# epMCA.inference.battery

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##### epMCA.inference.battery: Inference tests for Multiple Correspondence Analysis (CA) via InPosition.

Multiple Correspondence Analysis (CA) and a battery of inference tests via InPosition. The battery includes permutation and bootstrap tests.

Keywords
Bootstrap, multivariate, Permutation
##### Usage
epMCA.inference.battery(DATA, make_data_nominal = TRUE, DESIGN = NULL,
make_design_nominal = TRUE, masses = NULL, weights = NULL,
hellinger = FALSE, symmetric = TRUE, correction = c("b"),
graphs = TRUE, k = 0,
test.iters = 100, constrained = FALSE, critical.value = 2)
##### Arguments
DATA

original data to perform a MCA on. This data can be in original formatting (qualitative levels) or in dummy-coded variables.

make_data_nominal

a boolean. If TRUE (default), DATA is recoded as a dummy-coded matrix. If FALSE, DATA is a dummy-coded matrix.

DESIGN

a design matrix to indicate if rows belong to groups.

make_design_nominal

a boolean. If TRUE (default), DESIGN is a vector that indicates groups (and will be dummy-coded). If FALSE, DESIGN is a dummy-coded matrix.

masses

a diagonal matrix or column-vector of masses for the row items.

weights

a diagonal matrix or column-vector of weights for the column it

hellinger

a boolean. If FALSE (default), Chi-square distance will be used. If TRUE, Hellinger distance will be used.

symmetric

a boolean. If TRUE symmetric factor scores for rows.

correction

which corrections should be applied? "b" = Benz<U+00E9>cri correction, "bg" = Greenacre adjustment to Benz<U+00E9>cri correction.

graphs

a boolean. If TRUE (default), graphs and plots are provided (via epGraphs)

k

number of components to return.

test.iters

number of iterations

constrained

a boolean. If a DESIGN matrix is used, this will constrain bootstrap resampling to be within groups.

critical.value

numeric. A value, analogous to a z- or t-score to be used to determine significance (via bootstrap ratio).

##### Details

epMCA.inference.battery performs multiple correspondence analysis and inference tests on a data matrix. If the expected time to compute the results (based on test.iters) exceeds 1 minute, you will be asked (via command line) if you want to continue.

##### Value

Returns two lists ($Fixed.Data and$Inference.Data). For $Fixed.Data, see epMCA, coreCA for details on the descriptive (fixed-effects) results.$Inference.Data returns:

components

Permutation tests of components. p-values ($p.vals) and distributions of eigenvalues ($eigs.perm) for each component

fj.boots

Bootstrap tests of measures (columns). See boot.ratio.test output details.

omni

Permutation tests of components. p-values ($p.val) and distributions of total inertia ($inertia.perm). This is only useful if corrections are performed. Total inertia is constant for permutation with no corrections in MCA.