Cluster Analysis Grouping Cases or Variables

Clustering Cases Goal is to cluster cases into groups based on shared characteristics. Start out with each case being a one-case cluster. The clusters are located in k-dimensional space, where k is the number of variables. Compute the squared Euclidian distance between each case and each other case.

Squared Euclidian Distance the sum across variables (from i = 1 to v) of the squared difference between the score on variable i for the one case (X i ) and the score on variable i for the other case (Yi)

Agglomerate The two cases closest to each other are agglomerated into a cluster. The distances between entities (clusters and cases) are recomputed. The two entities closest to each other are agglomerated. This continues until all cases end up in one cluster.

What is the Correct Solution? You may have theoretical reasons to expect a certain k cluster solution. Look at that solution and see if it matches your expectations. Alternatively, you may try to make sense out of solutions at two or more levels of the analysis.

Faculty Salaries Subjects were faculty in Psychology at ECU. Variables were rank, experience, number of publications, course load, and salary. Data are at ClusterAnonFaculty.savClusterAnonFaculty.sav Also see the statistical outputthe statistical output

Analyze, Classify, Hierarchical Cluster

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Proximity Matrix We did not request this, but if we had it would display a measure of dissimilarity for each pair of entities. The pair of cases with the smallest squared Euclidian distance are clustered.

Stage Cluster CombinedCoefficients Cluster 1 Cluster 2Cluster Look at the Agglomeration Schedule. Cases 32 and 33 are clustered. They are very similar (distance = 0.000)

Agglomeration Schedule Stage Cluster Combined Coefficient s Stage Cluster First Appears Next Stage Cluster 1Cluster 2Cluster 1Cluster 2Cluster 1Cluster Steps 2 Through 5

Stages 2-5 The agglomeration schedule show that in Stage 2 cases 41 and 42 are clustered. In Stage 3 cases 43 and 44 are clustered. In Stage 4 cases 37 and 38 are clustered. In Stage 5 case 39 is added to the cluster that contains cases 37 and 38. And so on.

Vertical Icicle, Two Clusters Look at the top of the display (next slide). You can see two clusters –On the left Boris through Willy –On the right, Deanna through Sunila The 2 cluster solution was adjuncts versus full time faculty.

Vertical Icicle, Three Clusters Look at the icicle second highest white bar. Now there are three clusters –Adjuncts –Junior faculty (Deanna through Mickey) –Senior faculty (Lawrence through Roslyn)

Vertical Icicle, Four Clusters Look at the white bar furthest to the right. Now there are four clusters –Adjuncts –Junior faculty –The acting chair (Lawrence) –The rest of the senior faculty (Catalina through Roslyn)

The Dendogram At the far right you can see the two cluster solution. The next step to the left shows the three cluster solution. The next step to the left shows the four cluster solution. And so on. Truncated and rotated dendogram on next slide.

Compare Two Clusters The 2 cluster solution was adjuncts versus everybody else. Look at the t tests in the output Adjuncts had lower rank, experience, number of publications, course load, and salary.

Compare Three Clusters Look at the ANOVAs and plots. The senior faculty had higher salary, experience, rank, and number of pubs. Compare Four Clusters The acting chair had a higher salary and number of publications.

I Could Not Help Myself With these data on hand, I could not resist predicting salary from the other variables. Salary was well correlated with Rank, FTEs, Publications, and Experience. In the multiple regression, only Rank and FTEs had significant unique effects. The residuals suggest who was being overpaid and who underpaid.

Split by Sex For men, the unique effect of number of publications was positive – more publications, higher salary. For women it was negative – more publications, lower salary. Curious.

Workaholism Aziz & Zickar (2005) Workaholics may be defined as those –High in work involvement, –High in drive to work, and –Low in work enjoyment. For each case, a score was obtained for each of these three dimensions.

The Three Cluster Solution Workaholics –High work involvement –High drive to work –Low work enjoyment Positively engaged workers –High work involvement –Medium drive to work –High work enjoyment

Unengaged workers –Low work involvement –Low drive to work –Low work enjoyment Past research/theory indicated there should be six clusters, but the theorized six clusters were not obtained.

Clustering Variables FactBeer.sav The statistical output.The statistical output Analyze, Classify, Hierarchical Cluster

Statistics

Plots

Method

Proximity Matrix Is simply the intercorrelation matrix The two most correlated variables are Color and Aroma (r =.909) – they are clustered on the first step. Stage 2: Size and Alcohol (r =.904) are clustered. Stage 3: Taste added to the cluster that already contains Color and Aroma

Also See Other Tables & Plots Stage 4: Cost added to the cluster that already contains Size and Alcohol. Stage 5: The two clusters are combined –But they are not very similar (similarity coefficient =.038) –Now we have one cluster with six variables and one with one (Reputation)