The function ltcmt conducts Line x Tester analysis for
multiple traits when the data contains only crosses. The
experimental design may be RCBD or Alpha lattice design.
# Load the package
library(gpbStat)
#Load the dataset
data("alphaltcmt")
# View the structure of dataframe.
str(alphaltcmt)
#> spc_tbl_ [60 × 7] (S3: spec_tbl_df/tbl_df/tbl/data.frame)
#> $ replication: chr [1:60] "r1" "r3" "r2" "r4" ...
#> $ block : chr [1:60] "b2" "b2" "b4" "b5" ...
#> $ line : chr [1:60] "DIL 2" "DIL 2" "DIL 2" "DIL 2" ...
#> $ tester : chr [1:60] "DIL-101" "DIL-101" "DIL-101" "DIL-101" ...
#> $ hsw : num [1:60] 25.7 24.5 23.7 25.1 23 ...
#> $ sh : num [1:60] 81.7 83.3 86 84.6 85.5 ...
#> $ gy : num [1:60] 25.9 41 65.7 47.3 30.8 ...
#> - attr(*, "spec")=List of 3
#> ..$ cols :List of 7
#> .. ..$ replication: list()
#> .. .. ..- attr(*, "class")= chr [1:2] "collector_character" "collector"
#> .. ..$ block : list()
#> .. .. ..- attr(*, "class")= chr [1:2] "collector_character" "collector"
#> .. ..$ line : list()
#> .. .. ..- attr(*, "class")= chr [1:2] "collector_character" "collector"
#> .. ..$ tester : list()
#> .. .. ..- attr(*, "class")= chr [1:2] "collector_character" "collector"
#> .. ..$ hsw : list()
#> .. .. ..- attr(*, "class")= chr [1:2] "collector_double" "collector"
#> .. ..$ sh : list()
#> .. .. ..- attr(*, "class")= chr [1:2] "collector_double" "collector"
#> .. ..$ gy : list()
#> .. .. ..- attr(*, "class")= chr [1:2] "collector_double" "collector"
#> ..$ default: list()
#> .. ..- attr(*, "class")= chr [1:2] "collector_guess" "collector"
#> ..$ delim : chr ","
#> ..- attr(*, "class")= chr "col_spec"
#> - attr(*, "problems")=<externalptr>
# Conduct Line x Tester analysis
result = ltcmt(alphaltcmt, replication, line, tester, alphaltcmt[,5:7], block)
#>
#> Analysis of Line x Tester for Multiple traits
#> Warning in sqrt(x): NaNs produced
#> Warning in sqrt(x): NaNs produced
#> Warning in sqrt(x): NaNs produced
#> Warning in sqrt(x): NaNs produced
#> Warning in sqrt(x): NaNs produced
#> Warning in sqrt(x): NaNs produced
# View the output
result
#> $Mean
#> $Mean$hsw
#> Tester
#> Line DIL 102 DIL-101 DIL-103
#> DIL 2 23.1800 24.7525 23.8525
#> DIL 3 25.0975 22.1300 25.4675
#> DIL 5 23.8625 24.4075 22.9050
#> DIL-1 24.3900 24.2800 26.4325
#> DIL-4 26.5250 25.3625 26.3225
#>
#> $Mean$sh
#> Tester
#> Line DIL 102 DIL-101 DIL-103
#> DIL 2 84.6225 83.8950 83.7725
#> DIL 3 84.4600 83.6100 83.0450
#> DIL 5 82.5875 83.0425 84.8300
#> DIL-1 83.8700 82.9375 84.2025
#> DIL-4 84.3250 84.2775 81.8175
#>
#> $Mean$gy
#> Tester
#> Line DIL 102 DIL-101 DIL-103
#> DIL 2 45.3125 44.9575 47.3975
#> DIL 3 54.7700 46.0625 55.0550
#> DIL 5 53.5300 58.2675 53.5525
#> DIL-1 48.8625 54.2675 44.7525
#> DIL-4 52.1400 60.5650 53.7975
