Computing subscores using Haberman's method based on observed total scores.
subscore.x.RdThis function estimates true subscores based on observed total scores using the method introduced by Haberman (2008) <doi:10.3102/1076998607302636>.
Value
- summary
Summary of obtained subscores (e.g., mean, sd).
- PRMSE
PRMSEs of obtained subscores (for Haberman's methods only).
- subscore.original
Original observed subscores and total score.
- subscore.x
Subscores that are estimated based on the observed total score.
References
Haberman, S. J. (2008). "When can subscores have value?." Journal of Educational and Behavioral Statistics, 33(2), 204-229.doi:10.3102/1076998607302636
Examples
test.data<-data.prep(scored.data,c(3,15,15,20),
c("Algebra","Geometry","Measurement", "Math"))
subscore.x(test.data)
#> $summary
#> Orig.mean Orig.sd subscore.x.mean subscore.x.sd
#> Algebra 9.773333 3.662153 9.773333 3.205978
#> Geometry 9.100000 3.626432 9.100000 3.132737
#> Measurement 13.060000 4.539506 13.060000 4.009099
#>
#> $Correlation
#> Algebra Geometry Measurement Math
#> Algebra 1.0000000 0.8143313 0.8336757 0.9357667
#> Geometry 0.8143313 1.0000000 0.8198970 0.9295419
#> Measurement 0.8336757 0.8198970 1.0000000 0.9507132
#> Math 0.9357667 0.9295419 0.9507132 1.0000000
#>
#> $Disattenuated.correlation
#> Algebra Geometry Measurement
#> Algebra 0.8169114 1.0081315 1.0096427
#> Geometry 0.8143313 0.7987169 1.0042016
#> Measurement 0.8336757 0.8198970 0.8346106
#>
#> $PRMSE
#> Original.reliability PRMSE.x
#> Algebra 0.8169114 0.9381521
#> Geometry 0.7987169 0.9343207
#> Measurement 0.8346106 0.9345284
#> Math 0.9311719 NA
#>
#> $subscore.original
#> Algebra Geometry Measurement Math
#> [1,] 15 15 20 50
#> [2,] 11 10 14 35
#> [3,] 13 13 20 46
#> [4,] 10 11 18 39
#> [5,] 9 11 15 35
#> [6,] 10 12 17 39
#> [7,] 10 11 18 39
#> [8,] 10 10 13 33
#> [9,] 13 11 17 41
#> [10,] 14 11 19 44
#> [11,] 12 12 16 40
#> [12,] 10 10 11 31
#> [13,] 11 12 15 38
#> [14,] 11 10 12 33
#> [15,] 12 13 13 38
#> [16,] 9 9 12 30
#> [17,] 9 5 10 24
#> [18,] 10 9 15 34
#> [19,] 10 8 13 31
#> [20,] 11 13 16 40
#> [21,] 13 11 13 37
#> [22,] 14 15 19 48
#> [23,] 14 15 19 48
#> [24,] 11 13 17 41
#> [25,] 12 11 17 40
#> [26,] 11 12 15 38
#> [27,] 13 12 18 43
#> [28,] 14 11 18 43
#> [29,] 15 13 17 45
#> [30,] 15 13 18 46
#> [31,] 14 11 17 42
#> [32,] 12 13 16 41
#> [33,] 12 13 19 44
#> [34,] 8 5 13 26
#> [35,] 13 13 18 44
#> [36,] 11 13 14 38
#> [37,] 14 14 19 47
#> [38,] 8 5 13 26
#> [39,] 14 13 20 47
#> [40,] 12 10 12 34
#> [41,] 14 11 18 43
#> [42,] 11 11 17 39
#> [43,] 15 14 18 47
#> [44,] 15 13 17 45
#> [45,] 14 10 17 41
#> [46,] 13 13 18 44
#> [47,] 12 10 19 41
#> [48,] 11 13 18 42
#> [49,] 12 8 14 34
#> [50,] 10 13 17 40
#> [51,] 13 14 16 43
#> [52,] 14 12 16 42
#> [53,] 15 13 19 47
#> [54,] 13 13 16 42
#> [55,] 12 13 16 41
#> [56,] 14 12 15 41
#> [57,] 15 8 18 41
