© 2006 American Thoracic Society
On the Usage of Principal Components Analysis and Multiple TestingFrom the Authors:We appreciate the opportunity to reply on the two issues raised by Teo and Chong with respect to the methods we used to identify dietary patterns in a Chinese Singapore cohort and their relation to cough with phlegm as reported in our recent article (1). Teo and Chong recommend the use of Kaiser's criterion as "the right way to interpret findings from principal components," and reference the original 1960 article describing the criterion. Kaiser's criterion has more recently been termed the eigenvalue-one criterion (2). As stated in METHODS of our article, "the number of components retained for rotation was based primarily on examination of scree plots and factor interpretability, but eigenvalues (> 1.0) and percent variance explained were also considered"(1). In fact, using Kaiser's criterion alone may greatly overestimate the number of factors to retain (3). So, our methods were actually more thorough than using Kaiser's criterion on its own. Ultimately, our decision to choose two principal components was clear when we considered the scree plot, in which the first component was the vegetable–fruit–soyfood pattern and the second component was the dim sum–meat pattern, and interpretability of the components. The second issue raised suggests that our findings lack "statistical rigor," because we did not adjust for multiple comparisons. Ironically, we chose to use the principal components method, because it is a solution to the multiple comparisons problem that can occur in conventional analyses of nutritional epidemiologic data. For example, by using principal components analysis, we reduced the extensive dataset of 165 food and beverage items to only two components representing dietary patterns. This is hardly an example of multiple comparisons even when looking at five outcomes. The conventional method would have been to examine each of the items individually in relation to each of the outcomes. In that setting it might have made sense to adjust for multiple comparisons even though it would not be standard in our field when evaluating observational (e.g., nonrandom) data (4, 5). Teo and Chong also suggest that our examination of several outcomes contributes to the problem of multiple comparisons. As we indicated in the introduction to our article (2), we examined dietary patterns in relation to cough with phlegm to follow up on our previous finding of an inverse association between fiber intake and that outcome. We included all of the other respiratory outcomes for completeness and based on requests during the review process. In summary, we incorporated the suggested Kaiser's criterion to decide on the number of components, and we avoided multiple comparisons by using principal components analysis.
University of California–Davis, Davis, California
National Institute of Environmental Health Sciences, Research Triangle Park, North Carolina
University of Minnesota, Minneapolis, Minnesota
Fox Chase Cancer Center, Philadelphia, Pennsylvania
National University of Singapore, Singapore FOOTNOTES Conflict of Interest Statement: None of the authors has a financial relationship with a commercial entity that has an interest in the subject of this manuscript. REFERENCES
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