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I see that the issue of splitting a variable into two categories has been discussed on this forum and I understand pros, cons as well as some ways of performing it. The issue that I am interested and can't seem to find anything on splitting a variable into three points.

For this to make sense let me briefly explain my data. I have used a psychographic scale (5 Point Likert) which consists of eight items where low scores indicate one trait and high scores indicate a different one. Theoretically, most people should fall into the mid group, with much smaller extreme groups which show clear tendencies for certain behaviour. Thus, I used this scale with an intention of grouping my respondents into low, middle, and high groups. This classification into three groups is supported conceptually by previous research but no study discloses how groups are split.

I tried using a composite score for the scale and e.g. correlate with a dependent variable. However, because extreme groups are relatively small the result for the whole sample indicates asssociation in the expected direction albeit very low. I have considered dichotomising but individuals with top or low scores on the eight variables get muddled up with middle scores that conceptually do not indicate any distinct group.

Having looked into graphical representation of the scale I can conclude that distribution is normal and indeed most people score in the middle. Thus, visually I can identify the cut-off points which seems to make sense, it produces group sizes supported theoretically and any further tests show significant differences between groups on dependent variables of interest. However, I understand that cutting data this way is very arbitrary. Is there any way I can actually justify doing this based on conceptual support for groups? Is there anything else anyone can suggest as I have run out of ideas. Any help will be much appreciated.

Many thanks in advance.

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    $\begingroup$ They say it is possible to say trochotomising as well. $\endgroup$
    – ttnphns
    Nov 8 '12 at 12:36
  • $\begingroup$ If you've got some external criterion categorical variable you can try optimal binning. $\endgroup$
    – ttnphns
    Nov 8 '12 at 13:51
  • $\begingroup$ Welcome to the site. You don't need to add your name, the system does it automatically. $\endgroup$
    – Peter Flom
    Nov 8 '12 at 13:53
  • $\begingroup$ Closely related topics may be worth some research, George, including Gaussian mixture models and Binning sorted data. $\endgroup$
    – whuber
    Nov 8 '12 at 14:29
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From your description, you seem to have 8 observed responses, each with 5 possible values. Your approach thus far seems to be adding up the total number of points (0-40) and then treating this like a continuous variable. Your question then is how to best categorize this variable.

Another option is to take a latent class approach (synonyms or closely related models you might run across are "model based clustering", "finite mixture modelling", "Gaussian mixture modelling", and "latent profile modelling" - the differences usually are due to the nature of variables used, but the underlying concept is the same for all of these).

The basic idea is to assume that your sample includes a set of unobserved (latent) groups, and that conditional on belonging to a specific group, your observed response items are independent (uncorrelated). This approach is data driven, in that you only specify the number of groups, and then the model will give you some idea of who goes in which group, based on their observed responses. In practice, you will likely try several different models, each specifying a different number of groups (e.g. 1,2,3,4,5) and select the "best model", usually based on some combination of theory/interpretation and model fit. Group membership can then be related to your dependent variable, assuming that your model does a good job of putting people into groups.

There is a really gentle introduction to this in a small, inexpensive book by Allan McCutcheon (http://books.google.co.uk/books/about/Latent_Class_Analysis.html?id=dCbJ6NcH4mAC). Otherwise search for the terms I listed above. You'll quickly find examples using Likert response data.

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  • $\begingroup$ Many thanks for responses - I will look into suggestions made $\endgroup$
    – George
    Nov 8 '12 at 18:52
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If your data is really normally distributed (or as close as can be, given 0-40 count) then it doesn't really split into 3 groups based on the data itself. However, since you say you can visually recognize three groups, it is unlikely that it is really normal.

However, given that, I think you can say that you split the data into three groups based on theory and on visual inspection of the data; you can then show the data (a density plot with a kernel smoother might be good; or a strip plot) and explain how you did this.

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