imputation: Imputation of missing cells in two-way data sets

In geneticae: Statistical Tools for the Analysis of Multi Environment Agronomic Trials

Imputation of missing cells in two-way data sets

Description

Missing values are not allowed by the AMMI or GGE 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", "Gabriel","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 (starting from the missing values in the first column). If omitted, the initial values will be obtained by the main effects from the corresponding model, that is, by the grand mean of the observed data increased (or decreased) by row and column main effects.
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 of missing cells (standard EM-AMMI algorithm). However, when 'change.factor' less than 1, then the new approximations are computed and the values of missing cells are changed in the direction of this new approximation but the change is smaller. It could be useful if the changes are cyclic and thus convergence could not be reached. Usually, this argument should not affect the final outcome (that is, the imputed values) as compared to the default value of 'change.factor' = 1.
simplified.model	the AMMI model contains the general mean, effects of rows, columns and interaction terms. So the EM-AMMI algorithm in step 2 calculates the current effects of rows and columns; these effects change from iteration to iteration because the empty (at the outset) cells in each iteration are filled with different values. In step 3 EM-AMMI uses those effects to re-estimate cells marked as missed (as default, simplified.model=FALSE). It is, however, possible that this procedure will not converge. Thus the user is offered a simplified EM-AMMI procedure that calculates the general mean and effects of rows and columns only in the first iteration and in next iterations uses these values (simplified.model=TRUE). In this simplified procedure the initial values affect the outcome (whilst EM-AMMI results usually do not depend on initial values). For the simplified procedure the number of iterations to convergence is usually smaller and, furthermore, convergence will be reached even in some cases where the regular procedure fails. If the regular procedure does not converge for the standard initial values, the simplified model can be used to determine a better set of initial values.
scale	boolean. By default TRUE leading to a same weight for each variable
method	"Regularized" by default or "EM"
row.w	row weights (by default, a vector of 1 for uniform row weights)
coeff.ridge	1 by default to perform the regularized imputePCA algorithm; useful only if method="Regularized". Other regularization terms can be implemented by setting the value to less than 1 in order to regularized less (to get closer to the results of the EM method
seed	integer, by default seed = NULL implies that missing values are initially imputed by the mean of each variable. Other values leads to a random initialization
nb.init	integer corresponding to the number of random initializations; the first initialization is the initialization with the mean imputation
Winf	peso inferior
Wsup	peso superior

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

• 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

Value

imputed data matrix

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.

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")

# Data with replications
data(plrv)
plrv[1,3] <- NA
plrv[3,3] <- NA
plrv[2,3] <- NA
imputation(plrv, genotype = "Genotype", environment = "Locality",
           response = "Yield", rep = "Rep", type = "EM-AMMI")

geneticae documentation built on July 20, 2022, 5:06 p.m.