#>
#>
#> $ANOVA
#> $ANOVA$hsw
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 3 123.534952 41.178317 5.2008236 0.006007676
#> Blocks within Replication 16 159.578141 9.973634 1.2596705 0.292005429
#> Crosses 14 95.647543 6.831967 0.8628778 0.602918614
#> Lines 4 44.421693 11.105423 1.0220298 0.406231362
#> Testers 2 6.558103 3.279052 0.3017705 0.740992561
#> Lines X Testers 8 44.667747 5.583468 0.5138454 0.839635289
#> Error 26 205.858982 7.917653 NA NA
#> Total 59 584.619618 NA NA NA
#>
#> $ANOVA$sh
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 3 47.847660 15.9492200 5.5792805 0.004311049
#> Blocks within Replication 16 61.895494 3.8684684 1.3532492 0.239549969
#> Crosses 14 39.935293 2.8525210 0.9978553 0.482967180
#> Lines 4 3.050693 0.7626733 0.1864544 0.944255260
#> Testers 2 2.468943 1.2344717 0.3017971 0.740973054
#> Lines X Testers 8 34.415657 4.3019571 1.0517198 0.413116072
#> Error 26 74.324946 2.8586518 NA NA
#> Total 59 224.003393 NA NA NA
#>
#> $ANOVA$gy
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 3 3171.01367 1057.00456 7.6631523 0.0007893935
#> Blocks within Replication 16 2338.12660 146.13291 1.0594455 0.4352040161
#> Crosses 14 1411.65982 100.83284 0.7310257 0.7261397075
#> Lines 4 787.60961 196.90240 0.9741847 0.4310920496
#> Testers 2 48.49009 24.24505 0.1199536 0.8872442280
#> Lines X Testers 8 575.56012 71.94502 0.3559517 0.9380005166
#> Error 26 3586.26808 137.93339 NA NA
#> Total 59 10507.06817 NA NA NA
#>
#>
#> $GCA.Line
#> hsw sh gy
#> DIL 2 -0.6695000 0.41033333 -5.6635000
#> DIL 3 -0.3661667 0.01866667 0.4098333
#> DIL 5 -0.8728333 -0.19966667 3.5640000
#> DIL-1 0.4363333 -0.01633333 -2.2585000
#> DIL-4 1.4721667 -0.21300000 3.9481667
#>
#> $GCA.Tester
#> hsw sh gy
#> DIL 102 0.01316667 0.2866667 -0.6296667
#> DIL-101 -0.41133333 -0.1338333 1.2713333
#> DIL-103 0.39816667 -0.1528333 -0.6416667
#>
#> $SCA
#> $SCA$hsw
#> Tester
#> Line DIL 102 DIL-101 DIL-103
#> DIL 2 -0.7615000 1.2355000 -0.4740000
#> DIL 3 0.8526667 -1.6903333 0.8376667
#> DIL 5 0.1243333 1.0938333 -1.2181667
#> DIL-1 -0.6573333 -0.3428333 1.0001667
#> DIL-4 0.4418333 -0.2961667 -0.1456667
#>
#> $SCA$sh
#> Tester
#> Line DIL 102 DIL-101 DIL-103
#> DIL 2 0.23916667 -0.06783333 -0.1713333
#> DIL 3 0.46833333 0.03883333 -0.5071667
#> DIL 5 -1.18583333 -0.31033333 1.4961667
#> DIL-1 -0.08666667 -0.59866667 0.6853333
#> DIL-4 0.56500000 0.93800000 -1.5030000
#>
#> $SCA$gy
#> Tester
#> Line DIL 102 DIL-101 DIL-103
#> DIL 2 0.053000 -2.203000 2.150000
#> DIL 3 3.437167 -7.171333 3.734167
#> DIL 5 -0.957000 1.879500 -0.922500
#> DIL-1 0.198000 3.702000 -3.900000
#> DIL-4 -2.731167 3.792833 -1.061667
#>
#>
#> $CV
#> hsw sh gy
#> 11.439351 2.020348 22.781566
#>
#> $Genetic.Variance.Covariance.
