Detecting the Guttman effect with the help of ordinal correspondence analysis in synchrotron X-ray diffraction data...

Area of Science:

• Statistics
• Data Analysis
• Psychometrics

Background:

• Detecting the Guttman effect is crucial for understanding response patterns in survey and test data.
• Existing methods may lack the precision to identify and quantify the Guttman effect, especially in complex datasets.

Purpose of the Study:

• To propose and validate a novel two-step method for detecting the Guttman effect in complete disjunctive tables.
• To assess the method's accuracy and robustness using simulated and real-world data.

Main Methods:

• A two-step approach combining Correspondence Analysis (CA) and Ordinal Correspondence Analysis (OCA).
• Utilizing the first singular vector from CA as a score for OCA.
• Employing hybrid decomposition of Pearson chi-squared statistics with permutation tests.

Main Results:

• The proposed method successfully detects the Guttman effect in artificial and real-world data.
• The method can determine the degree of the Guttman effect with accuracy dependent on signal-to-noise ratio.
• Demonstrated effectiveness on benchmark datasets and synchrotron X-ray diffraction data.

Conclusions:

• The novel CA-OCA method provides a robust framework for Guttman effect detection.
• This technique offers improved accuracy in identifying and quantifying the Guttman effect in various data structures.
• The method is applicable to diverse fields, including psychometrics and materials science.