Last data update: 2014.03.03

R: Concatenate bma objects
c.bmaR Documentation

Concatenate bma objects

Description

Combines bma objects (resulting from bms). Can be used to split estimation over several machines, or combine the MCMC results obtained from different starting points.

Usage

combine_chains(...)

 ## S3 method for class 'bma'
c(..., recursive = FALSE)

Arguments

...

At least two 'bma' objects (cf. bms)

recursive

retained for compatibility with c method

Details

Aggregates the information obtained from several chains. The result is a 'bma' object (cf. 'Values' in bms) that can be used just as a standard 'bma' object.
Note that combine_chains helps in particular to paralllelize the enumeration of the total model space: A model with K regressors has 2^K potential covariate combinations: With K large (more than 25), this can be pretty time intensive. With the bms arguments start.value and iter, sampling can be done in steps: cf. example 'enumeration' below.

Author(s)

Martin Feldkircher and Stefan Zeugner

See Also

bms for creating bma objects

Check http://bms.zeugner.eu for additional help.

Examples

 data(datafls)
  
 #MCMC case ############################
 model1=bms(datafls,burn=1000,iter=4000,mcmc="bd",start.value=c(20,30,35))
 model2=bms(datafls,burn=1500,iter=7000,mcmc="bd",start.value=c(1,10,15))
 
 model_all=c(model1,model2)
 coef(model_all)
 plot(model_all)
 
 
 
 #splitting enumeration ########################
 
 #standard case with 12 covariates (4096 differnt combinations):
 enum0=bms(datafls[,1:13],mcmc="enumerate")
 
 # now split the task:
 # enum1 does everything from model zero (the first model) to model 1999
 enum1=bms(datafls[,1:13],mcmc="enumerate",start.value=0,iter=1999)
 
 # enum2 does models from index 2000 to the index 3000 (in total 1001 models)
 enum2=bms(datafls[,1:13],mcmc="enumerate",start.value=2000,iter=1000)
 
 # enum3 does models from index 3001 to the end
 enum3=bms(datafls[,1:13],mcmc="enumerate",start.value=3001)
 
 enum_combi=c(enum1,enum2,enum3)
 coef(enum_combi)
 coef(enum0)
 #both enum_combi and enum0 have exactly the same results 
 #(one difference: enum_combi has more 'top models' (1500 instead of 500))

Results


R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
Platform: x86_64-pc-linux-gnu (64-bit)

R is free software and comes with ABSOLUTELY NO WARRANTY.
You are welcome to redistribute it under certain conditions.
Type 'license()' or 'licence()' for distribution details.

R is a collaborative project with many contributors.
Type 'contributors()' for more information and
'citation()' on how to cite R or R packages in publications.

Type 'demo()' for some demos, 'help()' for on-line help, or
'help.start()' for an HTML browser interface to help.
Type 'q()' to quit R.

