Class and methods to handle Multiscale Codependence Analysis (MMCA)
# S3 method for mca
print(x, ...)
# S3 method for mca
plot(x, col, col.signif=2, main="", ...)
# S3 method for mca
summary(object, ...)
# S3 method for mca
fitted(object, selection, components=FALSE, ...)
# S3 method for mca
residuals(object, selection, ...)
# S3 method for mca
predict(object, selection, newdata, components=FALSE, ...)A mca-class object.
A vector of color values to be used for plotting the multivariate codependence coefficients.
Color of the frame used to mark the statistically significant codependence coefficients .
Text for the main title of the plot.
A numeric vector of indices or character vector variable
names to test or force-use. Mandatory if object is
untested.
A boolean specifying whether the components of fitted or predicted values associated with single eigenfunctions in the map should be returned.
A list with elements $X, $meanY, and $target that contain the information needed to make predictions (see details).
Further parameters to be passed to other functions or methods.
mca-class objects contain:
A list with two elements: the first being a copy of the
response (Y) and the second being a copy of the explanatory
variables (X). This is the variables that were given to
MCA.
The eigenmap-class object that was given to
MCA.
A list with five elements: the first (UpY) is a
matrix of the cross-products of structuring variable (U) and
the response variable Y, the second (UpX) is a matrix
of the cross-product of the structuring variable and the explanatory
variables (X), the third (C) is a 3-dimensional array
of the codependence coefficients, the fourth (B) is a
3-dimensional array of the coregression coefficients, and the fifth
(CM) is a matrix of the multivariate codependence
coefficients.
Results of statistical testing as performed by
test.mca or permute.mca. NULL
if no testing was performed, such as when only MCA
had been called. The results of statistical testing is a list
containing the following members:
The number of randomized permutations used by
permute.mmca for permutation testing. 0 or FALSE
for parametric testing obtained using test.mca.
The indices of codependence coefficient describing
statistically significant codependence between Y and
X, in decreasing order of magnitude.
The testing table (a 5-column matrix) with \(\phi\) statistics, degrees-of-freedom, and testwise and familywise probabilities of type I (\(\alpha\)) error. It contains one line for each statistically significant global coefficient (if any) in addition to test results for the first, non-significant coefficient, on which the testing procedure stopped.
Tests of every single response variable (a
3-dimensional array), had such tests been requested while calling
the testing function, NULL otherwise.
Details about permutation testing not shown in
test$global or test$response. NULL for parametric
testing.
The fitted, residuals, and predict methods return
a matrix of fitted, residuals, or predicted values, respectively. The
fitted and predict methods return a list a list when the
parameter component is TRUE. The list contains the
fitted or predicted values as a first element and an
array components as a second. That 3-dimensional array has one
matrix for each statistically significant codependence coefficient.
For making predictions, parameter newdata may contain three
elements: $X, a matrix of new values of the explanatory
variables, $meanY, a vector of the predicted mean values of the
responses, and $target, a matrix of target scores for arbitraty
locations within the study area. When no $X is supplied, the
descriptor given to MCA is recycled, while when no
$meanY is supplied, the mean values of the response variables
given to MCA are used. Finally, when element
$target is omitted from newdata, predictions are made at
the sites were observations were done. When none of the above is
provided, or if newdata is omitted when calling the prediction
method, the behaviour of the predict method is identical to
that of the fitted method.
Gu<U+00E9>nard, G., Legendre, P., Boisclair, D., and Bilodeau, M. 2010. Multiscale codependence analysis: an integrated approach to analyse relationships across scales. Ecology 91: 2952-2964
Gu<U+00E9>nard, G. Legendre, P., and crews. 2016. Assessing multivariate relationships across spatial scales: introducing the Multivariate Multiscale Codependence Analysis. Ecology paper to be.