corAspect: Scaling by Maximizing Correlational Aspects

In aspect: A General Framework for Multivariate Analysis with Optimal Scaling

Scaling by Maximizing Correlational Aspects

Description

This function performs optimal scaling by maximizing a certain aspect of the correlation matrix.

Usage

corAspect(data, aspect = "aspectSum", level = "nominal", itmax = 100, eps = 1e-06, ...)

Arguments

data	Data frame or matrix
aspect	Function on the correlation matrix (see details)
level	Vector with scale level of the variables ("nominal" or "ordinal"). If all variables have the same scale level, only one value can be provided
itmax	Maximum number of iterations
eps	Convergence criterion
...	Additional parameters for aspect

Details

We provide various pre-specified aspects:

"aspectAbs" takes the sum of the absolute values of the correlations to the power pow. The optional argument pow = 1.

"aspectSum" the sum of the correlations to the power of pow. Again, as default pow = 1.

"aspectDeterminant" computes the determinant of the correlation matrix; no additional arguments needed.

"aspectEigen" the sum of the first p eigenvalues (principal component analysis). By default the argument p = 1.

"aspectSMC" the squared multiple correlations (multiple regression) with respect to a target variable. By default targvar = 1 which implies that the first variable of the dataset is taken as response.

"aspectSumSMC" uses the sum of all squared multiple correlations (path analysis).

Alternatively, the user can write his own aspect, e.g. the function myAspect(r, ...) with r as the correlation matrix. This function must return a list with the function value as first list element and the first derivative with respect to r as the second. Then aspect = myAspect and additional arguments go into ... in maxAspect().

Value

loss	Final value of the loss function
catscores	Resulting category scores (after optimal scaling)
cormat	Correlation matrix based on the scores
eigencor	Eigenvalues of the correlation matrix
indmat	Indicator matrix (dummy coded)
scoremat	Transformed data matrix (i.e with category scores resulting from optimal scaling)
burtmat	Burt matrix
niter	Number of iterations

Author(s)

Jan de Leeuw, Patrick Mair

References

Mair, P., & De Leeuw, J. (2010). Scaling variables by optimizing correlational and non-correlational aspects in R. Journal of Statistical Software, 32(9), 1-23. doi: 10.18637/jss.v032.i09

de Leeuw, J. (1988). Multivariate analysis with optimal scaling. In S. Das Gupta and J.K. Ghosh, Proceedings of the International Conference on Advances in Multivariate Statistical Analysis, pp. 127-160. Calcutta: Indian Statistical Institute.

See Also

lineals

Examples

## maximizes the first eigenvalue
data(galo)
res.eig1 <- corAspect(galo[,1:4], aspect = "aspectEigen")
res.eig1
summary(res.eig1)

## maximizes the first 2 eigenvalues
res.eig2 <- corAspect(galo[,1:4], aspect = "aspectEigen", p = 2)
res.eig2

## maximizes the absolute value of cubic correlations
res.abs3 <- corAspect(galo[,1:4], aspect = "aspectAbs", pow = 3)
res.abs3

## maximizes the sum of squared correlations
res.cor2 <- corAspect(galo[,1:4], aspect = "aspectSum", pow = 2)
res.cor2

## maximizes the determinant
res.det <- corAspect(galo[,1:4], aspect = "aspectDeterminant")
res.det

## maximizes SMC, IQ as target variable
res.smc <- corAspect(galo[,1:4], aspect = "aspectSMC", targvar = 2)
res.smc

## maximizes the sum of SMC
res.sumsmc <- corAspect(galo[,1:4], aspect = "aspectSumSMC")
res.sumsmc

aspect documentation built on May 4, 2022, 3 a.m.