# Clustering 5 dimensions into 4 based on mean?

In my project, one variable named Organizational Culture has 5 dimensions namely Employee Development, Harmony, Customer Orientation, Social Responsibility and Innovation. In SPSS, I need to configure these 5 dimensions into 4 types so that:

1. The highly integrative culture has high scores on all 5 dimensions.
2. The market oriented culture describes the organizations that emphasize customer orientation more than any other cultural dimension.
3. The moderately integrative culture shows average scores on all ?ve culture dimensions.
4. Lastly, hierarchy culture show low score on all culture dimensions.

In short, here is what I need:

I need to cluster the firms from which I got data into 4 types (highly integrative, moderately integrative and so on) on the basis of the score assigned by their (firms') managers to the the 5 culture dimensions. As a result I will have four types of firms which will have four different culture types. I do see some hope in the method you suggest in your above post. Thank you very much for your time and I appreciate any help :)

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What did you try so far? This sounds as if you want to set two thresholds... –  Anony-Mousse Jun 1 '12 at 20:51
I tried cluster analysis to divide the firms into 4 categories, but I'm not sure if I followed the right procedure. Besides I don't seem to be able to meet the criteria mentioned for configuration. I have seen this done in an article, but don't know how to post a screenshot here? Tx –  Muzi Jun 1 '12 at 21:56
Cluster analysis might not need your criterias. It may return anything. Did you consider setting up thresholds (high/low) to define these four groups manually? –  Anony-Mousse Jun 2 '12 at 8:20

Nice question, and nice dataset (+1)

Here you have to take decisions. You know where your clusters are intuitively since you are able to describe them. Cluster analysis, or Principal Component Analysis etc. would give you the "natural" segmentation of your dataset, not necessarily the one that you want to impose on it.

As I see it, you have to make the jump from "high score on all dimensions" to 5 defined numbers. You can make 4 centroids that correspond to the average 5 scores you expect from each type and assign each company to the type of the nearest centroid (Euclidean distance).

An alternative might be to use a trusted subset of the data where you know which class a company belongs to in order to train a model like Linear Discrimnant Analysis. Once the model is trained, you can use it to predict the class of the other companies.

In R this is really easy.

library(MASS)
trained <- lda(training_set, known_types)
types <- predict(trained, dataset)\$class

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I am agree with gui11aume. I just wanted to suggest that instead of using abstract centroids you may want to use one or more exact typical organizations for every class. In this case it is more classification with given samples, but if you have any expert bias it should work better. –  Dmitry Laptev Jun 2 '12 at 12:58
Thank you very much for your ideas. I will take sometime to implement these ideas, since I have to do a bit of related reading. Once I perform these analyses, I will post back. Thanks again for your time and efforts in helping me:) –  Muzi Jun 2 '12 at 14:39
[[[[[You can make 4 centroids that correspond to the average 5 scores you expect from each type and assign each company to the type of the nearest centroid (Euclidean distance).]]]]] Could you please explain how I can do this in SPSS. Thanks for your reply:) –  Muzi Jun 2 '12 at 15:22

Not sure, but I think the centroid-based suggestion by Gui11aume assumes that you are going to include each and every case in one of the clusters. In practice I often find that, when one sets up criteria such as yours to define the clusters, only perhaps 50% to 80% of cases will make a good fit to any of these descriptions. (Why should a priori profiles apply to everyone?) So if it is acceptable to you and/or consistent with your knowledge of the situation to have some cases left out, consider using a series of DO IF and ELSE IF statements to assign some cases to clusters, something like the following.

*For those high on all 5 dimensions.

DO IF EmployeeDevelopment > [threshold] and Harmony > [threshold] and CustomerOrientation > [threshold] and SocialResponsibility > [threshold] and Innovation > [threshold].

Compute Cluster = 1.

*For those high only on Customer Orientation.

ELSE IF EmployeeDevelopment < [threshold] and Harmony < [threshold] and CustomerOrientation > [threshold] and SocialResponsibility < [threshold] and Innovation < [threshold].

Compute Cluster = 2.

*Etc. for the other 2 clusters.

END IF.

EXE.

You may need to adjust the structure of this syntax a little. If it gives you problems, you can simplify using the following. It's just that on a very large data set it will require more computing time.

IF [cluster 1 criteria are met] cluster = 1.

IF [cluster 2 criteria are met] cluster = 2.

*Etc.

EXE.

With this framework, whatever command you include last will overwrite the earlier ones, so you'll need to be conscious of the order you choose.

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Thank you very much for your answer, rolando2. Yes, like you mentioned, meeting all my criteria may be difficult and I may have to leave out some cases which I don't want to do. I'm meeting my supervisor next week and let's see if she can save me! Thank you all very much for your help. You have been amazing! –  Muzi Jun 3 '12 at 23:06