0.0058896
v_std             0.296796  0.0703878   0.163715   0.249299   0.295934   0.340828  0.446858    0.0036655
v_subj(CP).17991   1.88959   0.206062     1.4977    1.75095    1.88535    2.02597    2.3015   0.00487744
v_subj(CP).18288   1.88243   0.215481    1.46728    1.73877     1.8786    2.02386   2.31288   0.00510464
v_subj(CP).18325   1.70193    0.20149    1.30282    1.56708     1.7017    1.83874   2.09761   0.00492046
v_subj(CP).18333   1.45607   0.203843    1.05268    1.31987    1.45659    1.58917   1.85561   0.00508924
v_subj(CP).18334   1.98139   0.229692    1.55763    1.82272    1.97244    2.13323   2.45162   0.00655873
v_subj(CP).18350   2.03443   0.270049    1.54262    1.84429    2.01826    2.21194   2.58175    0.0077642
v_subj(CP).18547   1.78277   0.224622    1.34726    1.62882    1.78055    1.93337   2.21911   0.00417821
v_subj(CP).18619   1.87575   0.211371    1.46212    1.73142    1.87376    2.01708   2.28694   0.00531059
v_subj(CP).18864     1.632   0.208436    1.22371    1.49335    1.62969    1.77293   2.04857   0.00420227
v_subj(CP).18919    1.5983   0.200256    1.19526     1.4641    1.60147    1.72806   1.99373   0.00451861
v_subj(CP).18977   1.51868    0.19607     1.1278    1.38804    1.51936    1.65184    1.9026   0.00469838
v_subj(CP).18978   1.72556   0.203379    1.33066    1.59001    1.72532    1.86179   2.13153   0.00455322
v_subj(CP).18979   1.52923   0.197912    1.13196    1.39786    1.52846    1.65985   1.91723    0.0044864
v_subj(CP).18988   1.67883    0.20508    1.27856     1.5422     1.6795    1.81658   2.07276   0.00465396
v_subj(CP).19686   1.62014   0.218177    1.19163    1.47061    1.62022    1.76933   2.04171   0.00484969
v_subj(CP).19687   1.46804   0.204552    1.05271    1.33046    1.47472    1.60927     1.855   0.00502746
v_subj(CS).17991   2.01646   0.199539    1.61871    1.88538    2.01954    2.15195   2.40214   0.00470397
v_subj(CS).18288   1.77236   0.201444    1.36725    1.63921    1.77594       1.91   2.15443   0.00505992
v_subj(CS).18325   1.97831   0.207566    1.55542    1.84275    1.97939    2.11905    2.3783   0.00524417
v_subj(CS).18333   2.27477   0.237529    1.82717     2.1149    2.26676     2.4279   2.77555    0.0062352
v_subj(CS).18334   2.30187   0.236519    1.85986    2.13765    2.29222    2.45663    2.7898   0.00702909
v_subj(CS).18350   2.58443   0.316281    2.01034    2.36119    2.56741    2.78849   3.26576    0.0115924
v_subj(CS).18547   2.43027    0.27155    1.93362    2.24166    2.41443    2.60544   2.99831   0.00898644
v_subj(CS).18619   2.16799   0.219201    1.73896    2.02627    2.16416    2.30911    2.6048   0.00577878
v_subj(CS).18864   2.40182   0.267633     1.9257    2.21358    2.38861     2.5798   2.94677   0.00890629
v_subj(CS).18919   1.95237   0.212393    1.52679    1.81338    1.95127     2.0924   2.36822   0.00507444
v_subj(CS).18977   2.05587   0.205412    1.65937    1.91626    2.05447    2.19172   2.45965   0.00477051
v_subj(CS).18978   2.04225   0.219256    1.60765    1.89834     2.0434    2.18558   2.48285   0.00593267
v_subj(CS).18979   2.03753   0.215036    1.60033    1.89578    2.03858    2.18477   2.46047   0.00545316
v_subj(CS).18988   2.23854   0.222252    1.81069    2.08725    2.23454    2.38737   2.67947   0.00624915
