- ratio MDS:
- (disparities) = b * (proximities in terms of dissimilarities; short for 'prox' below)
- interval MDS:
- (disparities) = a + b * (prox)
- logarithmic MDS:
- (disparities) = log(prox)
- (disparities) = b * log(prox)
- (disparities) = a + b * log(prox)
- exponential MDS
- (disparities) = exp(prox)
- (disparities) = b * exp(prox)
- (disparities) = a + b * exp(prox)
- power MDS (which includes square root with q = 0.5):
- (disparities) = (prox)^q
- (disparities) = b * (prox)^q
- (disparities) = a + b * (prox)^q
- polynomial MDS (i.e., spline MDS without interior knots)
- (disparities) = a + b * (prox) + c * (prox)^2
- (disparities) = a + b * (prox) + c * (prox)^2 + d * (prox)^3

Software Package | Program, version, date | Metric MDS supported |

MATLAB 7.8.0.347 (R2009a) | mdscale() 1.1.6.9, 12/01/08 Criterion = 'metricstress' | Ratio only |

smacof in R 0.9-0 (05/24/08) | smacofSym(), metric = TRUE | Ratio only |

SPSS 17.0.0 (08/23/08) | Proxscal version 1.0 | Ratio, Interval, Spline |

SYSTAT 12.02.00 | Multidimensional Scaling Shape = Square (similarities model) | Interval (Linear), Log, Power |

To date, no program in any of these software packages provide combinations of two or more than two transformations, but these could be very helpful. For example, log + polynomial may be of interest, because log may be used to normalize residuals, while polynomial may be able to pick up the trend of the data. That is,

- (disparities) = a + b * log(prox) + c * log(prox)^2
- (disparities) = a + b * log(prox) + c * log(prox)^2 + d * log(prox)^3

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