Rotation in factor analysis is a technique used to simplify the factor loadings matrix, making the underlying structure of the data more interpretable. Essentially, it re-orients the factors without changing the model's overall fit to the data. Since there are an infinite number of possible orientations, rotation helps identify a solution that is easier to understand.
Why is Rotation Necessary?
The initial factor solution often produces factors that are difficult to interpret because variables tend to load highly on multiple factors. Rotation aims to achieve a "simpler structure" where each variable loads highly on only one factor, making it easier to assign meaning to each factor. The goal is to find a rotation where each item loads strongly on one factor and weakly on the other factors.
Types of Rotation
There are two main categories of rotation: orthogonal and oblique.
Orthogonal Rotation
- Definition: Orthogonal rotation keeps the factors uncorrelated (independent) after rotation. This means the axes representing the factors remain at right angles (90 degrees).
- Goal: To find factors that explain the variance in the data without being related to each other.
- Common Methods:
- Varimax: Maximizes the variance of the squared loadings within each factor. This is the most commonly used orthogonal rotation method. It simplifies the factors by maximizing the number of high and low loadings for each factor.
- Quartimax: Maximizes the variance of the squared loadings for each variable. It tends to produce a general factor where most variables load high on that factor.
- Equamax: A compromise between Varimax and Quartimax.
Oblique Rotation
- Definition: Oblique rotation allows the factors to be correlated after rotation. This means the axes representing the factors are no longer constrained to be at right angles.
- Goal: To find factors that explain the variance in the data, allowing for the possibility that the factors are related to each other.
- Common Methods:
- Direct Oblimin: A popular oblique rotation method that allows for control over the degree of factor correlation.
- Promax: A computationally faster oblique rotation method that is often used with large datasets.
Choosing Between Orthogonal and Oblique Rotation
The choice between orthogonal and oblique rotation depends on the researcher's expectations about the relationships between the factors.
- Orthogonal: Use if you have a theoretical reason to believe that the underlying factors are uncorrelated.
- Oblique: Use if you suspect that the underlying factors are correlated. If an orthogonal rotation is performed when the underlying factors are correlated, the resulting factors may be more difficult to interpret.
Example:
Imagine a survey measuring personality traits. Without rotation, Factor 1 might be influenced by both "Extroversion" and "Conscientiousness," making it hard to label. After rotation, Factor 1 might primarily reflect "Extroversion" while Factor 2 reflects "Conscientiousness," thus creating two easily distinguishable factors.
In summary, rotation in factor analysis is a crucial step to make the factor structure easier to interpret by simplifying the factor loadings, either maintaining independence between factors (orthogonal) or allowing for correlation (oblique).
