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I have done a principal component analysis using SPSS and now have 3 components. 2 components have 4 items in the subscale, and 1 component has 3 items. Component scores using regression for each factor were added as variables to the data set by SPSS.

My question is: can the component scores (the new variables that SPSS added to the data set) be used as the variables for K-means cluster analysis to form clusters? My aim is to find out the exact number of cases in each factor, which I intend to do through cluster analysis. Is this the statistically correct method? Thank you for any input.

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    $\begingroup$ Questions like this have been asked on this site many times. The general answer for your title is Yes. However, if the number of components is less than the number of original variables, you are at risk to lose some important, for clustering, information. This picture is an example: the only one PC taken separates the two clouds considerably poorer than both PCs (= original variables). $\endgroup$ – ttnphns Mar 26 '14 at 8:38
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My impression is that yes, you can certainly do a cluster analysis using the component scores. If you are interested in clusters of individuals based on these component scores (can we say latent factors?) then doing the analysis using the component scores makes complete sense. Lets say you are measuring factors of personality, you would likely be far more interested in clusters determined using the component scores (i.e., measuring personality) than you would on individual items.

This, however, might not be the case if you are trying to do some sort of latent cluster analysis. In this case, you may want to use individual items to estimate the latent factors in the analysis.

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  • $\begingroup$ Thank you for your answer. Let's say I have done the K-means analysis and cluster membership has been assigned to the cases, would the cluster membership=factor membership? i.e. would a case belonging to cluster 1 indicates the case belongs to factor 1? I ask this as I want to calculate the exact number of cases in a factor, e.g.number of people belonging to factor of happy people. $\endgroup$ – StatsDummy Mar 26 '14 at 8:22
  • $\begingroup$ Cluster membership would reflect the factor, yes. So if you have a factor that is happiness, and your interpretation of the clusters is that one group is the "happy" group, then yes the number of people in that class would reflect the number of "happy people". That being said, you need to be careful in your interpretation of classes. The classes may or may not be "real" in truth. So the happy people may be the happiest in your data, but that doesn't mean that they are truly happy people or that happy people even exist. You may benefit from reading up on K-means if you think this is an issue. $\endgroup$ – Behacad Mar 26 '14 at 8:31

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