impRZilr: 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-transformations with special choice of balances.

Usage

impRZilr(x, maxit = 10, eps = 0.1, method = "pls", 
   dl = rep(0.05, ncol(x)), nComp="boot", bruteforce = FALSE,
   noisemethod="residuals", noise=FALSE, R=10, correction="normal", verbose=FALSE)

Arguments

data.frame or matrix

maxit

maximum number of iterations

eps

convergency criteria

method

either lm, MM or pls

Detection limit for each variable. zero for variables with variables that have no detection limit problems.

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)

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.

Value

ximputed data
criteriachange between last and second last iteration
iternumber of iterations
maxitmaximum number of iterations
windindex of zeros
nCompnumber of components for method pls
methodchosen method

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) an specific ilr transformation is applied (2) tobit regression is applied (3) the rounded zeros are replaced by the expected values (4) the corresponding inverse ilr transformation is applied. After all parts are imputed, the algorithm starts again until the imputations do not change.

Examples

Run this code

data(arcticLake)
x <- arcticLake
## generate rounded zeros artificially:
#x[x[,1] < 5, 1] <- 0
x[x[,2] < 44, 2] <- 0
xia <- impRZilr(x, dl=c(5,44,0), eps=0.01, method="lm")
xia$x