#> [58,] 14 14 20 48
#> [59,] 13 13 17 43
#> [60,] 15 13 19 47
#> [61,] 14 13 19 46
#> [62,] 11 10 14 35
#> [63,] 11 5 11 27
#> [64,] 8 8 12 28
#> [65,] 2 2 4 8
#> [66,] 7 6 5 18
#> [67,] 10 7 8 25
#> [68,] 15 15 18 48
#> [69,] 6 7 10 23
#> [70,] 13 11 15 39
#> [71,] 7 2 7 16
#> [72,] 8 5 8 21
#> [73,] 12 10 15 37
#> [74,] 9 7 11 27
#> [75,] 8 9 16 33
#> [76,] 8 2 8 18
#> [77,] 10 9 12 31
#> [78,] 5 7 10 22
#> [79,] 5 4 4 13
#> [80,] 12 11 18 41
#> [81,] 4 7 11 22
#> [82,] 13 12 12 37
#> [83,] 8 5 8 21
#> [84,] 7 9 15 31
#> [85,] 7 8 10 25
#> [86,] 1 2 6 9
#> [87,] 8 7 10 25
#> [88,] 3 2 9 14
#> [89,] 7 10 14 31
#> [90,] 5 8 6 19
#> [91,] 2 4 2 8
#> [92,] 3 4 9 16
#> [93,] 6 4 5 15
#> [94,] 5 5 8 18
#> [95,] 9 10 8 27
#> [96,] 13 11 17 41
#> [97,] 7 1 5 13
#> [98,] 2 3 6 11
#> [99,] 7 8 11 26
#> [100,] 10 10 14 34
#> [101,] 10 9 13 32
#> [102,] 4 2 8 14
#> [103,] 5 1 9 15
#> [104,] 10 10 9 29
#> [105,] 14 13 17 44
#> [106,] 8 8 10 26
#> [107,] 10 11 16 37
#> [108,] 6 3 9 18
#> [109,] 9 9 13 31
#> [110,] 13 12 17 42
#> [111,] 9 6 16 31
#> [112,] 7 4 11 22
#> [113,] 12 11 13 36
#> [114,] 13 11 14 38
#> [115,] 13 10 13 36
#> [116,] 2 5 7 14
#> [117,] 5 4 8 17
#> [118,] 9 5 11 25
#> [119,] 12 12 14 38
#> [120,] 3 4 4 11
#> [121,] 6 5 14 25
#> [122,] 3 4 4 11
#> [123,] 7 8 7 22
#> [124,] 5 4 6 15
#> [125,] 10 7 8 25
#> [126,] 14 10 18 42
#> [127,] 14 12 19 45
#> [128,] 10 5 8 23
#> [129,] 13 12 15 40
#> [130,] 14 11 20 45
#> [131,] 8 11 16 35
#> [132,] 4 2 7 13
#> [133,] 12 11 17 40
#> [134,] 9 9 14 32
#> [135,] 13 9 13 35
#> [136,] 7 10 14 31
#> [137,] 11 10 9 30
#> [138,] 10 10 13 33
#> [139,] 3 6 7 16
#> [140,] 5 7 5 17
#> [141,] 5 9 10 24
#> [142,] 5 5 5 15
#> [143,] 3 6 7 16
#> [144,] 6 8 5 19
#> [145,] 9 12 14 35
#> [146,] 4 4 9 17
#> [147,] 11 14 13 38
#> [148,] 5 7 11 23
#> [149,] 9 2 10 21
#> [150,] 14 12 17 43
#>
#> $subscore.x
#> Subscore.x.Algebra Subscore.x.Geometry Subscore.x.Measurement
#> [1,] 14.985083 14.192685 19.577330
#> [2,] 10.657984 9.964441 14.166263
#> [3,] 13.831190 13.065153 18.134379
#> [4,] 11.811877 11.091973 15.609214
#> [5,] 10.657984 9.964441 14.166263
#> [6,] 11.811877 11.091973 15.609214
#> [7,] 11.811877 11.091973 15.609214
#> [8,] 10.081038 9.400675 13.444787
#> [9,] 12.388824 11.655739 16.330690
#> [10,] 13.254243 12.501387 17.412903
#> [11,] 12.100351 11.373856 15.969952
#> [12,] 9.504092 8.836909 12.723311
#> [13,] 11.523404 10.810090 15.248476
#> [14,] 10.081038 9.400675 13.444787
#> [15,] 11.523404 10.810090 15.248476
#> [16,] 9.215618 8.555026 12.362574
#> [17,] 7.484779 6.863729 10.198147
#> [18,] 10.369511 9.682558 13.805525
#> [19,] 9.504092 8.836909 12.723311
#> [20,] 12.100351 11.373856 15.969952
#> [21,] 11.234931 10.528207 14.887738
#> [22,] 14.408136 13.628919 18.855855
#> [23,] 14.408136 13.628919 18.855855
#> [24,] 12.388824 11.655739 16.330690
#> [25,] 12.100351 11.373856 15.969952