#> Phenotypic Variance Genotypic Variance Environmental Variance
#> hsw -0.6689343 -8.586587 7.917653
#> sh -0.4155230 -3.274175 2.858652
#> gy -101.1095400 -239.042928 137.933388
#> Phenotypic coefficient of Variation Genotypic coefficient of Variation
#> hsw NaN NaN
#> sh NaN NaN
#> gy NaN NaN
#> Environmental coefficient of Variation Broad sense heritability
#> hsw 11.439351 12.836220
#> sh 2.020348 7.879648
#> gy 22.781566 2.364198
#>
#> $Std.Error
#> S.E. gca for line S.E. gca for tester S.E. sca effect S.E. (gi - gj)line
#> hsw 0.8122835 0.6291921 1.4069162 1.1487423
#> sh 0.4880789 0.3780643 0.8453774 0.6902478
#> gy 3.3903464 2.6261511 5.8722523 4.7946739
#> S.E. (gi - gj)tester S.E. (sij - skl)tester
#> hsw 0.8898120 1.989680
#> sh 0.5346636 1.195544
#> gy 3.7139384 8.304619
#>
#> $C.D.
#> C.D. gca for line C.D. gca for tester C.D. sca effect C.D. (gi - gj)line
#> hsw 1.669673 1.2933228 2.891958 2.361274
#> sh 1.003260 0.7771222 1.737698 1.418825
#> gy 6.968957 5.3981308 12.070587 9.855593
#> C.D. (gi - gj)tester C.D. (sij - skl)tester
#> hsw 1.829035 4.089846
#> sh 1.099017 2.457476
#> gy 7.634110 17.070388
#>
#> $Add.Dom.Var
#> Cov H.S. (line) Cov H.S. (tester) Cov H.S. (average) Cov F.S. (average)
#> hsw 0.4601629 -0.1152208 0.03310414 -0.3374874
#> sh -0.2949403 -0.1533743 -0.03843202 -0.1641164
#> gy 10.4131155 -2.3849984 0.76596517 -10.5696184
#> Addittive Variance(F=0) Addittive Variance(F=1) Dominance Variance(F=0)
#> hsw 0.1324166 0.06620828 -1.1670924
#> sh -0.1537281 -0.07686404 0.7216527
#> gy 3.0638607 1.53193033 -32.9941861
#> Dominance Variance(F=1)
#> hsw -0.5835462
#> sh 0.3608263
#> gy -16.4970931
#>
#> $Contribution.of.Line.Tester
#> Lines Tester Line x Tester
#> hsw 46.443110 6.856531 46.70036
#> sh 7.639091 6.182359 86.17855
#> gy 55.793159 3.434970 40.77187# Load the package
library(gpbStat)
#Load the dataset
data("rcbdltcmt")
# View the structure of dataframe.
str(rcbdltc)
#> tibble [60 × 4] (S3: tbl_df/tbl/data.frame)
#> $ replication: num [1:60] 1 2 3 4 1 2 3 4 1 2 ...
#> $ line : num [1:60] 1 1 1 1 1 1 1 1 1 1 ...
#> $ tester : num [1:60] 6 6 6 6 7 7 7 7 8 8 ...
#> $ yield : num [1:60] 74.4 70.9 60.9 68 91.8 ...
# Conduct Line x Tester analysis
result1 = ltcmt(rcbdltcmt, replication, line, tester, rcbdltcmt[,4:5])
# View the output
result1
#> $Mean
#> $Mean$ph
#> Tester
#> Line DIL-101 DIL-102 DIL-103
#> DIL 2 197.75 177.50 177.25
#> DIL 4 202.00 169.80 188.00
#> DIL- 3 183.25 172.00 171.25
#> DIL-1 175.50 197.75 202.00
#> DIL-5 168.40 188.25 184.65
#>
#> $Mean$eh
#> Tester
#> Line DIL-101 DIL-102 DIL-103
#> DIL 2 100.50 90.00 91.500
#> DIL 4 97.25 79.50 95.500
#> DIL- 3 88.00 81.00 80.000
#> DIL-1 87.00 102.25 102.500
#> DIL-5 72.25 71.45 80.675
#>
#>
#> $ANOVA
#> $ANOVA$ph
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 3 442.4927 147.4976 0.5028866 0.68235896
#> Crosses 14 7885.4240 563.2446 1.9203581 0.05197320
