Hello Manuela,

If your aim is identifying structure for the set of questions, then a factor analysis would be the logical place to start. If it makes sense to conceptualize the 1-4 scores as indicative of a continuum, you could elect to use polychoric correlations among the question scores (rather than Pearson correlations).

Should a multi-factor structure emerge, then you could use estimated factor scores as the values for any number of clustering algorithms. If a single factor structure was apparent, then you'd obviously need other variables in order to do much in the way of clustering (beyond, say, "high," "moderate," and "low" scores relative to your sample).

The alternate approach to factoring would be to apply a multidimensional item response theory model (e.g., partial credit or graded response) to the scores. Doing so will yield scores that can be defended as interval strength (just as factor scores can be characterized).

Good luck with your work.

If your goal is to reduce your data/variables, then with only four variables I don't think that factor analysis or any other similar technique such as PCA will give a useful result. It is more likely that only one factor will be extracted. In case where more than one factors will be extracted, then each one will include very few variables. In my opinion this is meaningless. Unless your goal is to identify a structure in your data.

With regard to cluster analysis, hierarchical cluster can treat mainly continuous variables. Social scientists use hierarchical algorithms with ordinal and binary variables also.

K-means and non hierarchical methods in general are employed with continuous data.

Two Step algorithm in SPSS can treat all types of variables.

I recommend the book of Hair et al (2010) for further reading. There are however many other useful textbooks.

Hi Manuela,

You can consider the following two-step approach:

1) Dimensionality reduction based on categorical data using Multiple Correspondence Analysis.

2) Apply any clustering method to the new continuous factor scores obtained in 1).

2.1) If you have an idea about the number of clusters, you can try K-Means.

2.2) If not, you can use the Ward method, followed by K-Means (I published a paper using this idea, but it is written in Spanish). 

Greetings,

Roberto

Thanks a lot for all these helpful answers! I will try to find the best suited method for my data, but all of them sound promising.