#> [26,] 11.523404 10.810090 15.248476
#> [27,] 12.965770 12.219505 17.052165
#> [28,] 12.965770 12.219505 17.052165
#> [29,] 13.542717 12.783270 17.773641
#> [30,] 13.831190 13.065153 18.134379
#> [31,] 12.677297 11.937622 16.691428
#> [32,] 12.388824 11.655739 16.330690
#> [33,] 13.254243 12.501387 17.412903
#> [34,] 8.061726 7.427495 10.919622
#> [35,] 13.254243 12.501387 17.412903
#> [36,] 11.523404 10.810090 15.248476
#> [37,] 14.119663 13.347036 18.495117
#> [38,] 8.061726 7.427495 10.919622
#> [39,] 14.119663 13.347036 18.495117
#> [40,] 10.369511 9.682558 13.805525
#> [41,] 12.965770 12.219505 17.052165
#> [42,] 11.811877 11.091973 15.609214
#> [43,] 14.119663 13.347036 18.495117
#> [44,] 13.542717 12.783270 17.773641
#> [45,] 12.388824 11.655739 16.330690
#> [46,] 13.254243 12.501387 17.412903
#> [47,] 12.388824 11.655739 16.330690
#> [48,] 12.677297 11.937622 16.691428
#> [49,] 10.369511 9.682558 13.805525
#> [50,] 12.100351 11.373856 15.969952
#> [51,] 12.965770 12.219505 17.052165
#> [52,] 12.677297 11.937622 16.691428
#> [53,] 14.119663 13.347036 18.495117
#> [54,] 12.677297 11.937622 16.691428
#> [55,] 12.388824 11.655739 16.330690
#> [56,] 12.388824 11.655739 16.330690
#> [57,] 12.388824 11.655739 16.330690
#> [58,] 14.408136 13.628919 18.855855
#> [59,] 12.965770 12.219505 17.052165
#> [60,] 14.119663 13.347036 18.495117
#> [61,] 13.831190 13.065153 18.134379
#> [62,] 10.657984 9.964441 14.166263
#> [63,] 8.350199 7.709377 11.280360
#> [64,] 8.638672 7.991260 11.641098
#> [65,] 2.869208 2.353602 4.426341
#> [66,] 5.753940 5.172431 8.033720
#> [67,] 7.773252 7.145612 10.558884
#> [68,] 14.408136 13.628919 18.855855
#> [69,] 7.196306 6.581846 9.837409
#> [70,] 11.811877 11.091973 15.609214
#> [71,] 5.176994 4.608665 7.312244
#> [72,] 6.619360 6.018080 9.115933
#> [73,] 11.234931 10.528207 14.887738
#> [74,] 8.350199 7.709377 11.280360
#> [75,] 10.081038 9.400675 13.444787
#> [76,] 5.753940 5.172431 8.033720
#> [77,] 9.504092 8.836909 12.723311
#> [78,] 6.907833 6.299963 9.476671
#> [79,] 4.311574 3.763016 6.230030
#> [80,] 12.388824 11.655739 16.330690
#> [81,] 6.907833 6.299963 9.476671
#> [82,] 11.234931 10.528207 14.887738
#> [83,] 6.619360 6.018080 9.115933
#> [84,] 9.504092 8.836909 12.723311
#> [85,] 7.773252 7.145612 10.558884
#> [86,] 3.157681 2.635485 4.787079
#> [87,] 7.773252 7.145612 10.558884
#> [88,] 4.600047 4.044899 6.590768
#> [89,] 9.504092 8.836909 12.723311
#> [90,] 6.042413 5.454314 8.394457
#> [91,] 2.869208 2.353602 4.426341
#> [92,] 5.176994 4.608665 7.312244
#> [93,] 4.888520 4.326782 6.951506
#> [94,] 5.753940 5.172431 8.033720
#> [95,] 8.350199 7.709377 11.280360
#> [96,] 12.388824 11.655739 16.330690
#> [97,] 4.311574 3.763016 6.230030
#> [98,] 3.734628 3.199250 5.508555
#> [99,] 8.061726 7.427495 10.919622
#> [100,] 10.369511 9.682558 13.805525
