Kernelized Discriminant Analysis for Joint Modeling of Multivariate Categorical Responses

This repository provides the simulation code for the paper titled Kernelized Discriminant Analysis for Joint Modeling of Multivariate Categorical Responses.

Running the Simulation

To execute the simulation:

1. Open the Sim.sh file.

2. Replace all instances of XX in the Sim.sh file with the desired model code: A4, A6, B4, or B6.

For instance, to run the simulation for Model A-4:

#!/bin/bash
#SBATCH --job-name=KernelDA
#SBATCH -o Results-A4/Rep_%a.Rout
#SBATCH --array=1-1200
#SBATCH --mail-user=xxx@xyz
#SBATCH --mail-type=END
#SBATCH --account=abc
#SBATCH --qos=abc
#SBATCH --mem=2gb
#SBATCH -t 96:00:00

ml R/4.2
R CMD BATCH --vanilla Main-A4.R Results-A4/Rep_${SLURM_ARRAY_TASK_ID}.Rout

3. Create a directory to store the results.

mkdir Results-A4

4. Execute the modified Sim.sh file.

This process will launch 1200 jobs, corresponding to 100 replicates for each combination of:

• $p$ values: 50, 100, 150
• $\nu$ values: 0.8, 1.0, 1.2, 1.4

For every replicate, the script will execute Main-A4.R to generate data based on the specified data-generating model, fit various models, and assess their performance. All the results are saved in RDS files under the Results-A4 directory.

All necessary functions can be found in the Functions directory.

Notes on Computing Environment

The provided workflow is configured for SLURM-based high-performance computing (HPC) environments. The Sim.sh script is a SLURM batch job script that manages parallel execution using job arrays.

If you wish to run the simulation on a different computing platform (e.g., a non-SLURM cluster, local multicore machine, or cloud environment), you will need to modify:

• The shell script Sim.sh: Replace SLURM-specific directives (e.g., #SBATCH flags) with those suitable for your job scheduling system (e.g., PBS, LSF, or a custom script for GNU parallel or background jobs).
• The R script Main-XX.R: Ensure that any job-specific environment variables (e.g., SLURM_ARRAY_TASK_ID) are replaced or emulated appropriately (e.g., using commandArgs() or manually setting replicate IDs).

Additionally, make sure all dependencies such as R packages and source files from the Functions directory are properly loaded in your environment.