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I need some help finding the correct direction to go in. Here is the problem:

I have a dataset of unique devices, and each device has a count of the number of service tickets opened in each of 4 categories. Here is some sample data.

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For each device ID separately, I need to determine if the ticket types are clustering or grouping in some way, and if so, which types are most common. A cursory look at these data might suggest that:

  • ID #1: there is grouping, Type 1 is most common
  • ID #2: does not appear to be grouping
  • ID #3: grouping, Type 1 and Type 3 most common
  • ID #4: grouping, Type 4 is most common

I realize that my definition of 'grouping' is very lax, and that is where I need assistance.

Should I be looking at particular distance metrics? perhaps proportional? Any advice would be much appreciated.

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  • $\begingroup$ As a first step, you may want to normalize each row by its vector norm. This will remove the effect of some IDs having more overall tickets. $\endgroup$ – user75138 Oct 29 '15 at 20:30
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Latent class analysis would be an appropriate choice for finding any underlying or hidden groupings in your typology. I made this same suggestion earlier today on a question about grouping illicit drug users by the drugs they ingested...here... What are the statistical methods I can use to find popular or common combinations of categorical variables?

Everything said there applies to your situation.

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  • $\begingroup$ the difference, I think, is that I have no real inherent variability in the data. In the illicit drug example, the latent classes use information from the distribution of respondents, whereas I am basically considering each device ID independently. $\endgroup$ – HEITZ Oct 29 '15 at 20:53
  • $\begingroup$ The LC model would cross-classify the types by ignoring the device IDs, thereby creating the "inherent variability" needed to partition the residual. $\endgroup$ – Mike Hunter Oct 29 '15 at 20:55
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This is not clustering what you are describing.

Instead, you apparently want to test uniform distribution of the ticket severities.

There are many measures from information theory such as Shannon entropy that may be of interest to you.

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