multLN {zCompositions}

Multiplicative lognormal replacement

Description

This function implements model-based multiplicative lognormal imputation of left-censored values (e.g. values below detection limit, rounded zeros) in compositional data sets.

Usage

multLN(X, label = NULL, dl = NULL, rob = FALSE, random = FALSE,
          z.warning = 0.8, z.delete = TRUE)

Arguments

X

Compositional data set (matrix or data.frame class).

label

Unique label (numeric or character) used to denote zeros/unobserved left-censored values in X.

dl

Numeric vector or matrix of detection limits/thresholds. These must be given on the same scale as X. If NULL the column minima are used as thresholds.

rob

Logical value. FALSE provides maximum-likelihood estimates of model parameters (default), TRUE provides robust estimates (see NADA package for details).

random

Logical value. Values imputed using either estimated geometric mean (FALSE, default) or random values (TRUE) below the limit of detection.

z.warning

Threshold used to identify individual rows or columns including an excess of zeros/unobserved values (to be specify in proportions, default z.warning=0.8).

z.delete

Logical value. If set to TRUE, rows/columns identified by z.warning are omitted in the imputed data set. Otherwise, the function stops in error when rows/columns are identified by z.warning (default z.delete=TRUE).

Details

By default, this function imputes left-censored compositional values by the estimated geometric mean of the values below the corresponding limit of detection or censoring threshold and applies a multiplicative adjustment to preserve the multivariate compositional properties of the samples. Alternatively, imputation can be carried out by random values below the limit of detection (random = TRUE) based on a normal distribution on the positive real line (see below).

It depends on package NADA to produce the required model parameter estimates (either maximum likelihood or robust regression on order statistics). It allows for either single (vector form) or multiple (matrix form, same size as X) limits of detection by component. Any threshold value can be set for non-censored elements (e.g. use 0 if no threshold for a particular column or element of the data matrix).

It produces an imputed data set on the same scale as the input data set. If X is not closed to a constant sum, then the results are adjusted to provide a compositionally equivalent data set, expressed in the original scale, which leaves the absolute values of the observed components unaltered. Note that a normal distribution on the positive real line is considered. That is, it is defined with respect to a measure according to own geometry of the positive real line, instead of the standard lognormal based on the Lebesgue measure in real space.

Value

A data.frame object containing the imputed compositional data set expressed in the original scale.

References

Mateu-Figueras G, Pawlowsky-Glahn V, Egozcue JJ. The normal distribution in some constrained sample spaces. SORT 2013; 37: 29-56.

Palarea-Albaladejo J, Martin-Fernandez JA. Values below detection limit in compositional chemical data. Analytica Chimica Acta 2013; 764: 32-43.

Palarea-Albaladejo J. and Martin-Fernandez JA. zCompositions – R package for multivariate imputation of left-censored data under a compositional approach. Chemometrics and Intelligence Laboratory Systems 2015; 143: 85-96.

See Also

zPatterns, lrEM, lrSVD, lrDA, multRepl, multKM, cmultRepl

Examples

# Data set closed to 100 (percentages, common dl = 1%)
X <- matrix(c(26.91,8.08,12.59,31.58,6.45,14.39,
              39.73,26.20,0.00,15.22,6.80,12.05,
              10.76,31.36,7.10,12.74,31.34,6.70,
              10.85,46.40,31.89,10.86,0.00,0.00,
              7.57,11.35,30.24,6.39,13.65,30.80,
              38.09,7.62,23.68,9.70,20.91,0.00,
              27.67,7.15,13.05,32.04,6.54,13.55,
              44.41,15.04,7.95,0.00,10.82,21.78,
              11.50,30.33,6.85,13.92,30.82,6.58,
              19.04,42.59,0.00,38.37,0.00,0.00),byrow=TRUE,ncol=6)
              
X_multLN <- multLN(X,label=0,dl=rep(1,6))

# Multiple limits of detection by component
mdl <- matrix(0,ncol=6,nrow=10)
mdl[2,] <- rep(1,6)
mdl[4,] <- rep(0.75,6)
mdl[6,] <- rep(0.5,6)
mdl[8,] <- rep(0.5,6)
mdl[10,] <- c(0,0,1,0,0.8,0.7)

X_multLN2 <- multLN(X,label=0,dl=mdl)

# Non-closed compositional data set
data(LPdata) # data (ppm/micrograms per gram)
dl <- c(2,1,0,0,2,0,6,1,0.6,1,1,0,0,632,10) # limits of detection (0 for no limit)

# Using ML for parameter estimation
LPdata_multLN <- multLN(LPdata,label=0,dl=dl) 
# For comparison
LPdata[30:35,1:10]
round(LPdata_multLN[30:35,1:10],1)

# Using ROS for parameter estimation
LPdata_multLNrob <- multLN(LPdata,label=0,dl=dl,rob=TRUE)
round(LPdata_multLNrob[30:35,1:10],1)

# Using random values < dl
LPdata_multRLN <- multLN(LPdata,label=0,dl=dl,random=TRUE)
round(LPdata_multRLN[30:35,1:10],1)

# Two subsets of limits of detection (using e.g. ML parameter estimation)
data(LPdata)
dl <- c(2,1,0,0,2,0,6,1,0.6,1,1,0,0,632,10) # limits of detection (0 for no limit)
 # DLs for first 50 samples of LPdata
dl1 <- matrix(rep(1,50),ncol=1)%*%dl
 # DLs for last 46 samples of LPdata
dl2 <- matrix(rep(1,46),ncol=1)%*%c(1,0.5,0,0,2.5,0,5.5,0.75,0.3,1.5,1,0,0,600,8) 

mdl <- rbind(dl1,dl2)
LPdata_multLN2 <- multLN(LPdata,label=0,dl=mdl)