zCompositions (version 1.0.0)

multLN: Multiplicative lognormal replacement

Description

This function implements the multiplicative lognormal univariate replacement 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)

Arguments

X

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

label

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

dl

Numeric vector of detection limits/thresholds (one per component/column, use e.g. 0 if no threshold for a particular one). These must be given on the same scale as X.

rob

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

random

Logical value. FALSE imputes using the estimated geometric mean of the values < threshold (default). TRUE imputes using random values below the limit of detection.

Value

• A data.frame object containing the replaced compositional data set.

Details

This function depends on package NADA to produce model parameter estimates (either maximum likelihood or robust regression on order statistics) from log-transformed censored data. It produces a 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, following Mateu-Figueras et al. (2013), a normal distribution representation on the own positive real line is assumed for the data instead of the standard lognormal model based on the Lebesgue measure.

References

Mateu-Figueras G, Pawlowsky-Glahn V, Egozcue JJ. The normal distribution in some constrained sample spaces. SORT 2013; 37(1): 29-56.

Palarea-Albaladejo J, Martin-Fernandez JA. Values below detection limit in compositional chemical data. Analytica Chimica Acta 2013; 764: 32-43. DOI: http://dx.doi.org/10.1016/j.aca.2012.12.029.

See Also

zPatterns, multRepl, lrEM, lrDA, 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))

# 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 MV 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)