#> Lines 4 1816.0907 454.0227 1.6010303 0.19053280
#> Testers 2 213.1320 106.5660 0.3757861 0.68888394
#> Lines X Testers 8 5856.2013 732.0252 2.5813568 0.02068038
#> Error 42 12318.6773 293.3018 NA NA
#> Total 59 20646.5940 NA NA NA
#>
#> $ANOVA$eh
#> Df Sum Sq Mean Sq F value Pr(>F)
#> Replication 3 162.4298 54.14328 0.6740871 5.727648e-01
#> Crosses 14 5957.8783 425.56274 5.2982817 1.239227e-05
#> Lines 4 3942.9167 985.72917 12.5449584 6.156545e-07
#> Testers 2 302.4323 151.21617 1.9244642 1.577768e-01
#> Lines X Testers 8 1712.5293 214.06617 2.7243296 1.541154e-02
#> Error 42 3373.4777 80.32090 NA NA
#> Total 59 9493.7858 NA NA NA
#>
#>
#> $GCA.Line
#> ph eh
#> DIL 2 0.4766667 6.041667
#> DIL 4 2.9100000 2.791667
#> DIL- 3 -8.1900000 -4.958333
#> DIL-1 8.0600000 9.291667
#> DIL-5 -3.2566667 -13.166667
#>
#> $GCA.Tester
#> ph eh
#> DIL-101 1.69 1.041667
#> DIL-102 -2.63 -3.118333
#> DIL-103 0.94 2.076667
#>
#> $SCA
#> $SCA$ph
#> Tester
#> Line DIL-101 DIL-102 DIL-103
#> DIL 2 11.89333 -4.036667 -7.856667
#> DIL 4 13.71000 -14.170000 0.460000
#> DIL- 3 6.06000 -0.870000 -5.190000
#> DIL-1 -17.94000 8.630000 9.310000
#> DIL-5 -13.72333 10.446667 3.276667
#>
#> $SCA$eh
#> Tester
#> Line DIL-101 DIL-102 DIL-103
#> DIL 2 5.458333 -0.8816667 -4.576667
#> DIL 4 5.458333 -8.1316667 2.673333
#> DIL- 3 3.958333 1.1183333 -5.076667
#> DIL-1 -11.291667 8.1183333 3.173333
#> DIL-5 -3.583333 -0.2233333 3.806667
#>
#>
#> $CV
#> [1] 9.323348 10.189134
#>
#> $Genetic.Variance.Covariance
#> Phenotypic Variance Genotypic Variance Environmental Variance
#> ph 397.2386 103.93675 293.3018
#> eh 173.1758 92.85487 80.3209
#> Phenotypic coefficient of Variation Genotypic coefficient of Variation
#> ph 10.85026 5.550078
#> eh 14.96120 10.955327
#> Environmental coefficient of Variation Broad sense heritability
#> ph 9.323348 0.2616482
#> eh 10.189134 0.5361886
#>
#> $Std.Error
#> S.E. gca for line S.E. gca for tester S.E. sca effect S.E. (gi - gj)line
#> ph 4.943867 3.829503 8.563029 6.991684
#> eh 2.587162 2.004007 4.481096 3.658800
#> S.E. (gi - gj)tester S.E. (sij - skl)tester
#> ph 5.415735 12.109951
#> eh 2.834094 6.337227
#>
#> $C.D.
#> C.D. gca for line C.D. gca for tester C.D. sca effect C.D. (gi - gj)line
#> ph 9.892655 7.662817 17.134581 13.990327
#> eh 5.176900 4.010009 8.966653 7.321242
#> C.D. (gi - gj)tester C.D. (sij - skl)tester
#> ph 10.836860 24.23196
#> eh 5.671009 12.68076
#>
#> $Add.Dom.Var
#> Cov H.S. (line) Cov H.S. (tester) Cov H.S. (average) Cov F.S. (average)
#> ph -23.16688 -31.27296 -4.475243 37.37585
#> eh 64.30525 -3.14250 5.607864 88.76549
#> Addittive Variance(F=0) Addittive Variance(F=1) Dominance Variance(F=0)
#> ph -17.90097 -8.950486 219.36166
#> eh 22.43145 11.215727 66.87263
#> Dominance Variance(F=1)
#> ph 109.68083
#> eh 33.43632
#>
#> $Contribution.of.Line.Tester
#> Lines Tester Line x Tester
#> ph 23.03098 2.702860 74.26616
#> eh 66.17988 5.076175 28.74395