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I have ordinal data on scale 1-5 for detected pollutants in water (1 = detectable in small proportions; 5= detectable in higher proportions; also 0 was asaigned - not detectable).

I want to do HCA in SPSS. For measure I will choose Count (chi-square). But there are different methods possible. I did cluster analysis with different methods, and the best one was Wards method.

Is it ok, to use Wards method for ordinal data, if not what clustering method would be appropriate for this type of dataset?

user49496
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  • For measure I will choose Count. Are your dataset counts to choose that? Ward is appropriate only for scale data and (squared) euclidean distance measure. – ttnphns Jul 14 '16 at 12:27
  • I read for SPSS: If we have ordinal data (counts) we can select between Chi-Square (think cross-tab) or a standardized Chi-Square called Phi-Square: http://www.statisticssolutions.com/cluster-analysis-2/.I have read that ward method is appropriate for continuous data, that why I was wondering which method could I use for dealing with ordinal data? – user49496 Jul 14 '16 at 12:33
  • Counts are counts, they aren't ordinal data values. – ttnphns Jul 14 '16 at 12:35
  • Thanks, could you suggest how to deal with ordinal data, because I want to try to verify the results of factor analysis with cluster analysis – user49496 Jul 14 '16 at 12:39
  • Classic factor analysis is not for ordinal data. If you did standard FA on your data that means you treated your data as scale. Then why not treat them as scale in a cluster analysis either? – ttnphns Jul 14 '16 at 12:47
  • I did factor analysis with ordinal data using polychoric correlation in R. – user49496 Jul 14 '16 at 12:50
  • OK, that's valid. But what do you mean saying I want to try to verify the results of factor analysis with cluster analysis? Maybe it is worth to describe your specific situation and aims right in your question? For as for now, the question looks a bit "too broad". – ttnphns Jul 14 '16 at 12:54
  • Ok, factor analysis extracted 4 Factors (different origin of pollutants). I want to try, if cluster analysis will give me the similar groups (clusters) of pollutants. – user49496 Jul 14 '16 at 12:58
  • Please describe everything in your question. What are the data rows, columns. Are you going to cluster rows or columns? Did you do factor analysis on columns? – ttnphns Jul 14 '16 at 13:08
  • Cases present sampling points (n=54) where the intensities (1-5) were measured in water and the columns present 12 variables (pollutants in water). I did factor analysis on columns (Factor - group of pollutants). I want to do cluster the same on columns (variables) to see if I will get the similar groups of pollutants. – user49496 Jul 14 '16 at 13:16
  • OK, factor analysis and cluster analysis are not techniques of the same breed, though FA is sometimes said to be forming "clusters" of attributes. At your place, if I wanted to "confirm" variable groups, given by FA, by a cluster analysis of the variables, I would use the same similarity measure as the FA used - i.e. the tetrachoric correlations. I would do HCA of the matrix of those correlations (abs. values). HCA in spss can take in arbitrary distance matrix if run via syntax. Read CLUSTER command chapter in "Command syntax reference". – ttnphns Jul 14 '16 at 19:31
  • thank you very much for your suggestions. I did the HCA with polychoric correlation matrix, which I have used in FA. I got exactly the same results as with FA. Now the question arises, namely, if we use the same matrix (i.e. polychoric matrix) in HCA and FA, isn`t it logical that you get the same results since it only show factors as dendrogram or am I wrong? – user49496 Jul 15 '16 at 09:29
  • As I've said before, cluster analysis and factor analysis are theoretically different methods (latent variable vs unsupervised classification), though they may and often do give similar groupings of items. – ttnphns Jul 15 '16 at 10:23

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