imputeBDLs: EM-based replacement of rounded zeros in compositional data

In robCompositions: Compositional Data Analysis

EM-based replacement of rounded zeros in compositional data

Description

Parametric replacement of rounded zeros for compositional data using classical and robust methods based on ilr coordinates with a special choice of balances.

Usage

imputeBDLs(
  x,
  maxit = 10,
  eps = 0.1,
  method = "subPLS",
  dl = rep(0.05, ncol(x)),
  variation = TRUE,
  nPred = NULL,
  nComp = "boot",
  bruteforce = FALSE,
  noisemethod = "residuals",
  noise = FALSE,
  R = 10,
  correction = "normal",
  verbose = FALSE,
  test = FALSE
)

adjustImputed(xImp, xOrig, wind)

checkData(x, dl)

## S3 method for class 'replaced'
print(x, ...)

Arguments

x	data.frame or matrix
maxit	maximum number of iterations
eps	convergency criteria
method	either "lm", "lmrob" or "pls"
dl	Detection limit for each variable. zero for variables with variables that have no detection limit problems.
variation,	if TRUE those predictors are chosen in each step, who's variation is lowest to the predictor.
nPred,	if determined and variation equals TRUE, it fixes the number of predictors
nComp	if determined, it fixes the number of pls components. If “boot”, the number of pls components are estimated using a bootstraped cross validation approach.
bruteforce	sets imputed values above the detection limit to the detection limit. Replacement above the detection limit are only exeptionally occur due to numerical instabilities. The default is FALSE!
noisemethod	adding noise to imputed values. Experimental
noise	TRUE to activate noise (experimental)
R	number of bootstrap samples for the determination of pls components. Only important for method “pls”.
correction	normal or density
verbose	additional print output during calculations.
test	an internal test situation (this parameter will be deleted soon)
xImp	imputed data set
xOrig	original data set
wind	index matrix of rounded zeros
...	further arguments passed through the print function

Details

Statistical analysis of compositional data including zeros runs into problems, because log-ratios cannot be applied. Usually, rounded zeros are considerer as missing not at random missing values.

The algorithm iteratively imputes parts with rounded zeros whereas in each step (1) compositional data are expressed in pivot coordinates (2) tobit regression is applied (3) the rounded zeros are replaced by the expected values (4) the corresponding inverse ilr mapping is applied. After all parts are imputed, the algorithm starts again until the imputations do not change.

Value

x	imputed data
criteria	change between last and second last iteration
iter	number of iterations
maxit	maximum number of iterations
wind	index of zeros
nComp	number of components for method pls
method	chosen method

Author(s)

Matthias Templ, method subPLS from Jiajia Chen

References

Templ, M., Hron, K., Filzmoser, P., Gardlo, A. (2016). Imputation of rounded zeros for high-dimensional compositional data. Chemometrics and Intelligent Laboratory Systems, 155, 183-190.

Chen, J., Zhang, X., Hron, K., Templ, M., Li, S. (2018). Regression imputation with Q-mode clustering for rounded zero replacement in high-dimensional compositional data. Journal of Applied Statistics, 45 (11), 2067-2080.

See Also

imputeBDLs

Examples

p <- 10
n <- 50
k <- 2
T <- matrix(rnorm(n*k), ncol=k)
B <- matrix(runif(p*k,-1,1),ncol=k)
X <- T %*% t(B)
E <-  matrix(rnorm(n*p, 0,0.1), ncol=p)
XE <- X + E
data <- data.frame(pivotCoordInv(XE))
col <- ncol(data)
row <- nrow(data)
DL <- matrix(rep(0),ncol=col,nrow=1)
for(j in seq(1,col,2))
{DL[j] <- quantile(data[,j],probs=0.06,na.rm=FALSE)}

for(j in 1:col){        
  data[data[,j]<DL[j],j] <- 0
}
## Not run: 
# under dontrun because of long exectution time
imp <- imputeBDLs(data,dl=DL,maxit=10,eps=0.1,R=10,method="subPLS")
imp
imp <- imputeBDLs(data,dl=DL,maxit=10,eps=0.1,R=10,method="pls", variation = FALSE)
imp
imp <- imputeBDLs(data,dl=DL,maxit=10,eps=0.1,R=10,method="lm")
imp
imp <- imputeBDLs(data,dl=DL,maxit=10,eps=0.1,R=10,method="lmrob")
imp

data(mcad)
## generate rounded zeros artificially:
x <- mcad
x <- x[1:25, 2:ncol(x)]
dl <- apply(x, 2, quantile, 0.1)
for(i in seq(1, ncol(x), 2)){
  x[x[,i] < dl[i], i] <- 0
} 
ni <- sum(x==0, na.rm=TRUE) 
ni/(ncol(x)*nrow(x)) * 100
dl[seq(2, ncol(x), 2)] <- 0
replaced_lm <- imputeBDLs(x, dl=dl, eps=1, method="lm",  
  verbose=FALSE, R=50, variation=TRUE)$x
replaced_lmrob <- imputeBDLs(x, dl=dl, eps=1, method="lmrob",  
  verbose=FALSE, R=50, variation=TRUE)$x
replaced_plsfull <- imputeBDLs(x, dl=dl, eps=1, 
  method="pls", verbose=FALSE, R=50, 
  variation=FALSE)$x 

## End(Not run)

robCompositions documentation built on Aug. 25, 2023, 5:13 p.m.