Main Function: SignifiTestCmplxConfounders.m

This MATLAB code is designed for mediation analysis where the mediator is a matrix, and both the exposure and outcome are scalars.

The method requires installing the following toolboxes:

• SparseReg Toolbox: SparseReg Toolbox Documentation
• TensorReg Toolbox: TensorReg Toolbox Documentation

In addition, the files inside the mex files.zip need to be extracted and added to the MATLAB path

Key stages in the code include:

1. Library and Path Setup: Adds essential toolboxes and directories to the MATLAB path for tensor and regression operations.

2. Data Loading and Simulation: Defines whether to use simulated or real data. For simulated data, it generates complex data; for real data, it loads predefined datasets.

3. Matrix and Parameter Initialization: Sets up matrices and parameters for the regression, including specifying bootstrap samples and confounders.

4. Regression Analysis: Calls Regressions_CovConf to estimate model parameters A and B, storing results as complex matrices.

5. Bootstrapping: Optionally performs bootstrapping to generate multiple estimates of A and B for statistical analysis.

6. Probability and Statistical Testing: Calculates p-values for matrix elements of A, B, and their element-wise product A * B. Applies False Discovery Rate (FDR) thresholds to identify significant elements.

7. Visualization: Creates figures showing absolute values and significance levels of matrices A, B, and A * B based on calculated p-values.

8. Timing: Outputs the total processing time in minutes.

This code is designed for high-dimensional data processing, leveraging complex-valued matrices and bootstrapping to enhance the robustness of regression analysis in tensor-based data. It is applicable to fields such as neuroimaging and signal processing.

Reference: C. Lopez Naranjo et al., “EEG functional connectivity as a Riemannian mediator: An application to malnutrition and cognition,” Human Brain Mapping, vol. 45, no. 7, p. e26698, May 2024, doi: 10.1002/hbm.26698.