Missing values are not allowed by the AMMI, GGE or SREG methods. This function provides several methods to impute missing observations in data from multi-environment trials and to subsequently adjust the mentioned methods.
Usage
imputation(
Data,
genotype = "gen",
environment = "env",
response = "yield",
rep = NULL,
type = "EM-AMMI",
nPC = 2,
initial.values = NA,
precision = 0.01,
maxiter = 1000,
change.factor = 1,
simplified.model = FALSE,
scale = TRUE,
method = "EM",
row.w = NULL,
coeff.ridge = 1,
seed = NULL,
nb.init = 1,
Winf = 0.8,
Wsup = 1
)Arguments
- Data
dataframe containing genotypes, environments, repetitions (if any) and the phenotypic trait of interest. Other variables that will not be used in the analysis can be present.
- genotype
column name containing genotypes.
- environment
column name containing environments.
- response
column name containing the phenotypic trait.
- rep
column name containing replications. If this argument is NULL, there are no replications available in the data. Defaults to NULL.
- type
imputation method. Either "EM-AMMI", "EM-GGE", "EM-SREG", "EM-bSREG", "Gabriel", "Eigenvector", "WGabriel", "EM-PCA". Defaults to "EM-AMMI".
- nPC
number of components used to predict the missing values. Default to 2.
- initial.values
initial values of the missing cells. It can be a single value or a vector of length equal to the number of missing cells.
- precision
threshold for assessing convergence.
- maxiter
maximum number of iteration for the algorithm.
- change.factor
When `change.factor` is equal to 1, the previous approximation is changed with the new values (standard EM). Smaller values can help convergence if changes are cyclic.
- simplified.model
logical. If TRUE, calculates effects only in the first iteration to speed up convergence or help in cases where the regular procedure fails.
- scale
boolean. By default TRUE for "EM-PCA".
- method
"Regularized" or "EM" for "EM-PCA".
- row.w
row weights for "EM-PCA".
- coeff.ridge
ridge coefficient for "EM-PCA".
- seed
integer for random initialization in "EM-PCA".
- nb.init
number of random initializations for "EM-PCA".
- Winf
lower weight for WGabriel.
- Wsup
upper weight for WGabriel.
Details
Often, multi-environment experiments are unbalanced because several genotypes are not tested in some environments. Several methodologies have been proposed in order to solve this lack of balance caused by missing values, some of which are included in this function:
EM-AMMI: an iterative scheme built round the above procedure is used to obtain AMMI imputations from the EM algorithm. The additive parameters are initially set by computing the grand mean, genotype means and environment means obtained from the observed data. The residuals for the observed cells are initialized as the cell mean minus the genotype mean minus the environment mean plus the grand mean, and interactions for the missing positions are initially set to zero. The initial multiplicative parameters are obtained from the SVD of this matrix of residuals, and the missing values are filled by the appropriate AMMI estimates. In subsequent iterations, the usual AMMI procedure is applied to the completed matrix and the missing values are updated by the corresponding AMMI estimates. The arguments used for this method are:initial.values, precision, maxiter, change.factor and simplified.model
EM-GGE: Iterative SVD-based imputation focusing on G+GE.
EM-SREG: Iterative algorithm using the Sites Regression model. Supports variants like standard SVD and Bayesian PCA (EM-bSREG).
Gabriel: combines regression and lower-rank approximation using SVD. This method initially replaces the missing cells by arbitrary values, and subsequently the imputations are refined through an iterative scheme that defines a partition of the matrix for each missing value in turn and uses a linear regression of columns (or rows) to obtain the new imputation. The arguments used for this method is only the dataframe.
WGabriel: is a a modification of Gabriel method that uses weights chosen by cross-validation. The arguments used for this method are Winf and Wsup.
EM-PCA: impute the missing entries of a mixed data using the iterative PCA algorithm. The algorithm first consists imputing missing values with initial values. The second step of the iterative PCA algorithm is to perform PCA on the completed dataset to estimate the parameters. Then, it imputes the missing values with the reconstruction formulae of order nPC (the fitted matrix computed with nPC components for the scores and loadings). These steps of estimation of the parameters via PCA and imputation of the missing values using the fitted matrix are iterate until convergence. The arguments used for this methods are: nPC, scale, method, row.w, coeff.ridge, precision, seed, nb.init and maxiter
References
Paderewski, J. (2013). An R function for imputation of missing cells in two-way data sets by EM-AMMI algorithm. Communications in Biometry and Crop Science 8, 60–69.
