A Regression Equation for Determining the Dimensionality of Data

Abstract

Parallel analysis has received much support and attention as a criterion for using eigenvalues to determine the dimensionality of data. Parallel analysis compares sample eigenvalues to expected eigenvalues of a sample from a correlation matrix generated by independent normally distributed random variables. To make parallel analysis more accessible to researchers, several studies have proposed multiple regression equations for estimating the expected value of the eigenvalues of a sample correlation matrix assuming that the population correlation matrix is the identity matrix. A new regression equation to estimate the mean value of eigenvalues is presented in this article and a comparative study reveals favorable performance of this proposed equation to previously published regression equations. This proposed technique has the advantage that a table of coefficients, listing regression coefficients for each eigenvalue root, is not needed.

The Scree Test and the Number of Factors: a Dynamic Graphics Approach

“…Additionally, we will display some basic improvements that are simpler and computationally less demanding than PA. Figure 2 shows three plots that have PA information included in the scree plot for the driving style data example. The top left plot displays the standard scree plot with a Keelling's regression line (Keeling, 2000). This line approximates the random cut-off eigenvalues given the sample size and number of variables.…”

Comparison of Urban Housing Satisfaction in Modern and Traditional Neighborhoods in Edirne, Turkey

“…Since we do not want the decision to be purely based on the scree criteria, which is known to be not very powerful and subjective (Zwick and Velicer, 1986), we decided to apply Horn's parallel procedure. Applying the parallel analysis method with the procedure developed by Keeling (2000) produced the parallel analysis criterion values shown in Table I, which also includes the observed eigenvalues. Horn's parallel analysis, which is the most accurate method for selecting the appropriate number of factors, suggests two underlying factors in both samples for all constructs except one.…”

Exploring the Sensitivity of Horn's Parallel Analysis to the Distributional Form of Random Data

“…Both the PCA or FA and the generation of random data sets were computationally quite expensive prior to the advent of cheap and ubiquitous computing. The computational costs of Horn’s PA method (and improvements on it) in the late 20 th century encouraged the development of computationally less expensive regression-based models to estimate PA results given only the parameters N and P (Allen & Hubbard, 1986; Keeling, 2000; Lautenschlager, 1989; Longman, Cota, Holden, & Fekken, 1989). However, these techniques have been found to be imprecise approximations to actual PA results, and, moreover, to perform less reliably in making component-retention or factor-retention decisions.…”