Non-Graphical Solutions for Cattell’s Scree Test

Abstract

Most of the strategies that have been proposed to determine the number of components that account for the most variation in a principal components analysis of a correlation matrix rely on the analysis of the eigenvalues and on numerical solutions. The Cattell’s scree test is a graphical strategy with a nonnumerical solution to determine the number of components to retain. Like Kaiser’s rule, this test is one of the most frequently used strategies for determining the number of components to retain. However, the graphical nature of the scree test does not definitively establish the number of components to retain. To circumvent this issue, some numerical solutions are proposed, one in the spirit of Cattell’s work and dealing with the scree part of the eigenvalues plot, and one focusing on the elbow part of this plot. A simulation study compares the efficiency of these solutions to those of other previously proposed methods. Extensions to factor analysis are possible and may be particularly useful with many low-dimensional components.

The Positivity Dimension of Well-Being: Adaptation and Psychometric Evidence of a Measure1

“…The Optimal Coordinates seek to ascertain the localization of the factor through simulations, verifying whether the eigenvalues found in the simulations are greater than the actual eigenvalues, defining the number of values to extract. The Acceleration Factor, on the other hand, aims to ascertain the point at which the gradient of the curve has an abrupt and meaningful change, thus identifying the number of factors found prior to the "elbow" (Raiche et al, 2013). The graphic distribution (scree plot) of these values is shown in Figure 1.…”

“…The 'R' statistical program was used for analyzing the data (R Development Core Team, 2011;Raiche, Walls, Magis, Riopel, & Blais, 2013;van der Ark, 2012). Initially, the item of discrimination was evaluated, Student t tests were calculated, and descriptive analyses were undertaken.…”

An Ungrateful Disposition: Psychometric Properties of the Dispositional Envy Scale in Brazil

“…To observe the number of components to be extracted, a PC analysis was conducted on five criteria: Kaiser values, Cattell criterion, parallel analysis, acceleration factor and optimal coordinates (Hayton, Allen, & Scarpello, 2004;Pasquali, 2010;Raiche, Walls, Magis, Riopel, & Blais, 2013). These analyses were performed using the Psych and nFactors statistical packages (Raiche & Magis, 2014;Revelle, 2014).…”

Variation in Multitrack Mixes: Analysis of Low-level Audio Signal Features

“…1. Using the nFactors package [20] a variety of methods were employed in order to determine the number of dimensions to keep in further analysis, shown in Fig. 1.…”

“…Kaiser's rule [21] suggests retaining those dimensions with eigenvalues greater than 1, which in this case was the first five components. The acceleration factor (AF) [20] determines the knee in the plot by examining the second derivative-this method would retain only the first dimension but is known to underestimate [22]. The optimal coordinates (OC) method [20] suggested that the first four dimensions be kept.…”