v_subj(CS).19686   2.07665   0.222049    1.63612    1.92933    2.07436    2.22471   2.50528   0.00470432
v_subj(CS).19687   1.84011   0.201263    1.44072    1.70381    1.84239    1.97433   2.22564   0.00454125
v_subj(SS).17991    2.5212    0.22913    2.07307    2.36797    2.52629    2.67651   2.97029   0.00710359
v_subj(SS).18288    2.8042   0.257249    2.30162     2.6268    2.79947    2.97723   3.31179   0.00783837
v_subj(SS).18325   2.55398   0.236337    2.08246    2.39574     2.5586    2.71143   3.01528   0.00724015
v_subj(SS).18333   2.79513   0.262191    2.28707    2.61858    2.78744    2.96754   3.32583   0.00832182
v_subj(SS).18334   2.98693   0.289485    2.46107    2.78714     2.9775    3.17835   3.57797    0.0108026
v_subj(SS).18350   2.94896   0.316233    2.37824    2.73409    2.92836    3.14871   3.61194    0.0114012
v_subj(SS).18547   2.48141    0.24919    1.97983    2.32111    2.48735    2.64928   2.97377   0.00678637
v_subj(SS).18619    2.3064   0.232647    1.83713    2.15172    2.31119    2.46402   2.74841   0.00693195
v_subj(SS).18864   2.82744   0.270738    2.32084    2.64598    2.81597    3.00333   3.39255    0.0078892
v_subj(SS).18919   2.31565   0.223842    1.87045    2.16552    2.31757     2.4695    2.7481   0.00695289
v_subj(SS).18977   2.58845   0.224135    2.14361    2.44319    2.59075    2.73704   3.02685   0.00660499
v_subj(SS).18978   2.38128   0.234641     1.9072    2.22235    2.38852    2.54215   2.83594   0.00640621
v_subj(SS).18979   2.75005   0.245127    2.28538    2.58667      2.743    2.90996   3.24749   0.00612384
v_subj(SS).18988   2.83274   0.252314    2.34808     2.6583    2.82951    3.00118   3.34681   0.00728314
v_subj(SS).19686   2.72373   0.265004    2.20659    2.54376    2.72285    2.89591   3.25117   0.00799773
v_subj(SS).19687   2.72441   0.245298    2.24013    2.56085    2.72294     2.8909   3.19724   0.00730216
v_subj(US).17991   2.20665   0.219956    1.76043    2.06096    2.21166    2.36071   2.62097   0.00665732
v_subj(US).18288   2.53797   0.232646    2.09033    2.38474    2.53887    2.69288   3.00238   0.00632924
v_subj(US).18325   2.40958   0.227217    1.95413    2.25416    2.41954     2.5646   2.84243   0.00613251
v_subj(US).18333   2.51646   0.227116    2.07248    2.36675    2.51791    2.66596   2.96117   0.00547049
v_subj(US).18334   2.77347   0.266618    2.27696    2.59223    2.76323    2.94426   3.32792   0.00919916
v_subj(US).18350   2.82724   0.280002     2.3083    2.64119    2.81523    2.99906   3.41122   0.00908353
v_subj(US).18547   2.68844   0.261132    2.18413    2.51024    2.68478    2.86116   3.22041   0.00724208
v_subj(US).18619   2.50219   0.227122    2.04374    2.34966    2.51053      2.651   2.94468   0.00563562
v_subj(US).18864   2.99552   0.302544    2.44592    2.78642    2.98048    3.19415   3.63066    0.0117702
v_subj(US).18919    2.6245   0.235264    2.15822    2.46905    2.62814    2.77997   3.09029   0.00663621
v_subj(US).18977   2.55012   0.221086       2.12    2.39726    2.55198    2.70015   2.97235   0.00613117
v_subj(US).18978   2.71782   0.257158    2.22297    2.54516    2.71372    2.88722   3.23582   0.00788448
