A Comparison of Principal Components from Real and Random Data

Abstract

JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org.. Abstract. We compared principal components derived from sets of real data with dimensions of 120 x 7, 120 x 4, 150 x 11, 150 x 8, 150 x 5, 454 x 12, 454 x 8, and 454 x 5, to those from sets of randomly generated data of corresponding size. Principal components from subsets of 25, 50, 75, and 100 observations from the 120-and 150-observation data sets and those from subsets of 25, 50, 75, 100, 150, 200, 300, and 400 observations from the 454-observation data sets were compared. Percent variance associated with components from real data was relatively constant over all sample sizes; percent variance decreased with larger samples of random data. A bootstrap method was used to develop standard error estimates on percent variance and percent of remaining variance associated with components from real data. Percent of remaining variance associated with the first four components from real data was significantly higher than analogous components from random data.

Geographic variability in demographic performance of the potato moth, Phthorimaea operculella(Zeller) (Lepidoptera: Gelechiidae), in Australia

“…2). As the remaining five components each accounted for less than one-sixth of the total variance, they represented less information than expressed in a single variable and were not considered further (see Stauffer et al, 1985). The latent vectors of the first principal component indicated that the three main parameters contributing to it were, in order of decreasing importance, fecundity, female weight and development rate at low temperatures (Table III).…”

A Critique of Factor Analysis of Interest Rates

“…8 The advantage of using the same variance σ 2 f for all forward rates is that the correlation matrix of the spot rates (12) does not depend on σ f , making the presentation more transparent. 9 For a more detailed examination of the results of factor analysis and principal components analysis of random data, see Stauffer, Garton, and Steinhorst [1985].…”

Range-wide analysis of northern spotted owl nesting habitat relations

“…While many studies support the utility of MaxEnt (Elith et al, 2006;Phillips et al, 2006;Phillips and Dudik, 2008;Phillips and Elith, 2013), others such as Torres et al (2012) and Royle et al (2012) have found MaxEnt may make poor predictions, may be based on unjustified assumptions (Haegeman and Etienne, 2010), and may use arbitrary parameters and data adjustments. Anderson et al (2001) also caution that any statistical tool characterized by many variables, screening (keeping only some variables), and a stepwise regression approach can result in ''good'' models even based on random data (see also Freedman, 1983;Stauffer et al, 1985;Flack and Chang, 1987). This caution dates back to the late 1800s (discussed by Aldrich, 1995) and applies to all applications of this approach (e.g., the stock market, Ferson et al, 2003).…”