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I have conducted a multiple choice survey, and now I want to analyze it using a cluster analysis.

Since it is a multiple choice, multiple variant survey k-mean clustering or fuzzy k-mean clustering seemed like the obvious choice. However, since I am completely new to clustering, I am not sure if it is the best approach after all.

Furthermore, the multiple answers are giving me a hard time, as it does not allow a clear clustering of one-to-one answers. Should I produce distinct data sets for each multiple answer? It would expand the data set way beyond 250 entries, and I am not even sure if it would provide any useful answers because it won't be able to represent when multiple answers were given.

Here is a [link][1] to my data sheet. In the data multiple answers are distinguished by ";" and blank answers are indicated by NULL.

Are there any algorithms that can deal with the data? How would you approach this data set?

Data Snippet:

|Z | A | B | C | |:--|:--:|:--:|-----:| |1 |1 |5 | 1;2;3| |2 |NULL|2 | 1;2| |3 |2 |3 | 1;2;3| |4 |3 |2 | 1;2| |5 |4 |3 | 1;2| |6 |2 |3 | 1;2| |7 |3 |3 | 2| |8 |2 |4 | 1;2| |9 |3 |2 | 1;2| |10 |3 |2 | 1;2| |11 |1 |3 | 1;2;3| |12 |2 |3 | 1;2;3| |13 |4 |3 | 1;2| |14 |4 |4 | 1;2;3| |15 |4 |6 | 1;2;3| |16 |3 |7 | 1;2| |17 |4 |NULL| 1;2| |18 |3 |3 | 1;2;3| [1]: https://docs.google.com/spreadsheets/d/1m7jv-CtHd7vAsRC5J3rK8lJuhnRB4ClCggyIltK_ytA/edit?usp=sharing

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  • $\begingroup$ What is "multiple variant survey k-mean clustering"? I tried to google it but nothing came up. Also better show some of your data here and explain it. By "multiple answers" you mean people get a number of choices and can choose more than one? $\endgroup$ Commented May 21, 2021 at 20:27
  • $\begingroup$ Hey, I want to analyze it using k-mean, but there are multiple questions in the survey. Hence multivariate analysis. By multiple answers I mean exactly what you said - more than one answer option is valid to enter as an answer. See the added snippet of the data above. $\endgroup$ Commented May 22, 2021 at 9:05
  • $\begingroup$ By the way, another note on terminology: "Multivariate" just means that there is more than one variable involved. Almost all clustering is multivariate, there's nothing particularly "multivariate" about yours. $\endgroup$ Commented May 23, 2021 at 9:08

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I assume you want to cluster respondents. I'd probably define a suitable distance between respondents (you could use the simple matching distance within each question and then average over questions if all questions have the same inportance) and do something distance-based such as Average Linkage or Partitioning Around Medoids. A Multidimensional Scaling could be useful for visualisation. k-means can only be run if you dummy-code your answers, and even then it'd not normally be recommended as it is meant for continuous data. There are many methods of cluster analysis (and in fact distance definition) and the choice of method depends on the clustering aim, precise meaning of the data, background information and the like, so I can't really say what is best for you. You may have a look at this: https://arxiv.org/abs/1503.02059

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  • $\begingroup$ Thanks. Yeah, I am completely new to cluster analysis and sorts. You make many valid points! I will have a look at Average Linkage and Partitioning Around Medoids. $\endgroup$ Commented May 22, 2021 at 12:03
  • $\begingroup$ Is there a way to represent the correlation between multiple given answers? By that I mean measuring the distance between multiple clusters. E.g. For question 3 participants have answered 2 | 1;2 | and | 1;2;3| in my understanding the respondents who answered only 2 should be significantly closer to the cluster that favors answer 2. However, participants that answer 1;2;3 should be equally close to all three. Is that understandable? $\endgroup$ Commented May 22, 2021 at 12:13
  • $\begingroup$ (a) You're using terminology wrongly. Correlation is something completely different. (b) When you have distances and run Partitioning Around Medoids, you can look at the distance between a participant and the different cluster medoids (which also give you an idea what characterises the cluster). (c) Your expectation what should happen can obviously be spoiled by what goes on in the other questions. $\endgroup$ Commented May 22, 2021 at 18:07

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