A Fundamental Problem in Key Factor Analysis
1996
Royama, T.
This paper reveals that key factor analysis, a popular method of life table analysis, cannot address the central issue of population dynamics: the pattern of population fluctuation and its causal mechanism. The basic idea of key factor analysis is to identify factors that contribute significantly to the variation in population. Several statistical methods to identify a key factor have subsequently been proposed in the literature. These are, in terms of the familiar relationship, K = k₁ + k₂ +... + kₙ, to correlate K with a k, regress K on a k, or regress a k on K, the last method being currently most frequently used. These methods, in effect, look for those k's whose variances and covariances constitute a significant part of the variance of K. The fundamental problem here is that the variation in population is inappropriately interpreted as the variance. I show that, in general, different factors play different roles in generating the pattern and that none of these aspects can be indicated merely by the variance of K and its components, the variances and covariances of the k's. I contend that, for judging which factor is major, criteria are multiple and subtle beyond the simplistic idea of key factors.
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