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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

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
Health stats visible at Monitor.