v_subj(US).18979   2.70637   0.241524    2.24547    2.54415     2.7043    2.86766   3.18277   0.00711448
v_subj(US).18988   2.49139    0.23379     2.0243    2.33798    2.49456    2.64732   2.95772   0.00631707
v_subj(US).19686   2.64689   0.247381    2.16539    2.48374     2.6448    2.81131   3.15256   0.00640982
v_subj(US).19687   2.45005   0.224068    1.99487     2.3059    2.45259    2.60102   2.88299   0.00546107
t                 0.559562  0.0737887   0.432199   0.509383   0.553196    0.60289   0.72089   0.00159028
t_std             0.299953  0.0733693   0.196967   0.249705   0.287335   0.335926  0.481177   0.00189391
t_subj.17991       0.18763  0.0278933   0.125159    0.17109   0.190634   0.207023  0.234143  0.000715253
t_subj.18288      0.904433  0.0265951   0.846545   0.887366   0.907051    0.92369  0.949502  0.000760754
t_subj.18325      0.357137  0.0462925   0.254439    0.32817   0.360585    0.38998  0.438519    0.0017939
t_subj.18333      0.752231   0.025329   0.697721   0.736162   0.754982   0.770555  0.794861  0.000901737
t_subj.18334      0.678471   0.031306   0.609486   0.659107   0.680988   0.700366  0.732563   0.00122884
t_subj.18350       0.56244   0.014953    0.52873   0.553166   0.564206   0.573434  0.586483  0.000556825
t_subj.18547      0.504669  0.0177686   0.464746   0.493753   0.506425   0.517672  0.533368  0.000514524
t_subj.18619      0.489185  0.0355394   0.406584   0.467466   0.493555   0.514917  0.547374    0.0011357
t_subj.18864       0.59905  0.0192933   0.554708   0.587133   0.601001   0.612842  0.630855  0.000583887
t_subj.18919       0.61712  0.0351947   0.539721   0.594783   0.619269   0.642337  0.678976   0.00119118
t_subj.18977      0.084703  0.0150397  0.0511263  0.0756192  0.0862754  0.0955538  0.109539  0.000374144
t_subj.18978      0.514866   0.028172    0.45171   0.498294   0.517934   0.534484  0.563011   0.00115065
t_subj.18979      0.608199  0.0364035   0.526177   0.585549   0.611962    0.63344  0.670947   0.00134155
t_subj.18988      0.522763  0.0252898   0.466667   0.507508   0.524929    0.54022  0.565664  0.000703955
t_subj.19686       0.76057  0.0242652   0.706548   0.746234   0.762389   0.777279  0.801691  0.000891568
t_subj.19687       0.79538  0.0304273   0.730387   0.775541   0.797982   0.817121   0.84757  0.000996644
z(CP)             0.404753  0.0222697     0.3625   0.389623   0.404394   0.419938  0.448922  0.000824511
z(CS)             0.423535  0.0238456   0.376358   0.407294   0.423823   0.439788  0.469242   0.00108747
z(SS)             0.404102  0.0249942   0.354682   0.388139   0.404036   0.420259   0.45234   0.00120698
z(US)             0.392763  0.0256483   0.341785   0.375622   0.392487   0.409838  0.444518   0.00125727
z_std              0.18778  0.0347632   0.118741   0.165585   0.188331   0.211014  0.255201   0.00193951
z_subj(CP).17991  0.448916  0.0451539   0.361516   0.418148   0.447767   0.479224  0.538765   0.00136952
z_subj(CP).18288  0.395648  0.0398017   0.320049   0.368345    0.39544   0.422886  0.474536  0.000972441
z_subj(CP).18325  0.414936  0.0416433   0.335527   0.386384   0.414499     0.4424  0.498501   0.00103862
z_subj(CP).18333  0.394726  0.0387848    0.31949   0.368214   0.394545    0.42079  0.471259  0.000890693
