tlsce {BCE} | R Documentation |
estimates a matrix X for which:
(A+ε_A)X = B+ε_B
minimize sum{ε_A^2 + ε_B^2}
sum{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, optimizationfunction="nlminb", 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
Wa=NULL , Wa defaults to 1. This parameter can be used to give
more importance to elements of A or A in total compared to
B. Weighting of B is not possible. the weights are implemented as
proportional to 1/s (as opposed to 1/s^2) with s the
standard deviation of the error term.
|
optimizationfunction |
the function used for the optimization of A (one of "nlminb","optim","constrOptim"). |
A_init |
a matrix with the same structure as A. a general,
non-linear optimization routine (default nlminb ) is used to
minimize the sum of squared residuals of A versus the fitted matrix
A_fit (see falue). This optimization routine requires a set of
starting values, by default the non-zero elements of A. This
provides a good fit, but when in doubt about the convergence of the
algorithm, one can provide different starting values for the
optimization routine in A_init. |
Xratios |
TRUE or FALSE: are the colSums of the matrix X equal to 1? This is for example the case in a compositional matrix. |
... |
Arguments to be passed to the optimization function in use. |
instead of a linear least squares regression, in which the
elements of A would be fixed, the function tlsce
includes the
non-zero elements of A in the least squares regression. This is
similar to other total least squares regression methods, with the main
difference that only non-zero elements of A contain an error term.
A list with the following elements:
X |
Array with dimension c(ncol(A ),ncol(B ),
iter ) containing the species composition of each sample
|
A_fit |
Array with same dimension as A , containing the
best-fit values of the input biomarker data per taxonomic group
|
B_fit |
Array with same dimension as B , containing the
biomarker field data, corresponding to Afit
|
solutionNorms |
a vector of 3 values:
the value of the minimised quadratic function at the solution, in this case sum((Afit-A)*Wa)^2 + (Bfit-B)^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, 190-199
A <- t(bceInput$Rat) B <- t(bceInput$Dat) tlsce(A,B) ## weighting Wa inversely proportional to A tlsce(A,B,Wa=1/A)