#> [101,] 9.792565 9.118792 13.084049
#> [102,] 4.600047 4.044899 6.590768
#> [103,] 4.888520 4.326782 6.951506
#> [104,] 8.927145 8.273143 12.001836
#> [105,] 13.254243 12.501387 17.412903
#> [106,] 8.061726 7.427495 10.919622
#> [107,] 11.234931 10.528207 14.887738
#> [108,] 5.753940 5.172431 8.033720
#> [109,] 9.504092 8.836909 12.723311
#> [110,] 12.677297 11.937622 16.691428
#> [111,] 9.504092 8.836909 12.723311
#> [112,] 6.907833 6.299963 9.476671
#> [113,] 10.946458 10.246324 14.527001
#> [114,] 11.523404 10.810090 15.248476
#> [115,] 10.946458 10.246324 14.527001
#> [116,] 4.600047 4.044899 6.590768
#> [117,] 5.465467 4.890548 7.672982
#> [118,] 7.773252 7.145612 10.558884
#> [119,] 11.523404 10.810090 15.248476
#> [120,] 3.734628 3.199250 5.508555
#> [121,] 7.773252 7.145612 10.558884
#> [122,] 3.734628 3.199250 5.508555
#> [123,] 6.907833 6.299963 9.476671
#> [124,] 4.888520 4.326782 6.951506
#> [125,] 7.773252 7.145612 10.558884
#> [126,] 12.677297 11.937622 16.691428
#> [127,] 13.542717 12.783270 17.773641
#> [128,] 7.196306 6.581846 9.837409
#> [129,] 12.100351 11.373856 15.969952
#> [130,] 13.542717 12.783270 17.773641
#> [131,] 10.657984 9.964441 14.166263
#> [132,] 4.311574 3.763016 6.230030
#> [133,] 12.100351 11.373856 15.969952
#> [134,] 9.792565 9.118792 13.084049
#> [135,] 10.657984 9.964441 14.166263
#> [136,] 9.504092 8.836909 12.723311
#> [137,] 9.215618 8.555026 12.362574
#> [138,] 10.081038 9.400675 13.444787
#> [139,] 5.176994 4.608665 7.312244
#> [140,] 5.465467 4.890548 7.672982
#> [141,] 7.484779 6.863729 10.198147
#> [142,] 4.888520 4.326782 6.951506
#> [143,] 5.176994 4.608665 7.312244
#> [144,] 6.042413 5.454314 8.394457
#> [145,] 10.657984 9.964441 14.166263
#> [146,] 5.465467 4.890548 7.672982
#> [147,] 11.523404 10.810090 15.248476
#> [148,] 7.196306 6.581846 9.837409
#> [149,] 6.619360 6.018080 9.115933
#> [150,] 12.965770 12.219505 17.052165
#>
subscore.x(test.data)$summary
#> Orig.mean Orig.sd subscore.x.mean subscore.x.sd
#> Algebra 9.773333 3.662153 9.773333 3.205978
#> Geometry 9.100000 3.626432 9.100000 3.132737
#> Measurement 13.060000 4.539506 13.060000 4.009099
subscore.x(test.data)$PRMSE
#> Original.reliability PRMSE.x
#> Algebra 0.8169114 0.9381521
#> Geometry 0.7987169 0.9343207
#> Measurement 0.8346106 0.9345284
#> Math 0.9311719 NA
subscore.x(test.data)$Correlation
#> Algebra Geometry Measurement Math
#> Algebra 1.0000000 0.8143313 0.8336757 0.9357667
#> Geometry 0.8143313 1.0000000 0.8198970 0.9295419
#> Measurement 0.8336757 0.8198970 1.0000000 0.9507132
#> Math 0.9357667 0.9295419 0.9507132 1.0000000
subscore.x(test.data)$Disattenuated.correlation
#> Algebra Geometry Measurement
#> Algebra 0.8169114 1.0081315 1.0096427
#> Geometry 0.8143313 0.7987169 1.0042016
#> Measurement 0.8336757 0.8198970 0.8346106
subscore.x(test.data)$subscore.x
#> Subscore.x.Algebra Subscore.x.Geometry Subscore.x.Measurement