> library(BMS)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/BMS/c.bma.Rd_%03d_medium.png", width=480, height=480)
> ### Name: c.bma
> ### Title: Concatenate bma objects
> ### Aliases: combine_chains c.bma
> ### Keywords: models
> 
> ### ** Examples
> 
>  data(datafls)
>   
>  #MCMC case ############################
>  model1=bms(datafls,burn=1000,iter=4000,mcmc="bd",start.value=c(20,30,35))
                PIP     Post Mean      Post SD Cond.Pos.Sign Idx
GDP60       1.00000 -1.608178e-02 3.032965e-03    0.00000000  12
Confucian   1.00000  6.089174e-02 1.390316e-02    1.00000000  19
LifeExp     0.98075  8.729354e-04 2.706093e-04    1.00000000  11
EquipInv    0.91975  1.322197e-01 6.427800e-02    1.00000000  38
SubSahara   0.91575 -1.679530e-02 7.396973e-03    0.00000000   7
Mining      0.82600  3.331080e-02 2.049371e-02    1.00000000  13
NequipInv   0.68400  3.488031e-02 2.939511e-02    1.00000000  39
Hindu       0.67500 -4.314928e-02 3.813677e-02    0.00407407  21
EcoOrg      0.65125  1.403726e-03 1.278067e-03    1.00000000  14
Protestants 0.60425 -6.382624e-03 6.639024e-03    0.00000000  25
RuleofLaw   0.59175  7.116776e-03 7.013043e-03    1.00000000  26
LatAmerica  0.58875 -6.017545e-03 6.221842e-03    0.00424628   6
LabForce    0.58875  1.448485e-07 1.435372e-07    0.99490446  29
Muslim      0.52800  5.910678e-03 6.813488e-03    0.99810606  23
BlMktPm     0.47575 -3.563679e-03 4.320894e-03    0.00000000  41
HighEnroll  0.45975 -3.879307e-02 4.923375e-02    0.00000000  30
EthnoL      0.43300  4.743771e-03 6.443617e-03    1.00000000  20
Buddha      0.38725  3.768500e-03 5.949566e-03    1.00000000  17
CivlLib     0.35175 -8.142978e-04 1.433562e-03    0.03624733  34
YrsOpen     0.34475  2.859814e-03 5.749789e-03    0.89412618  15
PrScEnroll  0.32275  5.940581e-03 1.028403e-02    0.97598761  10
Spanish     0.29925  2.663423e-03 5.159970e-03    0.97744361   2
English     0.29650 -1.879917e-03 3.724483e-03    0.00000000  35
WarDummy    0.23000 -8.088676e-04 1.902465e-03    0.00434783   5
French      0.22550  1.645017e-03 3.564330e-03    1.00000000   3
Catholic    0.22425 -4.253123e-04 2.839036e-03    0.35785953  18
Age         0.22375 -7.888752e-06 2.027023e-05    0.01675978  16
PolRights   0.21850 -1.721269e-04 8.508871e-04    0.25629291  33
Abslat      0.21725 -4.176041e-06 6.006711e-05    0.39585731   1
OutwarOr    0.18825 -5.549710e-04 1.437109e-03    0.00531208   8
stdBMP      0.18250 -5.845187e-07 5.268857e-06    0.29863014  40
RFEXDist    0.15950 -5.207810e-06 1.683545e-05    0.04545455  37
Popg        0.15025  8.209603e-03 8.337574e-02    0.60898502  27
Brit        0.14100  5.931238e-04 2.217540e-03    0.78900709   4
PublEdupct  0.12750  2.461075e-02 7.679309e-02    0.99019608  31
PrExports   0.11825 -4.921237e-04 2.449831e-03    0.13530655  24
Jewish      0.10900 -6.875219e-04 4.412089e-03    0.17889908  22
Foreign     0.10175  2.719025e-04 1.487504e-03    0.77886978  36
Area        0.09075  6.283143e-10 1.805018e-07    0.61983471   9
RevnCoup    0.06950 -2.529618e-05 1.277271e-03    0.45323741  32
WorkPop     0.04600 -1.339035e-04 1.686857e-03    0.22826087  28

Mean no. regressors               Draws             Burnins                Time 
          "16.7482"              "4000"              "1000"     "0.758888 secs" 
 No. models visited      Modelspace 2^K           % visited         % Topmodels 
             "1442"           "2.2e+12"           "6.6e-08"                "56" 
           Corr PMP            No. Obs.         Model Prior             g-Prior 
           "0.2069"                "72"     "random / 20.5"               "UIP" 
    Shrinkage-Stats 
        "Av=0.9863" 

