Business Context
Researchers are analyzing gene expression data that has been pre-normalized to be centered around zero. They want to perform PCA without an intercept (forcing the model through the origin). Additionally, the data contains highly collinear genes (redundant), which tests the solver's singularity handling.
Data Preparation
Creating a dataset with zero-centered data and near-perfect multicollinearity to test singularity limits.
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| 1 | |
| 2 | DATA casuser.genetics; |
| 3 | call streaminit(789); |
| 4 | DO sample_id = 1 to 200; |
| 5 | gene_A = rand('Normal', 0, 1); |
| 6 | gene_B = gene_A * 2 + rand('Normal', 0, 0.000001); |
| 7 | /* High correlation */ gene_C = rand('Normal', 0, 2); |
| 8 | OUTPUT; |
| 9 | END; |
| 10 | |
| 11 | RUN; |
| 12 |
Étapes de réalisation
1
Execute PCA forcing no intercept (noInt=true) and setting a strict singularity criterion.
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| 1 | |
| 2 | PROC CAS; |
| 3 | pca.eig / TABLE={name='genetics', caslib='casuser'} inputs={'gene_A', 'gene_B', 'gene_C'} noInt=true singular=1E-09 outStat={casOut={name='gene_stats', caslib='casuser', replace=true}}; |
| 4 | |
| 5 | RUN; |
| 6 |
2
Verify the results in the statistics table.
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| 1 | |
| 2 | PROC CAS; |
| 3 | TABLE.fetch / TABLE={name='gene_stats', caslib='casuser'}; |
| 4 | |
| 5 | RUN; |
| 6 |
Expected Result
The PCA runs without centering the data (No Intercept). Due to the high correlation between gene_A and gene_B, the smallest eigenvalue should be extremely close to zero, testing the singularity threshold.