How can I compute statistics by decile groups in data.table

Question 1

How about :

> DT[, mean(b), keyby=cut(a,quantile(a,probs=seq(.1,.9,.1)))]
                cut          V1
1:               NA -0.31359818
2:   (-1.05,-0.614] -0.14103182
3:  (-0.614,-0.375] -0.33474492
4: (-0.375,-0.0767]  0.20827735
5:  (-0.0767,0.114]  0.14890251
6:    (0.114,0.377]  0.16685304
7:    (0.377,0.581]  0.07086979
8:    (0.581,0.771]  0.17950572
9:     (0.771,1.18] -0.04951607

To have a look at that NA (and to check the results anyway), I next did :

> DT[, list(mean(b),.N,list(a)), keyby=cut(a,quantile(a,probs=seq(.1,.9,.1)))]
                cut          V1  N                                                                                                                      V3
1:               NA -0.31359818 20                1.59528080213779,1.51178116845085,-2.2146998871775,-1.98935169586337,-1.47075238389927,1.35867955152904,
2:   (-1.05,-0.614] -0.14103182 10        -0.626453810742332,-0.835628612410047,-0.820468384118015,-0.621240580541804,-0.68875569454952,-0.70749515696212,
3:  (-0.614,-0.375] -0.33474492 10        -0.47815005510862,-0.41499456329968,-0.394289953710349,-0.612026393250771,-0.443291873218433,-0.589520946188072,
4: (-0.375,-0.0767]  0.20827735 10      -0.305388387156356,-0.155795506705329,-0.102787727342996,-0.164523596253587,-0.253361680136508,-0.112346212150228,
5:  (-0.0767,0.114]  0.14890251 10 -0.0449336090152309,-0.0161902630989461,0.0745649833651906,-0.0561287395290008,-0.0538050405829051,-0.0593133967111857,
6:    (0.114,0.377]  0.16685304 10             0.183643324222082,0.329507771815361,0.36458196213683,0.341119691424425,0.188792299514343,0.153253338211898,
7:    (0.377,0.581]  0.07086979 10            0.487429052428485,0.575781351653492,0.389843236411431,0.417941560199702,0.387671611559369,0.556663198673657,
8:    (0.581,0.771]  0.17950572 10             0.738324705129217,0.593901321217509,0.61982574789471,0.763175748457544,0.696963375404737,0.768532924515416,
9:     (0.771,1.18] -0.04951607 10              1.12493091814311,0.943836210685299,0.821221195098089,0.918977371608218,0.782136300731067,1.10002537198388,

Aside: I've returned a list column (each cell is itself a vector) there to have a quick look at the values going into the bins, just to check. data.table displays commas when printing (and shows just the first 6 items per cell), but each cell of V3 there is actually a numeric vector.

So the values outside the first and last break are being coded together as NA. It's not obvious to me how to tell cut not to do that. So I just added -Inf and +Inf :

> DT[,list(mean(b),.N),keyby=cut(a,c(-Inf,quantile(a,probs=seq(.1,.9,.1)),+Inf))]
                 cut          V1  N
 1:     (-Inf,-1.05] -0.16938368 10
 2:   (-1.05,-0.614] -0.14103182 10
 3:  (-0.614,-0.375] -0.33474492 10
 4: (-0.375,-0.0767]  0.20827735 10
 5:  (-0.0767,0.114]  0.14890251 10
 6:    (0.114,0.377]  0.16685304 10
 7:    (0.377,0.581]  0.07086979 10
 8:    (0.581,0.771]  0.17950572 10
 9:     (0.771,1.18] -0.04951607 10
10:      (1.18, Inf] -0.45781268 10

That's better. Or alternatively :

> DT[, list(mean(b),.N), keyby=cut(a,quantile(a,probs=seq(0,1,.1)),include=TRUE)]
                 cut          V1  N
 1:    [-2.21,-1.05] -0.16938368 10
 2:   (-1.05,-0.614] -0.14103182 10
 3:  (-0.614,-0.375] -0.33474492 10
 4: (-0.375,-0.0767]  0.20827735 10
 5:  (-0.0767,0.114]  0.14890251 10
 6:    (0.114,0.377]  0.16685304 10
 7:    (0.377,0.581]  0.07086979 10
 8:    (0.581,0.771]  0.17950572 10
 9:     (0.771,1.18] -0.04951607 10
10:       (1.18,2.4] -0.45781268 10

That way you see what the min and max is, rather than it displaying -Inf and +Inf. Notice you need to pass include=TRUE to cut otherwise 11 bins will be returned with only 1 in the first.

