Varimax rotation is used across many quantitative fields, including Biology (analyzing gene expression patterns), Chemistry (spectral analysis), Computer vision (image processing), Economics (market factor analysis), Engineering (signal processing), and Social sciences. I am only familiar with the social sciences related to AI adoption and personality and leadership development. This method facilitates understanding patterns that might otherwise remain obscured. In traditional analyses, we’re used to simple weighting variables that often appear to load onto multiple factors, creating confusion and muddling insights. However, by ensuring that each variable loads strongly onto a single factor while maintaining weak associations with others, we achieve clarity that does not compromise the integrity of statistical relationships. For example, I recently researched at a higher education institution about adopting AI using Roger’s theoretical framework. When it came to perceptions of the persuasion phase of the five-stage model, we had to understand the significance of the five perceived characteristics. This offered a more precise roadmap for interpreting these micro-complex data sets.

Imagine a personality test with 40 questions about various behaviors and traits. After participants complete it, researchers might use varimax rotation to identify precise personality dimensions.

Raw data might show mixed patterns - a question like "I enjoy planning" could correlate with conscientiousness and neuroticism. After varimax rotation, the question would load strongly onto one factor (likely conscientiousness) and weakly onto others, making the personality dimensions clearer and more interpretable. This is how researchers developed the Big Five personality traits (Openness, Conscientiousness, Extraversion, Agreeableness, Neuroticism) - by using varimax rotation to identify distinct personality factors from questionnaire responses

What is mechanism of rotation.what exactly is done to data.

Is it interativr process

In social science research, varimax rotation is commonly used when conducting exploratory factor analysis (EFA), particularly in:

Survey Development:

• When researchers develop questionnaires to measure complex constructs like attitudes, beliefs, or behaviors
• Helps identify underlying dimensions in large sets of survey items
• Makes it easier to see which questions cluster together into meaningful factors

Example from Psychology: If you're studying personality traits with a 40-item questionnaire, varimax rotation might help reveal that certain questions naturally group into factors like "extraversion," "conscientiousness," and "neuroticism."

Research Applications:

Practical Benefits:

• Makes results more interpretable for non-technical audiences
• Helps researchers name and describe factors more clearly
• Supports decision-making about which items to keep or remove from surveys

The mathematical mechanism of varimax rotation step by step:

The primary goal is to maximize the variance of squared loadings for each factor by applying an orthogonal rotation. Here's how it works:

Where:

• V = variance to be maximized
• a_ij = loading of the ith variable on the jth factor
• p = number of variables

• Takes initial factor loadings matrix
• Applies an orthogonal transformation matrix
• Preserves the total variance explained
• Maintains 90-degree angles between factors

• Iteratively rotates pairs of factors
• For each pair, finds angle θ that maximizes variance
• Updates loadings after each rotation
• Continues until convergence (when changes become negligible)

• Calculate initial communalities
• Form pairs of factors
• For each pair:
  • Compute angle θ that maximizes variance
  • Apply rotation matrix [cos θ, -sin θ; sin θ, cos θ]
  • Update factor loadings
• Repeat until the convergence criterion is met

The result is a solution where each variable loads highly on one factor and near zero on others, making the factor structure more straightforward and interpretable.