Dear all,

My data includes almost three thousand people who rank ten categories into
three variables. The simple example below is almost same except I have many
missing values.

x <-

    cbind(

        sample( LETTERS[1:10] , 3000 , replace = TRUE ) ,

        sample( LETTERS[1:10] , 3000 , replace = TRUE ) ,

        sample( LETTERS[1:10] , 3000 , replace = TRUE )

    )

I try to figure out the pattern among the categories showing which
categories are ranked together by the respondents.

I need a scientific method to visualize this pattern among the categories.
Particularly, I do interest in constructing clusters, which shows the
proximity among the categories.

I am not sure if analytical strategy is the best decision, but I thought
MDS (Multi dimensional scaling) as a technique to reduce the ten categories
into three or two clusters, and show the similarities among them in a
figure.

When it comes to MDS, I could not convert the data into dissimilarity
matrix due to data structure.

I found out similar preference data in smacof package:

data(breakfast,package="smacof")

But, this data(breakfast)  includes ranking of  all the categories while my
data has limited place (three ranks/variables for ten categories). Plus,
while breakfast data includes limited cases and many variable, but my data
is individual based and so more cases little variables.

At first, I would like to ask you if MDS suits well for my strategy and the
structure of my data?

If this is the optimal way, I`d be more than happy if you can help me how
to figure out conversion of my data into dissimilarity index.

All the best,

Niklas

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