ltcmt: Analysing Line x Tester data containing only crosses for multiple traits.

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.

Example: Analyzing Line x Tester data (crosses) laid out in 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

Example: Analyzing Line x Tester data (crosses) laid out in RCBD.

# 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