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Perceptual maps and multidimensional scaling - Multidimensional scaling models - Nonmetric MDS

Q: What is the essence of the difference between metric and non-metric MDS?

That non-metric MDS uses a monotonic function , as it is about ranks instead of metric data .

Q: What are the steps of non-metric MDS?

Make a table with the data delta ij Assign ranks to the data and order the delta ij in a new table according to ranks. Have the model predict the distances and put them in column d ij . If the distances are not monotonically increasing , then average the two values where it is decreasing (the decreased and the one before). These adjusted distances are called disparities and are written in the final column d^ ij . Badness of fit is tested with Stress using the formula on the picture with the summation of i<j meaning to sum over all pairs. Larger numbers are worse.

Q: What is a monotonic function?

One that always rises or stays level, but never goes down.

3 important questions on Perceptual maps and multidimensional scaling - Multidimensional scaling models - Nonmetric MDS

What is the essence of the difference between metric and non-metric MDS?

That non-metric MDS uses a monotonic function, as it is about ranks instead of metric data.

What are the steps of non-metric MDS?

Make a table with the data delta_ij
Assign ranks to the data and order the delta_ij in a new table according to ranks.
Have the model predict the distances and put them in column d_ij.
If the distances are not monotonically increasing, then average the two values where it is decreasing (the decreased and the one before).
These adjusted distances are called disparities and are written in the final column d^_ij.
Badness of fit is tested with Stress using the formula on the picture with the summation of i<j meaning to sum over all pairs. Larger numbers are worse.