Multiple correspondence analysis in S-PLUS.

Area of Science:

• Statistics
• Data Analysis
• Multivariate Statistics

Background:

• Multiple Correspondence Analysis (MCA) is a key multivariate method for analyzing multidimensional contingency tables.
• Existing software procedures like SAS Proc CORRESP, SPAD CORMU, and S-PLUS mca function are commonly used for MCA.
• Discrepancies in output formats between these common MCA software tools hinder direct result comparison and interpretation.

Purpose of the Study:

• To demonstrate how to achieve MCA results from the S-PLUS mca function that are compatible with SAS and SPAD outputs.
• To provide modified code enabling consistent coordinate systems across different MCA software.
• To enhance the interpretability of MCA results by including additional analytical components.

Main Methods:

• Utilized the mca function from the MASS library in S-PLUS for performing Multiple Correspondence Analysis.
• Developed and proposed modified code to standardize the output coordinate system.
• Incorporated computations for factor level contributions to inertia, squared cosine of factor levels, and re-evaluated inertia per axis.

Main Results:

• The modified S-PLUS code successfully generates MCA results with coordinate systems identical to those produced by SAS Proc CORRESP and SPAD CORMU.
• The added computations provide detailed insights into factor level contributions and their significance in explaining variance.
• Enhanced interpretability of MCA decomposition results is achieved through standardized outputs and additional metrics.

Conclusions:

• The proposed modification bridges the output compatibility gap between different MCA software packages, specifically S-PLUS mca function, SAS, and SPAD.
• Standardized MCA outputs facilitate more reliable comparative analyses and meta-analyses across studies using different software.
• The inclusion of contribution and squared cosine metrics significantly improves the depth and accuracy of MCA result interpretation.