Cluster Analysis

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include between groups linkage, within-groups linkage, nearest neighbour, furthest

neighbour, centriod, median and Ward’s method (Everitt et al., 2001). As objects or variables are clustered into successively larger groups, these methods determine the way in which other objects or group of objects in the set combine to make higher level groups. Further

mathematical details of each method are given in Everitt (2001).

After the researcher selects the clustering algorithm, the third stage involves looking at the output of the clustering in the form of a diagrammatic hierarchical tree structure known as a dendrogram. It is a mathematical and pictorial representation of the entire clustering

procedure. Other output is provided including agglomeration schedules and icicle plots which give information on the clusters formed at each stage in the process. The final stage consists of interpreting the output and using the resulting clusters for the application at hand.

The dendrogram (see Figure 5-8) consists of objects or variables on the left side of the diagram and a line representing proximity or distance across the top. The diagram is read from left to right in the direction of increasing distance. The nodes of the dendrogram tree structure represent clusters, while the lengths of the stems represent the distances where clusters are joined. As the diagram is read left to right, the nodes and distances where clusters are formed become apparent, and the entire grouping structure can be seen at a glance.

The 7 capability and 15 health variables were clustered in SPSS data analysis software using all the agglomerative clustering algorithms available (between groups linkage, within-groups linkage, nearest neighbour, furthest neighbour, centriod, median and Ward’s method). The output was then collated in the form of clustering dendrograms. Split sample validation was performed on the data set by selecting 50% of all cases randomly and re-running the

clustering analyses. A similar structure was found for the split sample dendrograms compared to the full sample, providing evidence that the data set contains a consistent underlying structure.

5.6.2.2 Clustering disability scales

For the capability (or disability) scales, a Euclidean distance measure was selected for the proximity measure, and Ward’s method was found to be the most effective clustering algorithm. Figure 5-8 shows the clustering output for the seven disability scales. The proximity measure used gives the ‘distance’ between every pair of the seven disability variables, and could be interpreted as the physical distance between two multidimensional points. Therefore, in looking at the proximity matrix, the smaller the distance between any two variables, the closer they are in terms of the distance analogy. Because the scales measure

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the level of disability in the population given by the score on the scale, the distances represent how similar the two variables are in terms of the level of disability across the population.

For example, the distance between seeing and communication has the lowest distance (156.375). This means that across the disabled population, the levels of seeing and communication disabilities are relatively close to each other. The communication and locomotion scales have the greatest distance between them (344.641) which means that the levels of communication and locomotion disability vary more widely across the population.

The dendrogram shows that seeing and communication first group together, followed by hearing. Intellectual functioning and reaching/stretching are then joined to this group at a further distance. Locomotion and dexterity form their own group at a larger distance. This structure of the data indicates that levels of seeing and communication are very close together across the disabled population. Hearing, intellectual functioning and reaching/stretching disability levels have somewhat larger variation in levels across the population. However, the largest variation occurs between levels of locomotion and dexterity indicated by the large distances at which these two variables group.

Figure 5-8 Proximity matrix and dendrogram showing clusters of capability loss (based on similar levels of capability loss in the population)

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The implication if this is that across the disabled population, levels of seeing, communication, hearing, intellectual functioning and reaching disability tend to be similar. In other words, not only do these disabilities tend to co-occur, but also they tend to co-occur at a similar level or severity. Locomotion and dexterity disabilities tend to co-occur as well, however they manifest with greater differences in severity.

5.6.2.3 Clustering categories of disability

To further investigate the co-occurrence of disabilities in the population, the 7 capability (or disability) scale variables were converted to categorical disability variables i.e. the severity score value for each scale was replaced with a ‘1’ if it contained a non zero value, or a zero otherwise. This procedure in essence created profiles for each case in the data set showing if a person had a disability or not across the 7 areas of disability. A Jaccard measure of similarity was used, and complete linkage (furthest neighbour) was used as the clustering algorithm.

Figure 5-9 shows groupings for the variables representing similarity in terms of co-

occurrence. In this case, larger distance measures in the proximity matrix represent greater co- occurrence between two variables. It is evident from the dendrogram that that locomotion and dexterity disability are the most likely to co-occur. Reaching disability groups with these two variables to form a motor capability group at a greater distance. Hearing, intellectual

functioning and seeing also group together forming a sensory-cognitive group.

Communication is last to cluster with the previous two clusters due to lower levels of co- occurrence with the other groups.

Figure 5-9 Proximity matrix and dendrogram showing clusters of capability loss (based on co-occurrence)

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5.6.2.4 Clustering Health Conditions

To investigate co-occurrence of health conditions, the 15 disease category variables were clustered using a Jaccard measure of similarity and complete linkage (furthest neighbour) as the clustering algorithm (similar to the clustering of the categories of disability). Figure 5-10 shows groupings of medical conditions. Circulatory and musculo-skeletal conditions group at a very small distance, indicating that of all the medical conditions, these two tend to co-occur most frequently. Respiratory conditions tend to co-occur with circulatory and musculo- Skeletal diseases as well. Other co-occurring groups include eye and ear conditions, mental and nervous conditions, and neoplasms and genito-urinary conditions.

Figure 5-10 Proximity matrix and dendrogram showing clusters of health conditions (based on co-occurrence)

The groups generated by the clustering procedures were reliably structured but difficult to interpret, and it was decided to show the clustering dendrograms to two medical practitioners.

A medical doctor was approached at the Newnham Walk Surgery and a Gerontologist was approached at Addenbrookes Hospital (both in Cambridge) for their interpretation. After explaining how the clustering procedure worked and allowing them some time to study the

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diagrams, two main issues emerged. Firstly, they experienced difficulty in interpreting the cluster groupings directly from a dendrogram due to unfamiliarity with the representation.

Secondly, they found it difficult to give underlying reasons for clustering from broad categories of health (as opposed to specific diseases/conditions). It appears that due to medical training, medical practitioners are skilled at making diagnoses based on specific symptoms, and relating these to various individual diseases. But at a higher categorical disease level, it was more difficult to make interpretations and find reasons that link the capability category to the disease category. Possibly any number of factors could link a family of diseases to various capability losses either directly or indirectly. They indicated that the diagrams, though interesting, highlighted the fact that associating capability groupings with medical conditions is difficult. However, they stated that if these relationships could be better understood, then such information could benefit not only designers, but also medical

practitioners.