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Performs a joint analysis of variance to check for the presence of genotype-vs-environment interactions using both randomized complete block and alpha-lattice designs.
Arguments
- .data
The dataset containing the columns related to Environments, Genotypes, replication/block and response variable(s).
- env
The name of the column that contains the levels of the environments. The analysis of variance is computed for each level of this factor.
- gen
The name of the column that contains the levels of the genotypes.
- rep
The name of the column that contains the levels of the replications/blocks.
- resp
The response variable(s). To analyze multiple variables in a single procedure a vector of variables may be used. For example
resp = c(var1, var2, var3).- block
Defaults to
NULL. In this case, a randomized complete block design is considered. If block is informed, then a resolvable alpha-lattice design (Patterson and Williams, 1976) is employed. All effects, except the error, are assumed to be fixed.- verbose
Logical argument. If
verbose = FALSEthe code will run silently.
Value
A list where each element is the result for one variable containing the following objects:
anova: The two-way ANOVA table
model: The model of class
lm.augment: Information about each observation in the dataset. This includes predicted values in the
fittedcolumn, residuals in theresidcolumn, standardized residuals in thestdrescolumn, the diagonal of the 'hat' matrix in thehat, and standard errors for the fitted values in these.fitcolumn.details: A tibble with the following data:
Ngen, the number of genotypes;OVmean, the grand mean;Min, the minimum observed (returning the genotype and replication/block);Maxthe maximum observed,MinGENthe loser winner genotype,MaxGEN, the winner genotype.
References
Patterson, H.D., and E.R. Williams. 1976. A new class of resolvable incomplete block designs. Biometrika 63:83-92.
Author
Tiago Olivoto tiagoolivoto@gmail.com
Examples
# \donttest{
library(metan)
# traditional usage approach
j_an <- anova_joint(data_ge,
env = ENV,
gen = GEN,
rep = REP,
resp = everything())
#> variable GY
#> ---------------------------------------------------------------------------
#> Joint ANOVA table
#> ---------------------------------------------------------------------------
#> Source Df Sum Sq Mean Sq F value Pr(>F)
#> ENV 13.00 279.57 21.5057 62.33 3.90e-17
#> REP(ENV) 28.00 9.66 0.3451 3.57 3.59e-08
#> GEN 9.00 13.00 1.4439 5.41 3.44e-06
#> GEN:ENV 117.00 31.22 0.2668 2.76 1.01e-11
#> ENV/GEN 130.00 310.79 2.3907 24.72 9.58e-95
#> ENV/G1 13.00 32.69 2.5146 26.01 1.90e-39
#> ENV/G10 13.00 42.71 3.2855 33.98 4.72e-48
#> ENV/G2 13.00 34.03 2.6180 27.08 1.11e-40
#> ENV/G3 13.00 30.39 2.3380 24.18 2.83e-37
#> ENV/G4 13.00 26.80 2.0618 21.32 1.06e-33
#> ENV/G5 13.00 23.47 1.8050 18.67 3.66e-30
#> ENV/G6 13.00 22.02 1.6937 17.52 1.47e-28
#> ENV/G7 13.00 21.99 1.6917 17.50 1.58e-28
#> ENV/G8 13.00 32.45 2.4961 25.82 3.18e-39
#> ENV/G9 13.00 44.24 3.4028 35.19 2.97e-49
#> Residuals 252.00 24.37 0.0967 NA NA
#> CV(%) 11.63 NA NA NA NA
#> MSR+/MSR- 6.71 NA NA NA NA
#> OVmean 2.67 NA NA NA NA
#> ---------------------------------------------------------------------------
#>
#> variable HM
#> ---------------------------------------------------------------------------
#> Joint ANOVA table
#> ---------------------------------------------------------------------------
#> Source Df Sum Sq Mean Sq F value Pr(>F)
#> ENV 13.00 5710 439.26 57.22 1.22e-16
#> REP(ENV) 28.00 215 7.68 2.70 2.20e-05
#> GEN 9.00 270 29.98 3.19 1.76e-03
#> GEN:ENV 117.00 1101 9.41 3.31 1.06e-15
#> ENV/GEN 130.00 6811 52.39 18.45 9.92e-81
#> ENV/G1 13.00 621 47.74 16.81 1.50e-27
#> ENV/G10 13.00 1111 85.48 30.10 4.97e-44
#> ENV/G2 13.00 642 49.42 17.40 2.15e-28
#> ENV/G3 13.00 631 48.57 17.10 5.72e-28
#> ENV/G4 13.00 556 42.77 15.06 5.56e-25
#> ENV/G5 13.00 491 37.78 13.30 2.77e-22
#> ENV/G6 13.00 677 52.11 18.35 1.01e-29
#> ENV/G7 13.00 572 44.00 15.49 1.26e-25
#> ENV/G8 13.00 591 45.46 16.01 2.18e-26
#> ENV/G9 13.00 918 70.61 24.86 4.27e-38
#> Residuals 252.00 716 2.84 NA NA
#> CV(%) 3.50 NA NA NA NA
#> MSR+/MSR- 5.24 NA NA NA NA
#> OVmean 48.09 NA NA NA NA
#> ---------------------------------------------------------------------------
#>
#> All variables with significant (p < 0.05) genotype-vs-environment interaction
#> Done!
# Predicted values
get_model_data(j_an)
#> Class of the model: anova_joint
#> Variable extracted: fitted
#> # A tibble: 420 × 6
#> ENV GEN REP factors GY HM
#> <fct> <fct> <fct> <chr> <dbl> <dbl>
#> 1 E1 G1 1 G1_1 2.42 46.5
#> 2 E1 G1 2 G1_2 2.40 46.0
#> 3 E1 G1 3 G1_3 2.27 47.1
#> 4 E1 G2 1 G2_1 2.96 45.4
#> 5 E1 G2 2 G2_2 2.94 44.8
#> 6 E1 G2 3 G2_3 2.81 45.9
#> 7 E1 G3 1 G3_1 2.95 45.9
#> 8 E1 G3 2 G3_2 2.92 45.3
#> 9 E1 G3 3 G3_3 2.80 46.4
#> 10 E1 G4 1 G4_1 2.65 48.3
#> # ℹ 410 more rows
# Details
get_model_data(j_an, "details")
#> Class of the model: anova_joint
#> Variable extracted: details
#> # A tibble: 10 × 3
#> Parameters GY HM
#> <chr> <chr> <chr>
#> 1 Mean "2.67" "48.09"
#> 2 SE "0.05" "0.21"
#> 3 SD "0.92" "4.37"
#> 4 CV "34.56" "9.09"
#> 5 Min "0.67 (G10 in E11)" "38 (G2 in E14)"
#> 6 Max "5.09 (G8 in E5)" "58 (G8 in E11)"
#> 7 MinENV "E11 (1.37)" "E14 (41.03)"
#> 8 MaxENV "E3 (4.06)" "E11 (54.2)"
#> 9 MinGEN "G10 (2.47) " "G2 (46.66) "
#> 10 MaxGEN "G8 (3) " "G5 (49.3) "
# }