Theory. We are proponents of theory-driven analysis.[1] Researchers often perform an EFA because someone designed an instrument to measure particular constructs or factors. If the theoretical framework for the instrument is sound, we should start with the expectation that we should see that structure in the data. Instruments are rarely perfect (especially the first time they are examined), and theoretical expectations are not always supported. But unless one is on a fishing expedition in a data set with no a priori ideas about how the analysis should turn out,[2] this is as good a place as any to start. Regardless, the result of an EFA must be a sensible factor structure that is easily understood, whether that final structure matches the initial theoretical framework or not. The basic function of EFA, in our mind, is to make meaning of data.

The Kaiser Criterion. The Kaiser Criterion (Kaiser, 1960, 1970) proposes that an eigenvalue greater than 1.0 is a good lower bound for expecting a factor to be meaningful. This is because an eigenvalue represents the sum of the squared factor loadings in a column, and to get a sum of 1.0 or more, one must have rather large factor loadings to square and sum (e.g., four loadings of at least 0.50 each, three loadings of at least 0.60 each). But this criterion gets less impressive as more items are analyzed. It is easy to get many unimportant factors exceeding this criterion if you analyze 100 items in an analysis.

Despite the consensus in the literature that this is probably the least accurate method for selecting the number of factors to retain (Velicer, Eaton, & Fava, 2000; see also Costello & Osborne, 2005), it is often implemented as the default selection criterion in much statistical software (such as SPSS). Prior to the wide availability of powerful computing, this was a simple (and not unreasonable) decision rule. Toward the latter part of the 20th century, researchers suggested that combining this criterion with examination of the scree plot is better (Cattell, 1966).

Minimum eigenvalue. The Kaiser Criterion was built with PCA in mind. In PCA, each item contributes 100% of its variance, and thus an eigenvalue of 1 would be equivalent to 1 variable loading on a particular factor. When this is applied to factor analysis, the interpretation is different. An eigenvalue of 1 can be more than the average contribution of an item. For example, if eight items each contain 70% shared variance and 30% unique variance, the average eigenvalue for the items would be 0.70. The minimum eigenvalue criterion is a translation of the Kaiser Criterion to the factor analysis context, where the default minimum eigenvalue is the average amount of shared variance contributed by an item. In the above example, the default minimum eigenvalue would be 0.70. This means we would retain all factors with an eigenvalue above this value. The estimation of the default minimum eigenvalue differs slightly by extraction method, but they offer the same conceptual solution (see SAS, 2015). SAS prints the average eigenvalue at the top of any eigenvalue table for use in evaluating this criterion. (See Figure 3.1 Initial eigenvalue estimates below.) This method will yield results that are identical to the Kaiser Criterion when implemented in PCA (Kim, & Mueller, 1978).

Proportion of variance. The proportion of variance criterion examines the proportion of common or shared variance across all of the items. It proposes that when preliminary factors are ordered by descending eigenvalue, we retain all factors with a cumulative proportion of variance below or at a predefined level. For example, if we set the proportion of variance to 70%, we would extract factors until the sum of eigenvalues exceeds 70% of the common variance. The default proportion of variance used in SAS is 100%. This can be interpreted as a criterion that will retain the number of factors that explain all of the shared variance. The default proportion of variance to be used can be changed using the PROPORTION = option.

Scree plot. The scree test involves examining the graph of the eigenvalues (available in all software) and looking for the natural bend or “elbow” in the data where the slope of the curve changes (flattens) markedly. The number of data points above the “elbow” (i.e., not including the point at which the break occurs) is usually considered a good estimate of the ideal number of factors to retain. Although the scree plot itself is not considered sufficient to determine how many factors should be extracted (Velicer et al., 2000), many suggest that researchers examine solutions extracting the number of factors ranging from one to two factors above the elbow to one or two below. As this is an exploratory technique, one should be encouraged to explore. Some scree plots do not have one clear bend. Some have multiple possible points of inflection, and some have no clear inflection point (for a good example of this, see the SDQ example below). Combining theory, the Kaiser Criterion, and examination of the scree plot is usually a good basis for deciding the number of factors to extract in an exploratory factor analysis.

Parallel analysis was proposed by Horn (1965). A procedure for conducting this analysis is not included in most common statistical software, including SAS, and thus is not widely used. However, it is considered advantageous over the more classic approaches (although we will see in examples below that it is not always better; see also Velicer et al., 2000). Parallel analysis involves generating random uncorrelated data, and comparing eigenvalues from the EFA to those eigenvalues from that random data. Using this process, only factors with eigenvalues that are significantly above the mean (or preferably, the 95th percentile) of those random eigenvalues should be retained. Several prominent authors and journals have endorsed this as the most robust and accurate process for determining the number of factors to extract (Ledesma & Valero-Mora, 2007; Velicer et al., 2000).

Minimum average partial (MAP) analysis was proposed by Velicer (1976) as another more modern methodology for determining the number of factors to extract in the context of PCA. This procedure involves partialing out common variance as each successive component is created; this is a familiar concept to those steeped in the traditions of multiple regression. As each successive component is partialed out, common variance will decrease to a minimum. At that point, unique variance is all that remains. Velicer argued that a minimum point should be considered to be the criterion for the number of factors to extract (Velicer et al., 2000). MAP has been considered superior to the “classic” analysis, and probably is superior to parallel analysis, although neither is perfect, and all must be used in the context of a search for conceptually interpretable factors.

Which method? Although we can understand the value of parallel analysis or MAP analysis for deciding how many factors to extract, we have to remember our mantra: EFA is an exploratory technique. No criterion is perfect, and unless you are misusing EFA in a confirmatory fashion, it seems to me that worrying over a slightly better extraction criterion might be missing the point. The point is to get a reasonable model within a representative sample (that is sufficiently large to ensure a reasonable solution), and then to move into inferential statistics available in confirmatory factor analysis. EFA is merely a first stopping point on the journey, and researchers who forget this miss the point of the process. Thus, use theory along with parallel analysis or MAP analysis or any of the classic criteria that suit you and that are defensible. The goal of creating theory-driven, conceptually understandable solutions needs to prevail. And never forget that your journey is not done until you confirm the results of the EFA with different data in the context of CFA.