Time difference of 0.758888 secs
>  model2=bms(datafls,burn=1500,iter=7000,mcmc="bd",start.value=c(1,10,15))
                   PIP     Post Mean      Post SD Cond.Pos.Sign Idx
GDP60       1.00000000 -1.590151e-02 2.914313e-03    0.00000000  12
Confucian   1.00000000  5.977769e-02 1.367557e-02    1.00000000  19
SubSahara   0.98842857 -1.982018e-02 5.889752e-03    0.00000000   7
LifeExp     0.96957143  8.480364e-04 2.928248e-04    1.00000000  11
Mining      0.83442857  3.506547e-02 2.071799e-02    1.00000000  13
EquipInv    0.81828571  1.080049e-01 6.783300e-02    1.00000000  38
RuleofLaw   0.80000000  1.026599e-02 6.730391e-03    1.00000000  26
Hindu       0.78885714 -5.037836e-02 3.925688e-02    0.00434625  21
LatAmerica  0.76157143 -7.930144e-03 6.062410e-03    0.00018758   6
EcoOrg      0.76114286  1.750638e-03 1.241146e-03    0.99943694  14
NequipInv   0.72771429  3.828002e-02 2.933261e-02    1.00000000  39
Protestants 0.64000000 -7.448722e-03 6.793022e-03    0.00000000  25
LabForce    0.60471429  1.596409e-07 1.534547e-07    0.98866052  29
BlMktPm     0.60471429 -4.628262e-03 4.568936e-03    0.00070872  41
HighEnroll  0.54414286 -4.997965e-02 5.476083e-02    0.00945130  30
EthnoL      0.44271429  4.937741e-03 6.651597e-03    0.99548241  20
Spanish     0.33614286  3.107325e-03 5.450555e-03    0.98682533   2
Muslim      0.32100000  3.610762e-03 6.297493e-03    0.99910992  23
Age         0.29785714 -1.319350e-05 2.485153e-05    0.00000000  16
PublEdupct  0.29671429  6.173146e-02 1.140685e-01    0.99374097  31
Buddha      0.29328571  2.851567e-03 5.547070e-03    1.00000000  17
PolRights   0.27957143 -3.521612e-04 9.001595e-04    0.07256004  33
PrScEnroll  0.26271429  4.420366e-03 9.262979e-03    0.96193583  10
OutwarOr    0.25714286 -7.832003e-04 1.703333e-03    0.01222222   8
English     0.25700000 -1.731715e-03 3.685041e-03    0.00000000  35
French      0.25057143  1.882825e-03 3.982697e-03    0.97377423   3
Catholic    0.24571429 -6.004306e-04 3.299952e-03    0.30290698  18
CivlLib     0.21185714 -4.574767e-04 1.127430e-03    0.03304113  34
Brit        0.20742857  9.788368e-04 2.810361e-03    0.84366391   4
Abslat      0.19028571 -1.239869e-05 5.581074e-05    0.17192192   1
YrsOpen     0.17528571  1.155690e-03 3.987637e-03    0.81907090  15
PrExports   0.16657143 -9.295676e-04 3.370946e-03    0.15608919  24
WarDummy    0.15957143 -4.848127e-04 1.454471e-03    0.00000000   5
stdBMP      0.12271429 -7.150856e-07 4.417257e-06    0.14668219  40
Jewish      0.11914286 -1.826904e-04 3.843626e-03    0.42685851  22
Popg        0.11357143  1.545391e-02 7.515625e-02    0.84905660  27
WorkPop     0.11200000 -4.740670e-04 2.863695e-03    0.17346939  28
RFEXDist    0.10428571 -2.520389e-06 1.243424e-05    0.08356164  37
Foreign     0.08485714  9.068024e-05 1.193260e-03    0.55892256  36
Area        0.07514286 -2.320578e-08 2.099224e-07    0.23193916   9
RevnCoup    0.06271429  5.962213e-06 1.032998e-03    0.62642369  32

Mean no. regressors               Draws             Burnins                Time 
          "17.2894"              "7000"              "1500"    "0.7232931 secs" 
 No. models visited      Modelspace 2^K           % visited         % Topmodels 
             "2227"           "2.2e+12"             "1e-07"                "37" 
           Corr PMP            No. Obs.         Model Prior             g-Prior 
           "0.0106"                "72"     "random / 20.5"               "UIP" 
    Shrinkage-Stats 
        "Av=0.9863" 

