EMMA {EMMAgeo}  R Documentation 
A multivariate data set (m samples composed of n variables) is decomposed by eigenspace analysis and modelled with a given number of endmembers (q). Several steps of scaling, transformation, normalisation, eigenspace decomposition, factor rotation, data modelling and evaluation are performed.
EMMA(
X,
q,
l,
c,
Vqn,
classunits,
ID,
EM.ID,
rotation = "Varimax",
plot = FALSE,
...
)
X 

q 

l 

c 

Vqn 

classunits 

ID 

EM.ID 

rotation 

plot 

... 
Additional arguments passed to the plot function. Since the function returns two plots some additional graphical parameters must be specified as vector with the first element for the first plot and the second element for the second plot. 
The parameter Vqn
is useful when EMMA
shall be performed with
a set of prior unscaled endmembers, e.g. from other data sets that are to
be used as reference or when modelling a data set with mean endmembers, as
in the output of robust.loadings
.
The rotation type Varimax
was used by Dietze et al. (2012). In this
R package, one out of the rotations provided by the package GPArotation
is possible, as well. However, tests showed that the rotation type has no
dramatic consequences for the result.
The function values $loadings
and $scores
are redundant. They
are essentially the same as $Vqsn
and $Mqs
. However, they are
included for user convenience.
A list with numeric matrix objects.
loadings 
Normalised rescaled endmember loadings. 
scores 
Rescaled endmember scores. 
Vqn 
Normalised endmember loadings. 
Vqsn 
Normalised rescaled endmember loadings. 
Mqs 
Rescaled endmember scores. 
Xm 
Modelled data. 
modes 
Mode class of endmember loadings. 
Mqs.var 
Explained variance of endmembers 
Em 
Absolute rowwise model error. 
En 
Absolute columnwise model error. 
RMSEm 
rowwise root mean square erroe 
RMSEn 
columnwise root mean square erroe 
Rm 
Rowwise (samplewise) explained variance. 
Rn 
Columnwise (variablewise) explained variance. 
ol 
Number of overlapping endmembers. 
Michael Dietze, Elisabeth Dietze
Dietze E, Hartmann K, Diekmann B, IJmker J, Lehmkuhl F, Opitz S,
Stauch G, Wuennemann B, Borchers A. 2012. An endmember algorithm for
deciphering modern detrital processes from lake sediments of Lake Donggi
Cona, NE Tibetan Plateau, China. Sedimentary Geology 243244: 169180.
Klovan JE, Imbrie J. 1971. An Algorithm and FORTRANIV Program for
LargeScale QMode Factor Analysis and Calculation of Factor Scores.
Mathematical Geology 3: 6177. Miesch AT. 1976. QMode factor analysis of
geochemical and petrologic data matrices with constant row sums. U.S.
Geological Survey Professsional Papers 574.
test.parameters
, rotations
,
eigen
, nnls
## load example data and set phivector
data(example_X)
phi < seq(from = 1, to = 10, length.out = ncol(X))
## perform EMMA with 5 endmembers
EM < EMMA(X = X, q = 5, l = 0.05, c = 100, plot = TRUE)
## perform EMMA with 4 endmembers and more graphical settings
EM < EMMA(X = X, q = 4, l = 0.05, c = 100,
plot = TRUE,
EM.ID = c("EM 1", "EM 2", "EM 3", "EM 4"),
classunits = phi,
xlab = c(expression(paste("Class [", phi, "]")), "Sample ID"),
cex = 0.7,
col = rainbow(n = 4))