Question 2

I do this type of thing a lot, so I wrote a pretty flexible bin_data() method for it in my R package - mltools. It's entirely data.table based and makes use of the new non-equi joins.

To answer your specific question, set Bin1 as a column in DT, then group by Bin1

library(data.table)
library(mltools)

DT[, Bin1 := bin_data(vals=a, bins=seq(.1, .9, .1), binType="quantile")]
DT[, list(mean(b)), keyby=Bin1]

                                        Bin1          V1
1:                                        NA -0.31359818
2:   [-1.05265747329296, -0.613869230708978) -0.14103182
3:  [-0.613869230708978, -0.375342019639661) -0.33474492
4: [-0.375342019639661, -0.0767031289639095)  0.20827735
5:  [-0.0767031289639095, 0.113909160788544)  0.14890251
6:    [0.113909160788544, 0.377079930573521)  0.16685304
7:    [0.377079930573521, 0.581217342522697)  0.07086979
8:    [0.581217342522697, 0.771253599758546)  0.17950572
9:      [0.771253599758546, 1.1810650775142] -0.04951607

You can do other cool stuff too

Make 10 equally-spaced bins by quantile

DT[, Bin2 := bin_data(vals=a, bins=10, binType="quantile")]
DT[, list(mean(b)), keyby=Bin2]

                                         Bin2          V1
 1:     [-2.2146998871775, -1.05265747329296) -0.16938368
 2:   [-1.05265747329296, -0.613869230708978) -0.14103182
 3:  [-0.613869230708978, -0.375342019639661) -0.33474492
 4: [-0.375342019639661, -0.0767031289639095)  0.20827735
 5:  [-0.0767031289639095, 0.113909160788544)  0.14890251
 6:    [0.113909160788544, 0.377079930573521)  0.16685304
 7:    [0.377079930573521, 0.581217342522697)  0.07086979
 8:    [0.581217342522697, 0.771253599758546)  0.17950572
 9:      [0.771253599758546, 1.1810650775142) -0.04951607
10:       [1.1810650775142, 2.40161776050478] -0.45781268

Make the last boundary left-closed right-open

DT[, Bin3 := bin_data(vals=a, bins=10, binType="quantile", boundaryType="lcro)")]  
DT[, list(mean(b)), keyby=Bin2]

 1:                                        NA  0.42510038
 2:     [-2.2146998871775, -1.05265747329296) -0.16938368
 3:   [-1.05265747329296, -0.613869230708978) -0.14103182
 4:  [-0.613869230708978, -0.375342019639661) -0.33474492
 5: [-0.375342019639661, -0.0767031289639095)  0.20827735
 6:  [-0.0767031289639095, 0.113909160788544)  0.14890251
 7:    [0.113909160788544, 0.377079930573521)  0.16685304
 8:    [0.377079930573521, 0.581217342522697)  0.07086979
 9:    [0.581217342522697, 0.771253599758546)  0.17950572
10:      [0.771253599758546, 1.1810650775142) -0.04951607
11:       [1.1810650775142, 2.40161776050478) -0.55591413

Specify your own explicit bins (notice empty bins are returned)

bin_data(dt=DT, binCol="a", bins=seq(-5, 5, 1), returnDT=TRUE)

          Bin         a           b
  1: [-5, -4)        NA          NA
  2: [-4, -3)        NA          NA
  3: [-3, -2) -2.214700 -0.65069635
  4: [-2, -1) -1.989352 -0.17955653
  5: [-2, -1) -1.470752 -0.03763417
 ---                               
100:   [1, 2)  1.586833 -1.20808279
101:   [2, 3)  2.401618  0.42510038
102:   [2, 3)  2.172612  0.20753834
103:   [3, 4)        NA          NA
104:   [4, 5]        NA          NA

Use variable size bins

bin_data(dt=DT, binCol="a", bins=data.table(LB=c(-5, 0, 1), RB=c(0, 1, Inf)), returnDT=TRUE)

          Bin            a           b
  1:  [-5, 0) -0.626453811 -0.62036668
  2:  [-5, 0) -0.835628612 -0.91092165
  3:  [-5, 0) -0.820468384  1.76728727
  4:  [-5, 0) -0.305388387  1.68217608
  5:  [-5, 0) -0.621240581  1.43228224
 ---                               
 95: [1, Inf]  2.172611670  0.20753834
 96: [1, Inf]  1.178086997  0.21992480
 97: [1, Inf]  1.063099837  1.46458731
 98: [1, Inf]  1.207867806  0.40201178
 99: [1, Inf]  1.160402616 -0.73174817
100: [1, Inf]  1.586833455 -1.20808279
          Bin            a           b