z_subj(CP).18334  0.394605  0.0407184   0.315222   0.367614   0.393904   0.421166  0.476584  0.000973507
z_subj(CP).18350  0.391459  0.0393695   0.314982   0.365033   0.390505   0.417992  0.470539  0.000797165
z_subj(CP).18547  0.426871  0.0409342   0.349145   0.399452   0.426163   0.453124  0.510882  0.000904334
z_subj(CP).18619  0.408834  0.0410421   0.329848   0.380145   0.408805   0.436085  0.491711   0.00110578
z_subj(CP).18864   0.39455  0.0399693   0.319227   0.367142    0.39395    0.42077   0.47657   0.00091318
z_subj(CP).18919  0.374092  0.0392918   0.296902   0.347661   0.373654   0.400107  0.451611  0.000871748
z_subj(CP).18977  0.384237  0.0401024   0.306313   0.357779   0.384228   0.410819  0.463572   0.00095542
z_subj(CP).18978  0.398306   0.039697   0.322372   0.371334    0.39782   0.424225  0.477426  0.000911307
z_subj(CP).18979   0.46316  0.0441344   0.381472   0.432789   0.461333   0.492242  0.555078   0.00141535
z_subj(CP).18988  0.375887   0.039412   0.297023   0.349746   0.376258   0.403036  0.452251  0.000942765
z_subj(CP).19686  0.409864  0.0389686   0.333348   0.383988   0.408992    0.43617  0.486778  0.000978993
z_subj(CP).19687  0.395797  0.0397259   0.318741   0.368828   0.396409   0.422287  0.474859  0.000870342
z_subj(CS).17991  0.381967  0.0404028   0.300443    0.35578   0.381775   0.408825  0.459209   0.00100757
z_subj(CS).18288  0.427981  0.0420771    0.34939   0.398937    0.42675   0.455608  0.511661   0.00113895
z_subj(CS).18325  0.445166  0.0422332   0.364759   0.416028   0.444659   0.472708  0.530449   0.00131887
z_subj(CS).18333  0.414033  0.0428276   0.330203   0.385221   0.413264   0.442596  0.500686    0.0011915
z_subj(CS).18334  0.403841  0.0407882   0.324209   0.376457   0.404093   0.430666  0.486445   0.00106837
z_subj(CS).18350  0.434974  0.0422605   0.354511   0.405845   0.434453   0.463738  0.518129   0.00124374
z_subj(CS).18547  0.423179  0.0412023   0.342271    0.39556   0.423416   0.450479  0.504094   0.00117256
z_subj(CS).18619  0.429985  0.0425836    0.34826   0.401072   0.429914   0.458578  0.516791   0.00128341
z_subj(CS).18864  0.444081  0.0434421   0.361915   0.414538   0.443427   0.473474  0.530677   0.00140746
z_subj(CS).18919  0.452268  0.0437623   0.366952   0.423155   0.451962   0.481733  0.536307   0.00140419
z_subj(CS).18977  0.389611  0.0409189   0.310486    0.36234   0.389691   0.416886  0.470592   0.00113113
z_subj(CS).18978  0.464003  0.0439947   0.378951   0.433948   0.462882   0.492437  0.552743   0.00165301
z_subj(CS).18979  0.441841  0.0438409   0.358507   0.411312   0.442091   0.471376  0.529439    0.0014361
z_subj(CS).18988  0.406265  0.0414726   0.324772   0.378523   0.406423     0.4338  0.485927   0.00126297
z_subj(CS).19686  0.411914  0.0413219   0.333846   0.383039   0.411427   0.439189  0.493718   0.00105854
z_subj(CS).19687  0.401819  0.0403084   0.324373   0.374161    0.40168   0.428168  0.483105   0.00102963
z_subj(SS).17991  0.360931  0.0417519   0.277622   0.332752   0.361649   0.389318  0.443284   0.00126161
z_subj(SS).18288  0.422839  0.0436685   0.341025   0.392839   0.421716    0.45149  0.511878   0.00144138
