# ssq: Calculate SSQ (accuracy) of biplot representation for... In markheckmann/OpenRepGrid: Tools to Analyze Repertory Grid Data

## Description

Each construct and element are vectors in a multidimensional space. When reducing the representation to a lower dimensional space, a loss of information (sum-of-squares) will usually occur. The output of the function shows the proportion of sum-of-squares (SSQ) explained for the elements (constructs) and the amount explained by each principal component. This allows to assess which elements (construct) are represented how well in the current representation. Also it shows how much of the total variation is explained.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```ssq( x, along = 2, center = 1, normalize = 0, g = 0, h = 1 - g, col.active = NA, col.passive = NA, ... ) ```

## Arguments

 `x` `repgrid` object. `along` Numeric. Table of sum-of-squares (SSQ) for 1=constructs, 2=elements (default). Note that currently these calculations only make sense for biplot reperesentations with `g=1` and `h=1` respectively. `center` Numeric. The type of centering to be performed. 0= no centering, 1= row mean centering (construct), 2= column mean centering (elements), 3= double-centering (construct and element means), 4= midpoint centering of rows (constructs). The default is `1` (row centering). `normalize` A numeric value indicating along what direction (rows, columns) to normalize by standard deviations. `0 = none, 1= rows, 2 = columns` (default is `0`). `g` Power of the singular value matrix assigned to the left singular vectors, i.e. the constructs. `h` Power of the singular value matrix assigned to the right singular vectors, i.e. the elements. `col.active` Columns (elements) that are no supplementary points, i.e. they are used in the SVD to find principal components. default is to use all elements. `col.passive` Columns (elements) that are supplementary points, i.e. they are NOT used in the SVD but projecte into the component space afterwards. They do not determine the solution. Default is `NA`, i.e. no elements are set supplementary.

## Value

A list containing three wo elements

 `ssq.table` dataframe with sum-of-squares explained for element/construct by each dimension `ssq.table.cumsum` dataframe with cumulated sum-of-squares explained for element/construct number of dimensions `ssq.total` total sum-of-squares after pre-transforming grid matrix

## Note

TODO: if g or h is not equal to 1 the SSQ does not measure accuracy of representation as currently the ssq of each point are set in constrast with the pre-transformed matrix.

Mark Heckmann

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21``` ``` # explained sum-of-squares for elements ssq(bell2010) # explained sum-of-squares for constructs ssq(bell2010, along=1) # save results s <- ssq(bell2010) # printing options print(s) print(s, digits=4) print(s, dim=3) print(s, cumulated=FALSE) # access results names(s) s\$ssq.table s\$ssq.table.cumsum s\$ssq.total ```

markheckmann/OpenRepGrid documentation built on April 30, 2021, 2:33 a.m.