#> [1,] 14.985083 14.192685 19.577330
#> [2,] 10.657984 9.964441 14.166263
#> [3,] 13.831190 13.065153 18.134379
#> [4,] 11.811877 11.091973 15.609214
#> [5,] 10.657984 9.964441 14.166263
#> [6,] 11.811877 11.091973 15.609214
#> [7,] 11.811877 11.091973 15.609214
#> [8,] 10.081038 9.400675 13.444787
#> [9,] 12.388824 11.655739 16.330690
#> [10,] 13.254243 12.501387 17.412903
#> [11,] 12.100351 11.373856 15.969952
#> [12,] 9.504092 8.836909 12.723311
#> [13,] 11.523404 10.810090 15.248476
#> [14,] 10.081038 9.400675 13.444787
#> [15,] 11.523404 10.810090 15.248476
#> [16,] 9.215618 8.555026 12.362574
#> [17,] 7.484779 6.863729 10.198147
#> [18,] 10.369511 9.682558 13.805525
#> [19,] 9.504092 8.836909 12.723311
#> [20,] 12.100351 11.373856 15.969952
#> [21,] 11.234931 10.528207 14.887738
#> [22,] 14.408136 13.628919 18.855855
#> [23,] 14.408136 13.628919 18.855855
#> [24,] 12.388824 11.655739 16.330690
#> [25,] 12.100351 11.373856 15.969952
#> [26,] 11.523404 10.810090 15.248476
#> [27,] 12.965770 12.219505 17.052165
#> [28,] 12.965770 12.219505 17.052165
#> [29,] 13.542717 12.783270 17.773641
#> [30,] 13.831190 13.065153 18.134379
#> [31,] 12.677297 11.937622 16.691428
#> [32,] 12.388824 11.655739 16.330690
#> [33,] 13.254243 12.501387 17.412903
#> [34,] 8.061726 7.427495 10.919622
#> [35,] 13.254243 12.501387 17.412903
#> [36,] 11.523404 10.810090 15.248476
#> [37,] 14.119663 13.347036 18.495117
#> [38,] 8.061726 7.427495 10.919622
#> [39,] 14.119663 13.347036 18.495117
#> [40,] 10.369511 9.682558 13.805525
#> [41,] 12.965770 12.219505 17.052165
#> [42,] 11.811877 11.091973 15.609214
#> [43,] 14.119663 13.347036 18.495117
#> [44,] 13.542717 12.783270 17.773641
#> [45,] 12.388824 11.655739 16.330690
#> [46,] 13.254243 12.501387 17.412903
#> [47,] 12.388824 11.655739 16.330690
#> [48,] 12.677297 11.937622 16.691428
#> [49,] 10.369511 9.682558 13.805525
#> [50,] 12.100351 11.373856 15.969952
#> [51,] 12.965770 12.219505 17.052165
#> [52,] 12.677297 11.937622 16.691428
#> [53,] 14.119663 13.347036 18.495117
#> [54,] 12.677297 11.937622 16.691428
#> [55,] 12.388824 11.655739 16.330690
#> [56,] 12.388824 11.655739 16.330690
#> [57,] 12.388824 11.655739 16.330690
#> [58,] 14.408136 13.628919 18.855855
#> [59,] 12.965770 12.219505 17.052165
#> [60,] 14.119663 13.347036 18.495117
#> [61,] 13.831190 13.065153 18.134379
#> [62,] 10.657984 9.964441 14.166263
#> [63,] 8.350199 7.709377 11.280360
#> [64,] 8.638672 7.991260 11.641098
#> [65,] 2.869208 2.353602 4.426341
#> [66,] 5.753940 5.172431 8.033720
#> [67,] 7.773252 7.145612 10.558884
#> [68,] 14.408136 13.628919 18.855855
#> [69,] 7.196306 6.581846 9.837409
#> [70,] 11.811877 11.091973 15.609214
#> [71,] 5.176994 4.608665 7.312244
#> [72,] 6.619360 6.018080 9.115933
#> [73,] 11.234931 10.528207 14.887738
#> [74,] 8.350199 7.709377 11.280360
