Sufficient Dimension Reduction: An Information-Theoretic Viewpoint

“Automatic” interpretation of multiple correspondence analysis (MCA) results for nonexpert users, using R programming

Purpose

The purpose of this paper is to create an automatic interpretation of the results of the method of multiple correspondence analysis (MCA) for categorical variables, so that the nonexpert user can immediately and safely interpret the results, which concern, as the authors know, the categories of variables that strongly interact and determine the trends of the subject under investigation.

Design/methodology/approach

This study is a novel theoretical approach to interpreting the results of the MCA method. The classical interpretation of MCA results is based on three indicators: the projection (F) of the category points of the variables in factorial axes, the point contribution to axis creation (CTR) and the correlation (COR) of a point with an axis. The synthetic use of the aforementioned indicators is arduous, particularly for nonexpert users, and frequently results in misinterpretations. The current study has achieved a synthesis of the aforementioned indicators, so that the interpretation of the results is based on a new indicator, as correspondingly on an index, the well-known method principal component analysis (PCA) for continuous variables is based.

Findings

Two (2) concepts were proposed in the new theoretical approach. The interpretative axis corresponding to the classical factorial axis and the interpretative plane corresponding to the factorial plane that as it will be seen offer clear and safe interpretative results in MCA.

Research limitations/implications

It is obvious that in the development of the proposed automatic interpretation of the MCA results, the authors do not have in the interpretative axes the actual projections of the points as is the case in the original factorial axes, but this is not of interest to the simple user who is only interested in being able to distinguish the categories of variables that determine the interpretation of the most pronounced trends of the phenomenon being examined.

Practical implications

The results of this research can have positive implications for the dissemination of MCA as a method and its use as an integrated exploratory data analysis approach.

Originality/value

Interpreting the MCA results presents difficulties for the nonexpert user and sometimes lead to misinterpretations. The interpretative difficulty persists in the MCA's other interpretative proposals. The proposed method of interpreting the MCA results clearly and accurately allows for the interpretation of its results and thus contributes to the dissemination of the MCA as an integrated method of categorical data analysis and exploration.

Causal Inference in Radiomics: Framework, Mechanisms, and Algorithms

The widespread use of machine learning algorithms in radiomics has led to a proliferation of flexible prognostic models for clinical outcomes. However, a limitation of these techniques is their black-box nature, which prevents the ability for increased mechanistic phenomenological understanding. In this article, we develop an inferential framework for estimating causal effects with radiomics data. A new challenge is that the exposure of interest is latent so that new estimation procedures are needed. We leverage a multivariate version of partial least squares for causal effect estimation. The methodology is illustrated with applications to two radiomics datasets, one in osteosarcoma and one in glioblastoma.