Cluster analysis on ranked data (ordinal data)

[mdedeepya]

Hi,

I have around 90 respondents who have ranked certain values on a ranking scale (ordinal data). Now I want to do a cluster analysis to check if there are any groupings that would throw up. Few questions that I have:

1. Can we perform cluster analysis on ordinal (ranked) data? or do we need to change it to some other kind of data?
2. In SPSS, there are different kinds, 2 step, hierarchial etc. clustering. Which one is best suitable for this data?
3. What other statistical tools can be used to get some meaningful analysis for such ranked survey data?

Please respond as soon as possible. Thanks in advance

Regards
Dedu

[Sherman Whipple]

To your first question, yes, cluster analysis can be applied to ordinal data, as can various forms of threading or filtering. This said, 90 is kind of a small base, and depending on your control frame, relatively coarse.

Can't help you with SPSS

The method I would use is chi-square.

Sherman

[Statman]

For SPSS, this was posted on another forum that I believe offers a very good bit of information; you could treat your ordinal as continuous BUT as Sherman noted, 90 cases will provide limited results

The only clustering method in SPSS which can handle continuous and categorical variables simultaneously is two-step clustering. Although I personally prefer Latent Class Cluster analysis, I believe two-step clustering provides Goodness-of-fit indices (AIC and BIC) for intercomparison between models. However, I would not recommend to rely on just a statistical criterion. (How) can you describe your clusters? How many clusters do you propose and how large are they? Does the overall picture make any sense? Is the result actionable for you or your client? I find the answers to such questions more important than the AIC.

K-means clustering is based upon the concept of 'distances' between respondents (usually squared Euclidean distances). Such 'distances' make sense only for metric variables. For ordered Likert scales, you must be willing to make the assumption of equal distances (between answer categories) if you want to use them for k-means clustering.

In hierarchical clustering, either all variables must be binary, counts or metric but no mixture of these is allowed. It does, however, provide you with a 'dendrogram' which suggests a (statistical) optimum for the number of clusters.

All three clustering methods in SPSS depend upon the (arbitrary) order of cases so it is often recommended you compare a number of solutions from different random orderings of cases.

[UMG International]

Usually cluster work better in scaled data. You can use hierarchical or k-means clusters depending of our goal - (to understand the links - hierarchial, to group the data - k-means)

[sdobney]

Something else to consider - not clustering, so if grouping respondents is your aim it may not be the way to go - but you can analyse rankings using voting type systems to determine a smaller set of preferred options and then decide who prefers what. For instance you could apply a transferable vote system. You take the first preference of everyone to start and find the least preferred item. You 'eliminate' the least preferred item and take second preferences from these respondents. Then progressively eliminate options until you have a top 3 or 4 items. You could also exclude items having a rank below 4 or 5 and see how many respondents are covered. Then you can drill down into the preference groups for the determined top 3 or 4 items. Like I said, it's not clustering as such, but it might provide some other insights into groups with different preferences.


Saul

[mdedeepya]

Thanks Sherman for your reply. Yes i also understand 90 is a very small no.

i read a few papers, which have done hierarchial clustering to find theno.of clusters and then k means to do the cluster analysis on such ranked data. However, did not get conclusive results.

The survey that i have used is rokeach value survey. It has two sets of values , each of which needs to be ranked from 1 to 18. so there are two sets of 1-18 ranks.
My query is can we do cluster analysis on such values (Where in the ranks are repeated twice)? or shud we do analysis only on one set of values..with unique rankings?

anyone who could help me on this please..

regards
dedu

[mdedeepya]

thanks for your reply!

[mdedeepya]

thanks a ton for the reply.
yes my goal is to cluster the respondents..
so you say, we follow this transferable voting system to form clusters of respondents or to find preferences in the groups. ? i gt a bit confused.

The survey that i have used is rokeach value survey. It has two sets of values , each of which needs to be ranked from 1 to 18. so there are two sets of 1-18 ranks.
My query is can we do cluster analysis on such values (Where in the ranks are repeated twice)? or shud we do analysis only on one set of values..with unique rankings?

also, if you say cluster analysis is nt the solution, if would be great if you could suggest me some other stats which could be used to find sub groups in this data..

regards
dedu

[Sherman Whipple]

I have a very limited knowlege of Rokeach, mostly since since it was a competing methodology to VALs and more the specialty of academic psychologists and graduate students than in business intelligence. But, like VALs, the data is not ordinal or ranked, but rather psychograpic, part of the control or frame, not the data being analyzed.

Therefore, your comparison needs to be based upon representativeness against a control sample. Straight indexing or a chi-square overlay, if you have a control model, will accomplish this. This was the advantage of VALs. SRI has thousands of surveys of thousands of products so you could compare virtually any observation against a close comparable.

Fifteen years ago, in addition to the fact that it was a bit cumbersome to administer, the lack of comparables and control data was one of the drawbacks of Rokeach, but for what you have, that is the way to go.

[Saegetus]

Definitely yes, you can perform cluster analysis on ordinal data.

As about the clustering methods probably the best approach is to choose a Latent Class clustering (with Latent Gold for example).

Hierachical clustering at the respondent level is also a commonly used method.

But you have to compute the Canberra proximity (recommended for ordinal data) between respondents and then you can use this matrix as input for the SPSS hierachical cluster analysis (see Cluster command with Matrix IN).

In a similar way for a much more general case when you have a combination of variables with scale, nominal, ordinal and binary structure you can use the Gower proximity (similarity) measure as input for Cluster command in SPSS.

Unfortunately both proximity measurements are not available for the moment in the SPSS package but there are many other tools that might help you to calculate them.

Hope it helps!

Saegetus

[ruthevans41]

Hey even I used to know clustering can be done on scaled data. Just read it can be done on ranking scale. Nice post thanks a lot Saegetus for throwing light on some unknown facts.