Yan, W. (2013). Biplot analysis of incomplete two-way data. Crop Science, 53(1), 48-57. doi:10.2135/cropsci2012.05.0301
Arciniegas-Alarcón, S., García-Peña, M., Krzanowski, W., & Dias, C. T. S. (2014b). An alternative methodology for imputing missing data in trials with genotype-by-environment interaction: some new aspects. Biometrical Letters, 51(2), 75-88. doi:10.2478/bile-2014-0006
Angelini, J., Cervigni, G. D. L., & Quaglino, M. B. (2024). New imputation methodologies for genotype-by-environment data: an extensive study of properties of estimators. Euphytica, 220(6), 92. doi:10.1007/s10681-024-03344-z
Julie Josse, Francois Husson (2016). missMDA: A Package for Handling Missing Values in Multivariate Data Analysis. Journal of Statistical Software 70, 1-31.
Arciniegas-Alarcón S., García-Peña M., Dias C.T.S., Krzanowski W.J. (2010). An alternative methodology for imputing missing data in trials with genotype-by-environment interaction. Biometrical Letters 47, 1–14.
Arciniegas-Alarcón S., García-Peña M., Krzanowski W.J., Dias C.T.S. (2014). An alternative methodology for imputing missing data in trials with genotype-byenvironment interaction: some new aspects. Biometrical Letters 51, 75-88.
Examples
library(geneticae)
# Data without replications
library(agridat)
data(yan.winterwheat)
# generating missing values
yan.winterwheat[1,3]<-NA
yan.winterwheat[3,3]<-NA
yan.winterwheat[2,3]<-NA
imputation(yan.winterwheat, genotype = "gen", environment = "env",
response = "yield", type = "EM-AMMI")
#> BH93 EA93 HW93 ID93 KE93 NN93 OA93 RN93 WP93
#> Ann 4.150120 4.150 2.849 3.084 5.940 4.450 4.351 4.039 2.672
#> Ari 4.035814 4.771 2.912 3.506 5.699 5.152 4.956 4.386 2.938
#> Aug 4.305244 4.578 3.098 3.460 6.070 5.025 4.730 3.900 2.621
#> Cas 4.732000 4.745 3.375 3.904 6.224 5.340 4.226 4.893 3.451
#> Del 4.390000 4.603 3.511 3.848 5.773 5.421 5.147 4.098 2.832
#> Dia 5.178000 4.475 2.990 3.774 6.583 5.045 3.985 4.271 2.776
#> Ena 3.375000 4.175 2.741 3.157 5.342 4.267 4.162 4.063 2.032
#> Fun 4.852000 4.664 4.425 3.952 5.536 5.832 4.168 5.060 3.574
#> Ham 5.038000 4.741 3.508 3.437 5.960 4.859 4.977 4.514 2.859
#> Har 5.195000 4.662 3.596 3.759 5.937 5.345 3.895 4.450 3.300
#> Kar 4.293000 4.530 2.760 3.422 6.142 5.250 4.856 4.137 3.149
#> Kat 3.151000 3.040 2.388 2.350 4.229 4.257 3.384 4.071 2.103
#> Luc 4.104000 3.878 2.302 3.718 4.555 5.149 2.596 4.956 2.886
#> m12 3.340000 3.854 2.419 2.783 4.629 5.090 3.281 3.918 2.561
#> Reb 4.375000 4.701 3.655 3.592 6.189 5.141 3.933 4.208 2.925
#> Ron 4.940000 4.698 2.950 3.898 6.063 5.326 4.302 4.299 3.031
#> Rub 3.786000 4.969 3.379 3.353 4.774 5.304 4.322 4.858 3.382
#> Zav 4.238000 4.654 3.607 3.914 6.641 4.830 5.014 4.363 3.111
# Data with replications
data(plrv)
head(plrv)
#> Genotype Locality Rep WeightPlant WeightPlot Yield
#> 1 102.18 Ayac 1 0.5100000 5.10 18.88889
#> 2 104.22 Ayac 1 0.3450000 2.76 12.77778
#> 3 121.31 Ayac 1 0.5425000 4.34 20.09259
#> 4 141.28 Ayac 1 0.9888889 8.90 36.62551
#> 5 157.26 Ayac 1 0.6250000 5.00 23.14815
#> 6 163.9 Ayac 1 0.5120000 2.56 18.96296
plrv$Yield[plrv$Locality == "Ayac" & plrv$Rep %in% c(1, 2, 3) & plrv$Genotype == '102.18'] <- NA
imputation(plrv, nPC = 2,genotype = "Genotype", environment = "Locality",
response = "Yield", rep ='Rep', type = "EM-AMMI")
#> Ayac Hyo-02 LM-02 LM-03 SR-02 SR-03
#> 102.18 23.55025 28.888889 32.03704 46.77778 13.518519 11.769547
#> 104.22 21.45062 53.518519 39.19753 50.41838 16.049383 7.098765
#> 121.31 23.46022 41.296296 38.39506 63.70370 2.500000 11.255144
#> 141.28 31.84401 60.462963 33.95062 77.56790 19.234568 15.477366
