Exploratory factor analysis is meant to be exploratory in nature, and thus it is not desirable to prescribe a rigid formula or process for executing an EFA. The steps below are meant to be a loose guide, understanding that a factor analysis often requires returning to previous steps and trying other approaches to ensure the best outcome. The general pattern of performing an EFA falls into six general steps that will guide the discussion through the rest of the book:

Step 1: Data cleaning. Without clean data, what follows in almost any analysis is moot. This is another point where passions run high among researchers and statisticians because there is considerable controversy about any manipulations of the sample and data (e.g., how to treat outliers, missing data). We have a clear position on the issue—data should be cleaned and issues (e.g., failing to meet assumptions) should be addressed. The first author wrote an entire book on the topic, in which he demonstrated repeatedly how clean data produces results that are better estimates of population parameters and, therefore, more accurate and replicable (Osborne, 2013). Instead of debating the point here, allow me to assert that data that is filled with errors or that fails to meet assumptions of the analysis being performed is likely to lead to poorer outcomes than data that is free of egregious errors and that meets assumptions. We will discuss some other data quality issues later in the book, including the importance of dealing appropriately with missing data.

Step 2: Deciding on an extraction method. An extraction technique is one of a group of methods that examines the correlation/covariation between all the variables and seeks to “extract” the latent variables from the measured/manifest variables.

There are several factor analysis extraction methods to choose from. SAS has seven EFA extraction methods: unweighted least squares (ULS), maximum likelihood (ML), principal axis factoring (PAF), iterated principal axis factoring (iterated PAF), alpha factoring, image factoring, and Harris factoring.[2] Information about the relative strengths and weaknesses of these techniques is not easy to obtain. To complicate matters further, naming conventions for some extraction techniques are not consistent, leaving it difficult to figure out which method a textbook or journal article author is describing, and whether or not it is actually available in the software the researcher is using. This probably explains the popularity of principal components analysis – not only is it the default in much statistical software, but it is one of the more consistent names researchers will see there.

An article by Fabrigar, Wegener, MacCallum and Strahan (1999) argued that if data is relatively normally distributed, maximum likelihood is the best choice because “it allows for the computation of a wide range of indexes of the goodness of fit of the model [and] permits statistical significance testing of factor loadings and correlations among factors and the computation of confidence intervals.” (p. 277). If the assumption of multivariate normality is “severely violated” they recommend iterated PAF or ULS factoring (Fabrigar et al., 1999; Nunnally & Bernstein, 1994). Other authors have argued that in specialized cases, or for particular applications, other extraction techniques (e.g., alpha extraction) are most appropriate, but the evidence of advantage is slim. In general, ML, iterated PAF, or ULS will give you the best results, depending on whether your data is generally normally distributed or significantly non-normal. In Chapter 2, we will compare outcomes between the various factor extraction techniques.

Step 3: Deciding how many factors to retain for analysis. This, too, is an issue that suffers from anachronistic ideas and software defaults that are not always ideal (or even defensible). In this step, you (or the software) decide how many factors you are going to keep for analysis. The statistical software will always initially extract as many factors as there are variables (i.e., if you have 10 items in a scale, your software will extract 10 factors) in order to account for 100% of the variance. However, most of them will be meaningless. Remembering that the goal of EFA is to explore your data and reduce the number of variables being dealt with. There are several ways of approaching the decision of how many factors to extract and keep for further analysis. Our guide will always focus on the fact that extracted factors should make conceptual and theoretical sense, and be empirically defensible. We will explore guidelines for this later in Chapter 3.

Step 4: Deciding on a rotation method and rotating the factors. Rotation is often a source of some confusion. What exactly is rotation and what is happening when data is rotated? In brief, the goal is to clarify the factor structure and make the results of your EFA most interpretable. There are several rotation methodologies, falling into two general groups: orthogonal rotations and oblique rotations. Orthogonal rotations keep axes at a 90° angle, forcing the factors to be uncorrelated. Oblique rotations allow angles that are not 90°, thus allowing factors to be correlated if that is optimal for the solution. We argue that in most disciplines constructs tend to be at least marginally correlated with each other, and, as such, we should focus on oblique rotations rather than orthogonal. We will discuss these options in more detail in Chapter 4.

Step 5: Interpreting results. Remember that the goal of exploratory factor analysis is to explore whether your data fits a model that makes sense. Ideally, you have a conceptual or theoretical framework for the analysis—a theory or body of literature guiding the development of an instrument, for example. Even if you do not, the results should be sensible in some way. You should be able to construct a simple narrative describing how each factor, and its constituent variables, makes sense and is easily labeled. It is easy to get EFA to produce results. It is much harder to get sensible results.

Note also that EFA is an exploratory technique. As such, it should not be used, as many researchers do, in an attempt to confirm hypotheses or test competing models. That is what confirmatory factor analysis is for. It is a misapplication of EFA to use it in this way, and we need to be careful to avoid confirmatory language when describing the results of an exploratory factor analysis.

If your results do not make sense, it might be useful to return to an earlier step. Perhaps if you extract a different number of factors, the factors or solution will make sense. This is why it is an exploratory technique.

Step 6: Replication of results. One of the hallmarks of science is replicability, or the ability for other individuals, using the same materials or methods, to come to the same conclusions. We have not historically placed much emphasis on replication in the social sciences, but we should. As you will see in subsequent chapters, EFA is a slippery technique, and the results are often not clear. Even clear results often do not replicate exactly, even within an extremely similar data set. Thus, in our mind, this step is critical. If the results of your analysis do not replicate (or do not reflect the true nature of the variables in the “real world”), then why should anyone else care about them? Providing evidence that your factor structure is likely to replicate (either through another EFA or through CFA) makes your findings stronger and more relevant. In Chapter 6, we will explore a “traditional” method of replication[3] (similar to cross validation in regression models). In Chapter 7, we will play with the notion of applying a less traditional but perhaps more useful analysis using bootstrap analysis. Confirmatory factor analysis is outside the scope of this book, but is perhaps an even better method of replication.