Time difference of 0.7232931 secs
>  
>  model_all=c(model1,model2)
>  coef(model_all)
                   PIP     Post Mean      Post SD Cond.Pos.Sign Idx
GDP60       1.00000000 -1.596706e-02 2.959281e-03    0.00000000  12
Confucian   1.00000000  6.018280e-02 1.376920e-02    1.00000000  19
LifeExp     0.97363636  8.570906e-04 2.851985e-04    1.00000000  11
SubSahara   0.96200000 -1.872022e-02 6.639932e-03    0.00000000   7
EquipInv    0.85518182  1.168103e-01 6.757380e-02    1.00000000  38
Mining      0.83136364  3.442741e-02 2.065397e-02    1.00000000  13
Hindu       0.74745455 -4.774960e-02 3.900862e-02    0.00425687  21
RuleofLaw   0.72427273  9.120822e-03 7.000409e-03    1.00000000  26
EcoOrg      0.72118182  1.624488e-03 1.265747e-03    0.99962183  14
NequipInv   0.71181818  3.704376e-02 2.940087e-02    1.00000000  39
LatAmerica  0.69872727 -7.234653e-03 6.189627e-03    0.00143117   6
Protestants 0.62700000 -7.061050e-03 6.756920e-03    0.00000000  25
LabForce    0.59890909  1.542619e-07 1.500930e-07    0.99089253  29
BlMktPm     0.55781818 -4.241141e-03 4.509501e-03    0.00048892  41
HighEnroll  0.51345455 -4.591181e-02 5.309137e-02    0.00637394  30
EthnoL      0.43918182  4.867206e-03 6.577391e-03    0.99710205  20
Muslim      0.39627273  4.447095e-03 6.583505e-03    0.99862354  23
Buddha      0.32745455  3.184998e-03 5.713774e-03    1.00000000  17
Spanish     0.32272727  2.945906e-03 5.350978e-03    0.98366197   2
PrScEnroll  0.28454545  4.973171e-03 9.674462e-03    0.96773163  10
English     0.27136364 -1.785607e-03 3.700119e-03    0.00000000  35
Age         0.27090909 -1.126450e-05 2.342949e-05    0.00503356  16
CivlLib     0.26272727 -5.872298e-04 1.259227e-03    0.03460208  34
PolRights   0.25736364 -2.866942e-04 8.867997e-04    0.12928294  33
French      0.24145455  1.796350e-03 3.837552e-03    0.98268072   3
Catholic    0.23790909 -5.367512e-04 3.141313e-03    0.32174245  18
YrsOpen     0.23690909  1.775372e-03 4.776278e-03    0.85878741  15
PublEdupct  0.23518182  4.823302e-02 1.036504e-01    0.99304213  31
OutwarOr    0.23209091 -7.002078e-04 1.615356e-03    0.01018410   8
Abslat      0.20009091 -9.408634e-06 5.753118e-05    0.26033621   1
WarDummy    0.18518182 -6.026508e-04 1.639102e-03    0.00196367   5
Brit        0.18327273  8.385775e-04 2.616999e-03    0.82837302   4
PrExports   0.14900000 -7.704971e-04 3.075367e-03    0.15009152  24
stdBMP      0.14445455 -6.676067e-07 4.745064e-06    0.21648836  40
Popg        0.12690909  1.281962e-02 7.832268e-02    0.74570201  27
RFEXDist    0.12436364 -3.497633e-06 1.425223e-05    0.06578947  37
Jewish      0.11545455 -3.662655e-04 4.066818e-03    0.34173228  22
Foreign     0.09100000  1.565792e-04 1.310841e-03    0.64835165  36
WorkPop     0.08800000 -3.503712e-04 2.506024e-03    0.18388430  28
Area        0.08081818 -1.453883e-08 2.000549e-07    0.39032621   9
RevnCoup    0.06518182 -5.404477e-06 1.128063e-03    0.55927476  32
>  plot(model_all)
>  
>  
>  
>  #splitting enumeration ########################
>  
>  #standard case with 12 covariates (4096 differnt combinations):
>  enum0=bms(datafls[,1:13],mcmc="enumerate")
                 PIP     Post Mean      Post SD Cond.Pos.Sign Idx
GDP60      0.9999661 -1.948009e-02 3.201047e-03    0.00000000  12
SubSahara  0.9999333 -2.857041e-02 4.991078e-03    0.00000000   7
LifeExp    0.9912818  1.168628e-03 3.052639e-04    0.99999977  11
WarDummy   0.9870859 -1.106952e-02 3.222471e-03    0.00000000   5
LatAmerica 0.9855809 -1.565560e-02 4.496320e-03    0.00000000   6
PrScEnroll 0.2630332  3.671428e-03 8.137266e-03    0.99999771  10
Brit       0.1862789  5.704196e-04 1.826635e-03    0.99926156   4
Abslat     0.1771891 -1.981004e-05 6.971902e-05    0.00542193   1
Spanish    0.1511549  2.446922e-04 2.926712e-03    0.91084062   2
OutwarOr   0.1382977  1.529135e-04 1.187186e-03    0.92267652   8
French     0.1375714 -2.272925e-04 1.791920e-03    0.06822726   3
Area       0.1330138  2.641379e-08 2.549633e-07    0.98159721   9