#> 157.26 19.66980 41.388889 45.16049 76.98553 23.950617 14.555556
#> 163.9 17.53792 29.537037 28.88889 32.02949 12.716049 7.795414
#> 221.19 15.41358 32.037037 31.02469 43.45267 8.543210 7.437586
#> 233.11 24.28326 50.555556 29.19753 47.33333 13.148148 7.481481
#> 235.6 29.91358 73.518519 40.37037 56.13580 14.802469 17.067901
#> 241.2 20.44444 36.018519 35.74074 46.24691 11.086420 8.505291
#> 255.7 26.06702 47.037037 32.67901 40.79244 19.185185 17.777778
#> 314.12 17.32510 49.444444 34.50617 57.24588 8.530864 1.987654
#> 317.6 26.61376 53.425926 42.34568 64.01235 14.814815 10.742455
#> 319.20 25.77503 56.666667 32.96296 86.80802 21.209877 9.123457
#> 320.16 30.32922 31.111111 35.28395 43.29012 13.629630 4.444444
#> 342.15 19.89712 40.740741 27.53086 38.80033 17.592593 11.518519
#> 346.2 21.57476 32.685185 25.55556 32.03704 18.024691 13.173280
#> 351.26 31.74897 50.185185 29.25926 72.02407 20.370370 13.106996
#> 364.21 26.63933 52.407407 37.90123 57.06584 13.518519 16.826132
#> 402.7 19.29698 42.500000 31.23457 49.76543 12.839506 9.228395
#> 405.2 28.66735 35.740741 32.34568 43.25926 16.790123 17.116598
#> 406.12 19.58652 59.814815 37.77778 53.58848 13.827160 11.504605
#> 427.7 26.08907 55.648148 44.44444 58.33608 21.234568 11.388889
#> 450.3 28.72428 50.185185 36.88889 72.24198 15.432099 13.703704
#> 506.2 25.00000 46.759259 45.55556 53.24966 18.148148 10.884774
#> Canchan 21.32716 47.777778 21.60494 59.24691 9.629630 2.421125
#> Desiree 18.76543 8.888889 20.37037 27.42747 10.061728 11.420243
#> Unica 21.30144 72.222222 47.83951 57.53519 18.246914 17.478738
imputation(plrv, genotype = "Genotype", environment = "Locality",
response = "Yield", rep ='Rep', type = "EM-SREG")
#> Ayac Hyo-02 LM-02 LM-03 SR-02 SR-03
#> 102.18 21.67165 28.888889 32.03704 46.77778 13.518519 11.769547
#> 104.22 21.45062 53.518519 39.19753 50.41838 16.049383 7.098765
#> 121.31 23.46022 41.296296 38.39506 63.70370 2.500000 11.255144
#> 141.28 31.84401 60.462963 33.95062 77.56790 19.234568 15.477366
#> 157.26 19.66980 41.388889 45.16049 76.98553 23.950617 14.555556
#> 163.9 17.53792 29.537037 28.88889 32.02949 12.716049 7.795414
#> 221.19 15.41358 32.037037 31.02469 43.45267 8.543210 7.437586
#> 233.11 24.28326 50.555556 29.19753 47.33333 13.148148 7.481481
#> 235.6 29.91358 73.518519 40.37037 56.13580 14.802469 17.067901
#> 241.2 20.44444 36.018519 35.74074 46.24691 11.086420 8.505291
#> 255.7 26.06702 47.037037 32.67901 40.79244 19.185185 17.777778
#> 314.12 17.32510 49.444444 34.50617 57.24588 8.530864 1.987654
#> 317.6 26.61376 53.425926 42.34568 64.01235 14.814815 10.742455
#> 319.20 25.77503 56.666667 32.96296 86.80802 21.209877 9.123457
#> 320.16 30.32922 31.111111 35.28395 43.29012 13.629630 4.444444
#> 342.15 19.89712 40.740741 27.53086 38.80033 17.592593 11.518519
#> 346.2 21.57476 32.685185 25.55556 32.03704 18.024691 13.173280
#> 351.26 31.74897 50.185185 29.25926 72.02407 20.370370 13.106996
#> 364.21 26.63933 52.407407 37.90123 57.06584 13.518519 16.826132
#> 402.7 19.29698 42.500000 31.23457 49.76543 12.839506 9.228395
#> 405.2 28.66735 35.740741 32.34568 43.25926 16.790123 17.116598
#> 406.12 19.58652 59.814815 37.77778 53.58848 13.827160 11.504605
#> 427.7 26.08907 55.648148 44.44444 58.33608 21.234568 11.388889
#> 450.3 28.72428 50.185185 36.88889 72.24198 15.432099 13.703704
#> 506.2 25.00000 46.759259 45.55556 53.24966 18.148148 10.884774
#> Canchan 21.32716 47.777778 21.60494 59.24691 9.629630 2.421125
#> Desiree 18.76543 8.888889 20.37037 27.42747 10.061728 11.420243
#> Unica 21.30144 72.222222 47.83951 57.53519 18.246914 17.478738