Statistical Methods in Medical Research 4ed

462 Multivariate methods
eigenvalues exceeding 1, they lie in the tail of the scree plot. Most importantly, when three
components were fitted, there was a clear interpretation, but adding another component
did not give a fourth interpretable component. Accordingly, three components were
retained.
In Table 13.2 the first three components are given. The variables have been reordered,
and component correlations exceeding 0 5 are given in bold type, to show the main
features of each component. The first component is correlated more with variables 1, 3,
4, 5, 6, 7, 8, 9, 14 and 17, and may be interpreted as `physical health'. The second
component is correlated with variables 2, 10, 11, 12, 18, 19 and 20, and may be interpreted
as `optimism'. The third component is correlated with variables 13, 15 and 16, and may be
interpreted as `socializing'. The identification of the components in terms of the original
variables is clearer for the rotated components. These three components accounted for
57% of the total variation and, since no clear interpretation was made of the next
component, attention was restricted to these three.
In the above example the dimensionality of the data was reduced from 20 to 3
by the use of principal component analysis. It would appear that the method was
highly effective. However, the original questions were chosen to represent a few
characteristics and, before the data were collected, groupings of the questions
Table 13.2 Component correlations (loadings) for the first three principal components.
Component Rotated component
Variable 1 2 3 1 2 3
1 Physical health good 0 67 0 02 0 01 0 59 0 32 0 07
3 Never breathless 0 63 0 02 0 08 0 55 0 28 0 14
4 Breathlessness does not distress me 0 69 0 28 0 10 0 53 0 51 0 13
5 Rarely cough 0 76 0 31 0 24 0 86 0 00 0 04
6 Coughing does not trouble me 0 77 0 23 0 26 0 84 0 07 0 08
7 Never wheezy 0 77 0 29 0 12 0 77 0 13 0 29
8 Hardly ever feel ill 0 81 0 08 0 08 0 67 0 45 0 12
9 Condition has improved 0 68 0 47 0 30 0 86 0 19 0 04
14 Wife happy with my condition 0 66 0 29 0 04 0 69 0 06 0 21
17 Support the family 0 59 0 19 0 13 0 63 0 06 0 00
2 Optimistic about future 0 22 0 66 0 08 0 07 0 68 0 15
10 Never worry about future 0 23 0 74 0 14 0 04 0 69 0 38
11 Confident could cope 0 43 0 64 0 04 0 13 0 75 0 16
12 Health depends on me 0 29 0 41 0 47 0 01 0 61 0 31
18 Making a useful contribution 0 43 0 49 0 32 0 12 0 70 0 15
19 Accept my condition 0 52 0 44 0 13 0 27 0 64 0 10
20 Feel happy 0 14 0 61 0 15 0 40 0 50 0 00
13 Worth trying anything 0 09 0 37 0 68 0 10 0 15 0 76
15 Feel like going out 0 33 0 27 0 68 0 23 0 12 0 76
16 Relaxing with other people 0 01 0 43 0 64 0 00 0 18 0 75