Mean no. regressors               Draws             Burnins                Time 
           "6.1504"              "4096"                 "0"    "0.3733745 secs" 
 No. models visited      Modelspace 2^K           % visited         % Topmodels 
             "4096"              "4096"               "100"                "12" 
           Corr PMP            No. Obs.         Model Prior             g-Prior 
               "NA"                "72"        "random / 6"               "UIP" 
    Shrinkage-Stats 
        "Av=0.9863" 

Time difference of 0.3733745 secs
>  
>  # now split the task:
>  # enum1 does everything from model zero (the first model) to model 1999
>  enum1=bms(datafls[,1:13],mcmc="enumerate",start.value=0,iter=1999)
                 PIP     Post Mean      Post SD Cond.Pos.Sign Idx
GDP60      0.9999761 -1.966784e-02 3.137932e-03    0.00000000  12
SubSahara  0.9999322 -2.831658e-02 4.920806e-03    0.00000000   7
LifeExp    0.9906952  1.167709e-03 3.065897e-04    0.99999972  11
WarDummy   0.9860885 -1.104015e-02 3.241361e-03    0.00000000   5
LatAmerica 0.9848062 -1.532753e-02 4.361645e-03    0.00000000   6
PrScEnroll 0.2574544  3.676725e-03 8.166954e-03    0.99999715  10
Brit       0.1811703  5.776004e-04 1.820420e-03    0.99999167   4
Spanish    0.1437823  2.286690e-04 2.892770e-03    0.90036166   2
OutwarOr   0.1311783  1.683224e-04 1.163028e-03    0.99197928   8
French     0.1295152 -2.309937e-04 1.750807e-03    0.05971735   3
Area       0.1248893  2.720280e-08 2.483040e-07    0.98117034   9
Abslat     0.0000000  0.000000e+00 0.000000e+00            NA   1

Mean no. regressors               Draws             Burnins                Time 
           "5.9295"              "2000"                 "0"    "0.2333915 secs" 
 No. models visited      Modelspace 2^K           % visited         % Topmodels 
             "2000"              "4096"                "49"                "25" 
           Corr PMP            No. Obs.         Model Prior             g-Prior 
               "NA"                "72"        "random / 6"               "UIP" 
    Shrinkage-Stats 
        "Av=0.9863" 

Time difference of 0.2333915 secs
>  
>  # enum2 does models from index 2000 to the index 3000 (in total 1001 models)
>  enum2=bms(datafls[,1:13],mcmc="enumerate",start.value=2000,iter=1000)
                 PIP     Post Mean      Post SD Cond.Pos.Sign Idx
Spanish    1.0000000  1.720055e-03 6.977639e-03     0.9485941   2
GDP60      0.9999489 -1.885964e-02 3.405390e-03     0.0000000  12
SubSahara  0.9998723 -2.943026e-02 5.218073e-03     0.0000000   7
Abslat     0.9987746 -9.618432e-05 1.342822e-04     0.0159139   1
LifeExp    0.9945354  1.162997e-03 3.075459e-04     1.0000000  11
WarDummy   0.9929087 -1.120479e-02 3.137409e-03     0.0000000   5
LatAmerica 0.9499824 -1.784212e-02 7.239832e-03     0.0000000   6
PrScEnroll 0.3742007  4.790402e-03 8.862937e-03     1.0000000  10
Brit       0.2898725  8.159065e-04 2.236539e-03     0.9983797   4
French     0.2362095 -1.587092e-04 2.442589e-03     0.3663766   3
OutwarOr   0.2361064  1.033924e-04 1.530843e-03     0.5914303   8
Area       0.2358730  3.930291e-08 3.434966e-07     0.9659913   9

Mean no. regressors               Draws             Burnins                Time 
           "8.3083"              "1001"                 "0"    "0.1447463 secs" 
 No. models visited      Modelspace 2^K           % visited         % Topmodels 
             "1001"              "4096"                "24"                "50" 
           Corr PMP            No. Obs.         Model Prior             g-Prior 
               "NA"                "72"        "random / 6"               "UIP" 
    Shrinkage-Stats 
        "Av=0.9863" 