#> [75,] 10.081038 9.400675 13.444787
#> [76,] 5.753940 5.172431 8.033720
#> [77,] 9.504092 8.836909 12.723311
#> [78,] 6.907833 6.299963 9.476671
#> [79,] 4.311574 3.763016 6.230030
#> [80,] 12.388824 11.655739 16.330690
#> [81,] 6.907833 6.299963 9.476671
#> [82,] 11.234931 10.528207 14.887738
#> [83,] 6.619360 6.018080 9.115933
#> [84,] 9.504092 8.836909 12.723311
#> [85,] 7.773252 7.145612 10.558884
#> [86,] 3.157681 2.635485 4.787079
#> [87,] 7.773252 7.145612 10.558884
#> [88,] 4.600047 4.044899 6.590768
#> [89,] 9.504092 8.836909 12.723311
#> [90,] 6.042413 5.454314 8.394457
#> [91,] 2.869208 2.353602 4.426341
#> [92,] 5.176994 4.608665 7.312244
#> [93,] 4.888520 4.326782 6.951506
#> [94,] 5.753940 5.172431 8.033720
#> [95,] 8.350199 7.709377 11.280360
#> [96,] 12.388824 11.655739 16.330690
#> [97,] 4.311574 3.763016 6.230030
#> [98,] 3.734628 3.199250 5.508555
#> [99,] 8.061726 7.427495 10.919622
#> [100,] 10.369511 9.682558 13.805525
#> [101,] 9.792565 9.118792 13.084049
#> [102,] 4.600047 4.044899 6.590768
#> [103,] 4.888520 4.326782 6.951506
#> [104,] 8.927145 8.273143 12.001836
#> [105,] 13.254243 12.501387 17.412903
#> [106,] 8.061726 7.427495 10.919622
#> [107,] 11.234931 10.528207 14.887738
#> [108,] 5.753940 5.172431 8.033720
#> [109,] 9.504092 8.836909 12.723311
#> [110,] 12.677297 11.937622 16.691428
#> [111,] 9.504092 8.836909 12.723311
#> [112,] 6.907833 6.299963 9.476671
#> [113,] 10.946458 10.246324 14.527001
#> [114,] 11.523404 10.810090 15.248476
#> [115,] 10.946458 10.246324 14.527001
#> [116,] 4.600047 4.044899 6.590768
#> [117,] 5.465467 4.890548 7.672982
#> [118,] 7.773252 7.145612 10.558884
#> [119,] 11.523404 10.810090 15.248476
#> [120,] 3.734628 3.199250 5.508555
#> [121,] 7.773252 7.145612 10.558884
#> [122,] 3.734628 3.199250 5.508555
#> [123,] 6.907833 6.299963 9.476671
#> [124,] 4.888520 4.326782 6.951506
#> [125,] 7.773252 7.145612 10.558884
#> [126,] 12.677297 11.937622 16.691428
#> [127,] 13.542717 12.783270 17.773641
#> [128,] 7.196306 6.581846 9.837409
#> [129,] 12.100351 11.373856 15.969952
#> [130,] 13.542717 12.783270 17.773641
#> [131,] 10.657984 9.964441 14.166263
#> [132,] 4.311574 3.763016 6.230030
#> [133,] 12.100351 11.373856 15.969952
#> [134,] 9.792565 9.118792 13.084049
#> [135,] 10.657984 9.964441 14.166263
#> [136,] 9.504092 8.836909 12.723311
#> [137,] 9.215618 8.555026 12.362574
#> [138,] 10.081038 9.400675 13.444787
#> [139,] 5.176994 4.608665 7.312244
#> [140,] 5.465467 4.890548 7.672982
#> [141,] 7.484779 6.863729 10.198147
#> [142,] 4.888520 4.326782 6.951506
#> [143,] 5.176994 4.608665 7.312244
#> [144,] 6.042413 5.454314 8.394457
#> [145,] 10.657984 9.964441 14.166263
#> [146,] 5.465467 4.890548 7.672982
#> [147,] 11.523404 10.810090 15.248476
#> [148,] 7.196306 6.581846 9.837409
#> [149,] 6.619360 6.018080 9.115933
#> [150,] 12.965770 12.219505 17.052165