z_subj(SS).18325   0.38433  0.0424493   0.301723   0.355959   0.384446   0.412976  0.469643    0.0012415
z_subj(SS).18333  0.477513  0.0492818   0.383575   0.443316   0.477818   0.510447  0.573343   0.00216073
z_subj(SS).18334  0.438766  0.0454909   0.351767   0.406534   0.438208   0.469478  0.528622    0.0017473
z_subj(SS).18350  0.468852  0.0497332   0.372011   0.435267   0.468279   0.501393  0.567528   0.00215106
z_subj(SS).18547   0.39201  0.0379534   0.318136   0.365551   0.391486   0.417722  0.467734   0.00103663
z_subj(SS).18619  0.387762  0.0415533   0.308898   0.359584   0.386484   0.415175  0.473085   0.00121258
z_subj(SS).18864  0.391334   0.041118   0.312424   0.363289   0.390987   0.419056  0.474786   0.00117267
z_subj(SS).18919  0.403703  0.0418437   0.321679   0.375825    0.40272   0.430984   0.48884   0.00122847
z_subj(SS).18977  0.284174   0.039816   0.209654   0.256919   0.283397   0.311313  0.363658   0.00143538
z_subj(SS).18978  0.390133    0.03998   0.312436   0.363549   0.389155   0.416301  0.469474   0.00114045
z_subj(SS).18979  0.395964  0.0411568   0.316139   0.368843   0.394315   0.422905  0.478806   0.00125519
z_subj(SS).18988  0.361692  0.0411194   0.280655   0.333807   0.361513   0.389093  0.440974   0.00122469
z_subj(SS).19686  0.479797  0.0494407   0.385702   0.445111   0.478706   0.513105  0.576387   0.00207709
z_subj(SS).19687  0.435347  0.0461094   0.347101   0.404204   0.434645   0.465857  0.529747   0.00165154
z_subj(US).17991  0.363928  0.0423021   0.279386   0.335519   0.364211   0.392388  0.448779   0.00130405
z_subj(US).18288  0.371136  0.0409447   0.291311   0.343808   0.371441   0.398995  0.450356   0.00116546
z_subj(US).18325  0.402079  0.0439538   0.317694   0.372473   0.401034    0.43049   0.49127   0.00133537
z_subj(US).18333  0.360937   0.040252   0.282367   0.333678   0.359911   0.388353  0.439625   0.00115873
z_subj(US).18334   0.43008  0.0464512   0.341376   0.398219   0.429519    0.46143  0.521831   0.00159821
z_subj(US).18350  0.366526   0.040009   0.290691   0.338951   0.365991   0.393879  0.446564    0.0011289
z_subj(US).18547  0.409818  0.0424198   0.330103   0.380384   0.408868   0.438644  0.496496    0.0012783
z_subj(US).18619  0.394906  0.0430904   0.312967   0.365178   0.393965   0.423746  0.481198   0.00130201
z_subj(US).18864  0.421335  0.0452936   0.333328    0.39093   0.420558   0.450583  0.513507   0.00165044
z_subj(US).18919  0.411961  0.0452271   0.324218   0.380967   0.411842   0.442769  0.502233   0.00161131
z_subj(US).18977  0.345765  0.0414032   0.263604   0.317715   0.345875   0.374291  0.425697   0.00134172
z_subj(US).18978   0.43191  0.0470416   0.341187   0.400029   0.431063   0.463638   0.52583   0.00188955
z_subj(US).18979  0.407369  0.0436133   0.324149   0.376883   0.406621   0.436255  0.497258   0.00151197
z_subj(US).18988  0.403893  0.0427819   0.323586   0.375016   0.402961   0.431537  0.492488   0.00136715
z_subj(US).19686  0.399859  0.0421577   0.319097   0.370796   0.398809   0.427977  0.486289   0.00140767
z_subj(US).19687  0.362256  0.0403855   0.283779   0.335166   0.361668    0.38948   0.44198    0.0011899
DIC: 784.850834
deviance: 698.619830
pD: 86.231004

z values don't appear to significantly vary