Number of Dimensions
mds (prodedural topics | metric output data)

In the example in which paired-city distances were plotted on a two dimensional map with north-south and east-west dimensions both the number and interpretation of the dimensions were known before the experiment was conducted. This is often not the case when performing experiments with stimulus sets, whose nonmetric ordering depends on standards of comparison that are only vaguely understood by the respondent and whose dimensions can only be ascertained after the statistical procedure has been run.

In order to help the analyst statistical routines and measures have been designed to identify the appropriate number of dimensions. (Kruskall1964a and1964b)

Interpretation of Dimensions
mds (prodedural topics)

The interpretation of dimensions is almost always a matter of judgment and should only be undertaken by those very familiar with the stimulus set and population under investigation. In this regard multidimensional scaling differs little from other statistical techniques such as factor and cluster analysis. There are no obvious clues, but careful inspection of outliers and/or the inclusion of known elements in the stimulus set can often provided helpful starting points.

In order to lighten the researchers task it is wise to query individual respondents about the standards they are likely to employ in the ranking of paired or unpaired elements. Such queries not only provide the researcher important clues about the meaning of the resulting dimensions, but also stimulate the respondent to be more thoughtful about his ranking of the stimulus set when finally presented with the task.

A more direct approach is to ask respondents to list the criteria they employed in ranking elements, and then to rate, or alternatively rank, each element of the stimulus set against the listed criteria. If metric interval data is employed, additional statistical procedures such as regression analysis can then be employed and the dimensions better understood. See the section entitled Criteria Ordering for more details.

statsitical modelling (mds)

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statistical modelling (diagnostics)