The Hull Method for Selecting the Number of Common Factors

Abstract

A common problem in exploratory factor analysis is how many factors need to be extracted from a particular data set. We propose a new method for selecting the number of major common factors: the Hull method, which aims to find a model with an optimal balance between model fit and number of parameters. We examine the performance of the method in an extensive simulation study in which the simulated data are based on major and minor factors. The study compares the method with four other methods such as parallel analysis and the minimum average partial test, which were selected because they have been proven to perform well and/or they are frequently used in applied research. The Hull method outperformed all four methods at recovering the correct number of major factors. Its usefulness was further illustrated by its assessment of the dimensionality of the Five-Factor Personality Inventory ( Hendriks, Hofstee, & De Raad, 1999 ). This inventory has 100 items, and the typical methods for assessing dimensionality prove to be useless: the large number of factors they suggest has no theoretical justification. The Hull method, however, suggested retaining the number of factors that the theoretical background to the inventory actually proposes.

El análisis factorial exploratorio de los ítems: una guía práctica, revisada y actualizada

“…En la actualidad se recomienda con insistencia que la decisión acerca del número de factores se tome tras considerar: 1) varios criterios objetivos, y siempre teniendo en cuenta 2) la interpretabilidad de la solución encontrada y 3) la teoría de partida (Lorenzo-Seva et al, 2011).…”

Thinking about assessment: Further evidence of the validity of the Movie for the Assessment of Social Cognition as a measure of mentalistic abilities.

“…We performed dimensionality analyses of the MASC items based on differing criteria; in particular, the minimum average partial statistic (MAP; Zwick & Velicer, 1986), quasi-inferential parallel analysis (Buja & Eyuboglu, 1992), and Hull's method (Lorenzo-Seva, Timmerman, & Kiers, 2011;Wilderjans, Ceulemans, & Meers, 2013) were used for determining the number of latent dimension underlying the tetrachoric correlation matrix of the MASC items.…”

Estudos psicométricos da Escala de Avaliação da Percepção da Religiosidade

“…A verificação da estrutura interna da EAPRE não resultou em ajuste adequado, o que indica que novas análises precisam ser realizadas com outras amostras e por métodos distintos (Horn, 1965;Hu & Bentler, 1999;Lorenzo-Seva et al, 2011;O'connor, 2000). Adicionalmente, deve-se ter clareza de que o método utilizado, a análise dos componentes principais, por se basear na correlação linear das variáveis observadas, não caracteriza a variância comum distinta da específica, não se revelando o mais adequado, o que reitera a importância de que outros estudos sejam desenvolvidos (Damásio, 2012).…”