How to Use Model-Based Cluster Analysis Efficiently in Person-Oriented Research.

Area of Science:

• Statistics
• Machine Learning
• Data Mining

Background:

• Traditional clustering methods often involve subjective model selection.
• Model-based cluster analysis (MBCA) automates this using finite mixture modeling.
• MBCA typically employs the Bayesian Information Criterion (BIC) for model selection.

Purpose of the Study:

• To investigate the adequacy of automatic model selection in MBCA using BIC.
• To explore alternative model selection criteria like Integrated Completed Likelihood Criterion (ICL) and Baudry's method.
• To refine MBCA procedures using quality coefficients (QCs) for improved cluster structure identification.

Main Methods:

• MBCA with BIC, ICL, and Baudry's method were evaluated.
• Quality coefficients (QCs) were integrated to aid in selecting cluster structures.
• Performance was compared against hierarchical and k-center clustering methods.
• Analyses used datasets with known theoretical cluster structures (seven and four types) with added measurement error.

Main Results:

• Automatic BIC-based model selection in MBCA rarely yielded optimal solutions.
• Refined MBCA procedures, by excluding irregular BIC curves and using QCs, achieved optimal solutions.
• Refined MBCA performance was comparable to or better than hierarchical and k-center methods.
• MBCA demonstrated superiority in identifying four-type cluster structures.

Conclusions:

• Automatic model selection in MBCA requires refinement for optimal performance.
• Integrating quality coefficients and alternative criteria enhances MBCA's ability to identify true cluster structures.
• Refined MBCA is a robust method, particularly effective for specific cluster configurations and data reliability levels.