cosNominal {qlcMatrix}

Associations-measures for sparsely encoded nominal variables

Description

Nominal variables can be encoded as a combination of a sparse incidence and index matrix. Various functions to compute variations of assocSparse and cosSparse for such data are described here.

Usage

cosCol(X, colGroupX, Y = NULL, colGroupY = NULL, norm = norm2 )
assocCol(X, colGroupX, Y = NULL, colGroupY = NULL, method = res, sparse = TRUE)

cosRow(X, rowGroup, Y = NULL, norm = norm2 , weight = NULL)
assocRow(X, rowGroup, Y = NULL, method = res)

Arguments

X, Y

sparse matrices in a format of the Matrix package, typically dgCMatrix . When Y = NULL, then the similarity between the columns of X and itself will be taken. If Y is specified, the similarity between the columns of X and the columns of Y will be calculated.

colGroupX, colGroupY

sparse matrices (typically pattern matrices) with the same number of columns as X and Y, respectively, indicating which columns belong to the same group. Each row of these matrices represents a group.

rowGroup

sparse matrix (typically pattern matrices) with the same number of rows as X (and Y when not NULL), indicating which rows belong to the same group. Each column of these matrices represents a group.

norm

norm to be used. See cosSparse for details.

weight

weighting of rows. See cosSparse for details. Note that row-weighting only makes sense with cosRow.

method

method to be used. See assocSparse for details.

sparse

All methods try to be as sparse as possible. Specifically, when there are no observed co-occurrence, then nothing is computed. This might lead to slight deviations in the results for some methods. Set sparse=F to force computation for all cells. This leads to non-sparse results, so use with caution with large datasets.

Details

The approaches assoc and cos are described in detail in assocSparse and cosSparse, respectively. Those methods are extended here in case either the columns (.col) or the rows (.row) form groups. Specifically, this occurs with sparse encoding of nominal variables (see splitTable). In such encoding, the different values of a nominal variable are encoded in separate columns. However, these columns cannot be treated independently, but have to be treated as groups.

The .col methods should be used when similarities between the different values of nominal variables are to be computed. The .row methods should be used when similarities between the observations of nominal variables are to be computed.

Note that the calculations of the assoc functions really only makes sense for binary data (i.e. matrices with only ones and zeros). Currently, all input is coerced to such data by as(X, "nMatrix")*1, meaning that all values that are not one or zero are turned into one (including negative values!).

Value

When Y = NULL, then all methods return symmetric similarity matrices in the form dsCMatrix, only specifying the upper triangle. The only exception is when sparse=T is chose, then the result will be in the form dsyMatrix.

When a second matrix Y is specified, the result will be of the kind dgCMatrix or dgeMatrix, respectively.

Note

Note that these methods automatically take missing data into account. They also work with large amount of missing data, but of course the validity of any similarity with much missing data is problematic.

Author(s)

Michael Cysouw

See Also

sim.att, sim.obs for convenient shortcuts around these methods.

Examples

# convenience functions are easiest to use
# first a simple example using the farms-dataset from MASS
library(MASS)

# to investigate the relation between the individual values
# This is similar to Multiple Correspondence Analysis (see mca in MASS)
f <- splitTable(farms)
s <- assocCol(f$OV,f$AV)
rownames(s) <- f$values
plot(hclust(as.dist(-s)))