On the Use of Component Scores in the Presence of Group Structure

Environment-quality management coalignment across industrial contexts: An empirical investigation of performance implications

“…We decided not to perform a previous factor analysis of these items and thus not to use factors to form the clusters, since this could lead to inaccurate representation of the true structure of the data. Dillon, Mulani, and Frederick (1989) confirm that the application of only those factors that explain the greatest variance allows us to exclude other factors or items relevant to the formation of clusters.…”

A simulation study of the use of principal components in linear discriminant analysis

“…They also note, and illustrate with a theoretical example, the possible difference in ordering of the 6, and the A, , but they give no example of the implementation of their proposed procedure. Dillon et al (1989) also mention O: , citing Chang (1983), and show with a theoretical example that 9: can be largest for the smallest A, . In addition they include an example with three groups, where selection of components is based on a quantity which they call 'the proportion of across group variance (AGV) accounted for' by the kth component.…”

“…It is well-known that the best principal components for discrimination are not necessarily those with the largest variance, and there has been discussion in the literature of which components make the best discriminators. Chang (1983), Dillon et al (1989) and Kshirsagar et al (1990) all identify a quantity 8, which is of central importance in deciding which principal components (PCs) should be used in discrimination. In practice, 8, must be estimated from a sample of data and none of the needed in order to choose the 'best' PCs from a sample, and we show that there is a simple approximation to the distributions.…”

Dimensionality Reduction on the Cartesian Product of Embeddings of Multiple Dissimilarity Matrices

“…Trunk (1979) affirmed this phenomenon by investigating an illuminating simple example. Chang (1983), Dillon, Mulani, and Frederick (1989), Kshirsagar, Kocherlakota, and Kocherlakota (1990) all established a statistic θ k for the kth principal component (PC) and use θ k to decide which PCs should be used in discrimination. Jolliffe, Morgan, and Young (1996) observed that, for two-class problem, the sample estimateθ k is equivalent to a t-statistic and the hypothesis test based on θ k to decide whether or not to include the kth PC is equivalent to the t-test with null hypothesis H 0k that there is no difference between the two class means.…”