Factor Analysis Orthogonal Rotation Explained

In factor analysis, rotation is a common technique used after the initial factor extraction. The main purpose of rotation is to simplify the factor structure and improve the interpretability of the results. It transforms the original factor loadings into a new set, making it easier to identify which variables load strongly onto which factors.

Understanding Orthogonal Rotation

The specific technique mentioned is 'orthogonal rotation'. This method aims to rotate the factor axes while keeping them perpendicular (at a 90-degree angle) to each other. This mathematical constraint means that the resulting factors remain statistically independent or 'uncorrelated'.

Key characteristics of orthogonal rotation include:

• Preservation of factor uniqueness.
• Factors are uncorrelated ( $r=0$ ).
• Simplification often focuses on maximizing the variance of the squared loadings on a factor (e.g., Varimax rotation).

Analyzing Factor Relationships in Rotation

The choice between different rotation methods depends heavily on the assumed or observed relationship between the underlying factors. Let's examine the options in the context of orthogonal rotation:

• Uncorrelated: Orthogonal rotation is specifically designed for situations where the factors are assumed to be 'uncorrelated'. This assumption allows the rotation to maintain the orthogonality of the factor axes.
• Correlated: If factors are expected or found to be correlated (i.e., they share common variance), an orthogonal rotation is not appropriate. In such cases, 'oblique' rotation methods (like Promax or Oblimin) are used, as they allow the factor axes to be correlated.
• Dependent upon each other: This implies a correlation or relationship between factors. Similar to the 'Correlated' option, this scenario requires oblique rotation, not orthogonal rotation.
• Placed at 180 degree to each other: Factors at 180 degrees are perfectly negatively correlated ( $r=-1$ ). Orthogonal rotation requires factors to be uncorrelated ( $r=0$ ). While 180 degrees describes a specific relationship (perfect negative correlation), it's not the condition under which orthogonal rotation is chosen; orthogonality specifically means zero correlation.

Conclusion on Orthogonal Rotation Application

Based on the principles of factor analysis rotation techniques, 'orthogonal rotation' is the correct method to use when the factors derived from the analysis are 'uncorrelated'. This approach simplifies the interpretation by ensuring the factors are statistically independent.