A method, similar to exploratory factor analysis, that takes a dataset of values for a number of objects (usually people in our fields) on a number of variables and gives a mapping in a number of dimensions, fewer than the number of variables, of those objects. A typical use is to take scores on items in a questionnaire, say the 14 item Hospital Anxiety and Depression Scales (HADS) from a good number of people. That might show the people on a 2D map where one axis is probably an anxiety dimension (hence the “dimensional” in “multidimensional scaling”, the other (hence the “multi” = more than one dimension) is probably a depression dimension. (Apologies for perhaps sounding as if I believe in mental health diagnoses. I do think that these two ideas, anxiety and depression, don’t have to be reduced to diagnoses and can be helpful.)
Details #
What’s nice about the methods is that they don’t assume Gaussian distributions of scores nor even that there is some linear meaning to the scores, they simply assume “montonicity”: that a higher score is higher than a lower score, they are (generally) ranking methods, i.e. they treat the scores as having only ordinal scaling properties. They can be instructed to treat ties, i.e.where two different scored the same on an item as genuine equality, or can allow that that is implausible and allow “untying” of ties. They can handle different numbers of dimensions and have methods that suggest, given the model, an appropriate number to use. They seem to have rather fallen out of favour in our fields since probably the late 1980s.
In our fields MDS was mainly applied to questionnaire or rating data as a psychometric method, i.e. looking for metrics in psychological things. Outside of psychometrics they underpinned “smallest space analysis” but I haven’t seen that for a long time now.
Try also #
Exploratory factor analysis (EFA)
Factor analysis
Factor scores
Ordinal scaling
Psychometrics
Ranking
Rank correlation
Scaling
Stevens’ levels of measurement/scaling
Ties
Chapters #
Not covered in the OMbook.
Online resources #
None forseeable.
Dates #
First created 24.xi.24.
