corAspect | R Documentation |

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

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

`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 |

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()`

.

`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 |

Jan de Leeuw, Patrick Mair

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`

## 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

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