DSC 410/510 - Multivariate Statistical Methods

Assignment 14 (deadline: 4pm on Wednesday, November 17)

Practical matters

Illustration of MDS from p555-559:

• Reproduce the analysis described in the book with the help of the "Illustration of MDS from p555-559" handout. This provides guidance on using SAS to run a multidimensional scaling on the hatco data (available in the "hatcomds.xls" spreadsheet on the data page). The handout only goes as far as p559 - the book goes on to talk about incorporating preferences and interpreting results in an "objective" way, but we won't be covering that in this course.
• Note that the data have been transformed so that "1" corresponds to "very similar" and "9" corresponds to "not at all similar."
• You'll get slightly different results to those in the book (which uses different software), but your map should be similar to Figure 10.11 on p558 if you switch the axes so dimension 1 is horizontal and dimension 2 is vertical (use Graph > Axis Variables > Exchange X and Y).
• Two ways of finding "potentially unusual" customers are:
  1. If you change the "coordinates" map to "coefficients" (use Graph > Axis Variables > Change) you'll see how individual customers differ from the group solution (the group solution is the (1, 1) position on this graph, so the further an individual is from here, the more weight they put on one dimension over the other). Identify the "most different" individual and investigate how different they are (for example, create an Excel spreadsheet with just their similarity matrix and use SAS to produce their individual map - compare it to the group map, remembering to switch the axes if necessary so the dimension labels match).
  2. Select Results > Fit Statistics to find the "Badness-of-Fit Criterion" (stress) for each customer. Identify the two customers with the highest stress values (whose surveyed responses are most poorly represented by the group perceptual map) and investigate how different they are (by comparing individual maps with the group map).
• After investigating these three individuals (one far from (1, 1) on the coefficients map and two with high stress values), send an e-mail to ipardoe at lcbmail.uoregon.edu with the numbers of these individuals matched to the following descriptions (i.e. your answer should be in the form: "customer a is individual x, customer b is individual y, customer c is individual z"):
  1. This customer provided survey responses that are poorly represented by both the group perceptual map and their individual perceptual map (for example, they say firms E and H are very similar while firms B and E are not at all similar, but on the maps E and H are as far apart or even further apart than B and E).
  2. This customer provided survey responses that are reasonably well represented by both the group perceptual map and their individual map; however, while the relative positions of the firms along the first dimension of the group and individual maps are consistent, the relative positions of the firms along the second dimension of the group and individual maps are less consistent.
  3. This customer provided survey responses that are poorly represented by the group perceptual map but reasonably well represented by their individual map; their individual map indeed looks very different to the group map.

This assignment is worth 15 points rather than the usual 10.