When variables are factored (for a discussion of factoring people, see Campbell,1996; Thompson, 2000b), the total number of possible factors equals the number of variables factore(assuming all of the variance in the original variables is not reproduced). However, because many of these factors may not contribute substantially to the overall solution or be interpretable,some factors arenot useful to retain in the analysis and generally represent noise or error.Given that the goal of EFA is toretain the fewest possible factors while explaining the most variance of the observed variables,it is critical that there searcher extract the correct number of factors because this decision will affect results directly. Many rules can be used to determine the number of factors to reta(cf.Zwick & Velicer, 1986), including the eigenvalue > 1 rule (EV > 1; Kaiser, 1960), scree test (Cattell, 1966), minimum average partial correlation (Velicer, 1976), Bartlett’s chi-square test (Bartlett, 1950, 1951), and parallel analysis (Horn, 1965; Turner, 1998).Thompson and Daniel (1996) and Zwick and Velicer (1986) elaborated these approaches. The most frequently used method is the EV > 1 rule. As Thompson and Daniel noted“This extraction rule is the defaul top tionin most statistics packages and therefore may be the most widely used decision rule, also by default” (p. 200). Importantly,these rules donot necessarily lead to the same decision regarding the number of factors to retain. For example, in a Monte Carlo evaluation, Zwick and Velicer (1986) found that the EV > 1 rule almost always severely overestimated the number of factors to retain. Their findings were consistent with those of Cattell and Jaspers(1967),Linn(1968),Yeomans and Golder(1982),and Zwickand Velicer (1982), but they were contrary to those of Humphreys(1964) and Mote(1970), who noted that the EV > 1 rule may underestimate the number of factors. Bartlett’s chi-square test was very inconsistent. Because EFA studies typically involve large samples, this statistical significance test may have little utility as it is heavily influenced by sample size. Despite its subjective nature in interpretation, the scree test was much more accurate but also tended to over extract factors. Importantly, parallel analysis was the most accurate procedure,followed closely by the minimum average partial method. Unfortunately,these methods are seldom employed in published research.Asanadditional option,Thompson(1988)suggested using a boot strap method to determine the number of factors and provided a program to automate the process. Because the factor retention decision directly affects the EFA results obtained,researchers are advised to use both multiple criteria and reasoned reflection. Researchers should also explicitly inform readers about the strategies used in making factor retention decisions.
|
|