tlsce {BCE}  R Documentation 
estimates a matrix X for which:
(A+ε_A)X = B+ε_B
minimize ∑{ε_A^2 + ε_B^2}
∑{X_{i,}}=1 \forall i
X>0
the elements of ε_A are NULL if the corresponding elements of A are NULL. A typically contains biomarker concentrations for several taxonomic groups, and B field measurements of the same biomarkers. X is then an estimate of the taxonomic composition of the field sample.
tlsce(A, B, Wa=NULL, Wb=NULL, minA=NULL, maxA=NULL, A_init=A, Xratios=TRUE, ...)
A 
a matrix or data frame. If A contains biomarker data for taxonomic groups, the biomarkers have to be organized per row, and the taxonomic groups per column. 
B 
a matrix or data frame. If B contains biomarker field data, the biomarkers have to be organized per row, and the samples per column. 
Wa 
weighting of A, a matrix with the same dimensions of A. If

Wb 
weighting of B, a matrix with the same dimensions of B. If

minA 
minimum values for A 
maxA 
maximum values for A 
A_init 
a matrix with the same structure as A. a general,
nonlinear optimization routine (default 
Xratios 
TRUE or FALSE: are the colSums of the matrix X equal to 1? This is for example the case in a compositional matrix. (only if A and B are both expressed relative to the unit of biomass) if Xratios =TRUE, A has pigment concentrations per biomass unit, B has pigment concentrations per biomass unit per sample, and X contains ratios of biomass unit per sample. if Xratios =FALSE, A has pigment concentrations per biomass unit, B has pigment concentrations per sample, and X has biomass units per sample 
... 
Arguments to be passed to lsei() or to modFit() 
instead of a linear least squares regression, in which the
elements of A would be fixed, the function tlsce
includes the
nonzero elements of A in the least squares regression. This is
similar to other total least squares regression methods (also called
orthogonal regression), with the main
difference that only nonzero elements of A contain an error term.
A list with the following elements:
X 
Array with dimension c(ncol( 
A\_fit 
Array with same dimension as 
B\_fit 
Array with same dimension as 
solutionNorms 
a vector of 3 values: the value of the minimised quadratic function at the solution, in this case sum((AfitA)*Wa)^2 + (BfitB)^2), and the shares of this value attributed to A and to B 
convergence 
An integer code. '0' indicates successful convergence. 
Karel Van den Meersche <k.vdmeersche@nioo.knaw.nl>, Karline Soetaert <k.soetaert@nioo.knaw.nl>
Van den Meersche, K., K. Soetaert and J.J. Middelburg (2008) A Bayesian compositional estimator for microbial taxonomy based on biomarkers, Limnology and Oceanography Methods 6, 190199
A < t(bceInput$Rat) B < t(bceInput$Dat) tlsce(A,B) ## weighting Wa inversely proportional to A tlsce(A,B,Wa=1/A)