# corAspect: Scaling by Maximizing Correlational Aspects In aspect: A General Framework for Multivariate Analysis with Optimal Scaling

 corAspect R Documentation

## 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.

`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 6, 2022, 9:06 a.m.