A Comparison of the Next Eigenvalue Sufficiency Test to Other Stopping Rules for the Number of Factors in Factor Analysis

A plethora of techniques exist to determine the number of factors to retain in exploratory factor analysis. A recent and promising technique is the Next Eigenvalue Sufficiency Test (NEST), but has not been systematically compared with well-established stopping rules. The present study proposes a simulation with synthetic factor structures to compare NEST, parallel analysis, sequential <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup><mml:mrow><mml:mi>χ</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msup> </mml:mrow> </mml:math> test, Hull method, and the empirical Kaiser criterion. The structures were based on 24 variables containing one to eight factors, loadings ranged from .40 to .80, inter-factor correlations ranged from .00 to .30, and three sample sizes were used. In total, 360 scenarios were replicated 1,000 times. Performance was evaluated in terms of accuracy (correct identification of dimensionality) and bias (tendency to over- or underestimate dimensionality). Overall, NEST showed the best overall performances, especially in hard conditions where it had to detect small but meaningful factors. It had a tendency to underextract, but to a lesser extent than other methods. The second best method was parallel analysis by being more liberal in harder cases. The three other stopping rules had pitfalls: sequential <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup><mml:mrow><mml:mi>χ</mml:mi></mml:mrow> <mml:mrow><mml:mn>2</mml:mn></mml:mrow> </mml:msup> </mml:mrow> </mml:math> test and Hull method even in some easy conditions; the empirical Kaiser criterion in hard conditions.