Factor Analysis: Oblique Rotation

Difference Between EFA and CFA

If one wants to measure an attitude toward eating fruit, one might generate the following three items: (a) I like apples, (b) I like pears, and (c) I like cherries. All the items provide a response to examples of fruits. However, fruits contain a large variety of elements (e.g., grapes, raspberries, lemons, limes, mangoes, star fruit, watermelons, grapefruits, bananas, and coconuts). Some are sour, some are sweet, some have a lot of seeds, some have no seeds, some are dry and pulpy, and some are wet and juicy. Yet, all of the individual fruits are considered by most persons as individual members of the class of things called fruit. So instead of three items (apples, pears, cherries), one might decide to generate 60 items, each listing a different fruit.

One question is whether an attitude toward fruit operates as a single solitary and unified attitude or whether the attitude breaks up into specific groups (e.g., berries, citrus, vine). If one believes that one knows what groups exist (e.g., tree fruits, citrus fruits, berries), then one may propose that the construct fruits comprises various groupings and tests to see if that theoretical understanding is correct. The technique is referred to as CFA because the scientist tries to verify or evaluate a structural equation model that corresponds to the underlying theoretical model.

Suppose no such model exists, then one could run an analysis that examines the potential to create vectors or linear combinations of variables (each considered a group) that share a commonality as perceived by the persons filling out the scale. The process employs an algorithm to generate a solution. Often the process involves the generation of vectors using a principal components analysis (PCA) that is rotated to create vectors or lines that provide a better fit to explain the available variance in the answers. Use of this process usually is considered an EFA because the investigator is “exploring” the potential for underlying relationships within the pattern of responses. Strangely enough, the statistics for CFA using correlations was developed decades before PCA and EFA, which both require computers for adequate analysis.

Orthogonal Versus Oblique Analysis

When rotating to create the vectors to explain or match the underlying data, the process generates a series of equations. The term orthogonal indicates that the outcome of each equation will be uncorrelated to the outcome of any other equation. Each iteration generates a linear combination of the variables in the analysis to explain the available variability in the set of responses. The term orthogonal simply means that each combination is uncorrelated with any of the other combinations reported.

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