Time difference of 0.1447463 secs
>  
>  # enum3 does models from index 3001 to the end
>  enum3=bms(datafls[,1:13],mcmc="enumerate",start.value=3001)
                    PIP     Post Mean      Post SD Cond.Pos.Sign Idx
Abslat     1.0000000000 -1.153223e-04 1.299134e-04    0.00303879   1
SubSahara  0.9999532601 -2.982125e-02 5.123757e-03    0.00000000   7
GDP60      0.9999128136 -1.855141e-02 3.326949e-03    0.00000000  12
LatAmerica 0.9980913973 -1.702774e-02 4.013571e-03    0.00000000   6
LifeExp    0.9938844956  1.175146e-03 2.969702e-04    1.00000000  11
WarDummy   0.9914452244 -1.120613e-02 3.127916e-03    0.00000000   5
PrScEnroll 0.2695405978  3.386772e-03 7.764374e-03    1.00000000  10
Brit       0.1918295650  4.736739e-04 1.750320e-03    0.99563545   4
French     0.1610445098 -2.217996e-04 1.847473e-03    0.00777334   3
OutwarOr   0.1566219163  7.637330e-05 1.229934e-03    0.70549111   8
Area       0.1559166186  1.898662e-08 2.682484e-07    0.98891462   9
Spanish    0.0001222297  4.705967e-07 1.030573e-04    0.90716254   2

Mean no. regressors               Draws             Burnins                Time 
           "6.9184"              "1095"                 "0"    "0.1339428 secs" 
 No. models visited      Modelspace 2^K           % visited         % Topmodels 
             "1095"              "4096"                "27"                "46" 
           Corr PMP            No. Obs.         Model Prior             g-Prior 
               "NA"                "72"        "random / 6"               "UIP" 
    Shrinkage-Stats 
        "Av=0.9863" 

Time difference of 0.1339428 secs
>  
>  enum_combi=c(enum1,enum2,enum3)
>  coef(enum_combi)
                 PIP     Post Mean      Post SD Cond.Pos.Sign Idx
GDP60      0.9999661 -1.948009e-02 3.201047e-03    0.00000000  12
SubSahara  0.9999333 -2.857041e-02 4.991078e-03    0.00000000   7
LifeExp    0.9912818  1.168628e-03 3.052639e-04    0.99999977  11
WarDummy   0.9870859 -1.106952e-02 3.222471e-03    0.00000000   5
LatAmerica 0.9855809 -1.565560e-02 4.496320e-03    0.00000000   6
PrScEnroll 0.2630332  3.671428e-03 8.137266e-03    0.99999771  10
Brit       0.1862789  5.704196e-04 1.826635e-03    0.99926156   4
Abslat     0.1771891 -1.981004e-05 6.971902e-05    0.00542193   1
Spanish    0.1511549  2.446922e-04 2.926712e-03    0.91084062   2
OutwarOr   0.1382977  1.529135e-04 1.187186e-03    0.92267652   8
French     0.1375714 -2.272925e-04 1.791920e-03    0.06822726   3
Area       0.1330138  2.641379e-08 2.549633e-07    0.98159721   9
>  coef(enum0)
                 PIP     Post Mean      Post SD Cond.Pos.Sign Idx
GDP60      0.9999661 -1.948009e-02 3.201047e-03    0.00000000  12
SubSahara  0.9999333 -2.857041e-02 4.991078e-03    0.00000000   7
LifeExp    0.9912818  1.168628e-03 3.052639e-04    0.99999977  11
WarDummy   0.9870859 -1.106952e-02 3.222471e-03    0.00000000   5
LatAmerica 0.9855809 -1.565560e-02 4.496320e-03    0.00000000   6
PrScEnroll 0.2630332  3.671428e-03 8.137266e-03    0.99999771  10
Brit       0.1862789  5.704196e-04 1.826635e-03    0.99926156   4
Abslat     0.1771891 -1.981004e-05 6.971902e-05    0.00542193   1
Spanish    0.1511549  2.446922e-04 2.926712e-03    0.91084062   2
OutwarOr   0.1382977  1.529135e-04 1.187186e-03    0.92267652   8
French     0.1375714 -2.272925e-04 1.791920e-03    0.06822726   3
Area       0.1330138  2.641379e-08 2.549633e-07    0.98159721   9
>  #both enum_combi and enum0 have exactly the same results 
>  #(one difference: enum_combi has more 'top models' (1500 instead of 500))
> 
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>