Fig. 1. **Scree plot of eigenvalues**

How many principal components we should use depends on how big an *qr* we need. This criterion involves retaining all components up to a total percent variance (Lebart, Morineau & Piron, 1995; Jolliffe, 2002). It is recommended that the components retained account for at least 60% of the variance. The principal components that offer little increase in the total variance explained are ignored; those components are considered to be noise. When PCA works well, the first two eigenvalues usually account for more than 60% of the total variation in the data.

In our current example, the percentage of variance accounted for by each component and the cumulative percent variance appear in Table 3. From this Table we can see that the first component alone accounts for 53.057% of the total variance and the second component alone accounts for 39.597% of the total variance. Adding these percentages together results in a sum of 92.65%. This means that the cumulative percent of variance accounted for by the first two components is about 93%. This provides a reasonable summary of the data. Thus we can keep the first two components and "throw away" the other components.

A number of other criteria have been proposed to select the number of components in PCA and factorial analysis. Users can read Lawley (1956), Horn (1965), Humphreys and Montanelli (1975), Horn and Engstrom (1979), Zwick and Velicer (1986), Hubbard and Allen (1987) and Jackson (1993), among others.

192 Principal Component Analysis

How many principal components we should use depends on how big an *qr* we need. This criterion involves retaining all components up to a total percent variance (Lebart, Morineau & Piron, 1995; Jolliffe, 2002). It is recommended that the components retained account for at least 60% of the variance. The principal components that offer little increase in the total variance explained are ignored; those components are considered to be noise. When PCA works well, the first two eigenvalues usually account for more than 60% of the total

In our current example, the percentage of variance accounted for by each component and the cumulative percent variance appear in Table 3. From this Table we can see that the first component alone accounts for 53.057% of the total variance and the second component alone accounts for 39.597% of the total variance. Adding these percentages together results in a sum of 92.65%. This means that the cumulative percent of variance accounted for by the first two components is about 93%. This provides a reasonable summary of the data. Thus we

A number of other criteria have been proposed to select the number of components in PCA and factorial analysis. Users can read Lawley (1956), Horn (1965), Humphreys and Montanelli (1975), Horn and Engstrom (1979), Zwick and Velicer (1986), Hubbard and Allen

can keep the first two components and "throw away" the other components.

Fig. 1. **Scree plot of eigenvalues** 

(1987) and Jackson (1993), among others.

variation in the data.
