R - Multidimensional Scaling and Missing Values

Question

I include MDS analysis in a customer survey and have about 10 brands I want to include in the perceptual map at the end. Meaning the customers would have to rate 45 comparisons and give a similarity rating of 1 to 7 to each of the 45 comparisons.

Now my question. Is it a problem when NOT all customer rate the similarity of all comparisons? Meaning, I would have missing values for certain similarities between two brands. Especially for the case when I aggregate the individual answers to create an aggregate solution.

I plan to do the analysis with R and don't know exactly how I can handle missing values in a MDS analysis and if they will have an impact on the explanatory power at the end.

Answer 1

This question is quite old, but I have the same issue and potential solutions.

Options:

1. Exclude rows with missing data
2. Impute values (e.g. using median or more sophisticated approaches, such as nearest neighbour, maximum likelihood, etc.)

This article has an overview of imputation methods http://www.amstat.org/sections/SRMS/webinarfiles/ModernMethodWebinarMay2012.pdf

In general, your analysis will have less power by either reducing the sample size (option 1) or estimating values (option 2).

Answer 2

The question is very old, but although Minnow is perfectly right, his answer only gives general hints to data preparation rather than offers any MDS-related tips.

While classical MDS is not able to process the dissimilarity (distance) matrix, there are some MDS types which are able to do that (as pointed out f.e. in Groenen 2013)

I am myself not an expert, however a keyword to look at could be The Isomap algorithm of Tenenbaum, De Silva, and Langford (2000) and the article Data Visualisation with Multidimendimensional Scaling (Buja et al. 2008) could also help.