Last updated: 2018-01-30

Code version: 5442ab8

Introduction

Similar to previous simulation, only that the design matrix \(X\) is simulated such that the columns in \(X\) have high collinearity.

Each row of \(X\) is independently drawn from a \(N(0, \Sigma_X)\) distribution, where \(\Sigma_X = B_{p \times d} \cdot B_{p \times d}^T + I\), where \(B_{i, j} \stackrel{\text{iid}}{\sim} N(0, 1)\). Then transform \(\Sigma_X\) to a correlation matrix.

\(d = 5\), the sparsity \(\eta \in \{0.5, 0.6, 0.7, 0.8, 0.9\}\)

Overall across all sparsity

Low sparsity: \(50\%\) true signal

No id variables; using all as measure variables

No id variables; using all as measure variables

Warning in bplt(at[i], wid = width[i], stats = z$stats[, i], out = z$out[z
$group == : Outlier (-Inf) in boxplot 1 is not drawn

High sparsity: \(10\%\) true signal

No id variables; using all as measure variables

No id variables; using all as measure variables

Warning in bplt(at[i], wid = width[i], stats = z$stats[, i], out = z$out[z
$group == : Outlier (-Inf) in boxplot 1 is not drawn

Session information

sessionInfo()
R version 3.4.3 (2017-11-30)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.2

Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.4/Resources/lib/libRlapack.dylib

locale:
[1] en_US.UTF-8/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
 [1] ggplot2_2.2.1     reshape2_1.4.3    ashr_2.2-2       
 [4] Rmosek_8.0.69     PolynomF_1.0-1    CVXR_0.94-4      
 [7] REBayes_1.2       Matrix_1.2-12     SQUAREM_2017.10-1
[10] EQL_1.0-0         ttutils_1.0-1     knockoff_0.3.0   

loaded via a namespace (and not attached):
 [1] gmp_0.5-13.1      Rcpp_0.12.14      pillar_1.0.1     
 [4] plyr_1.8.4        compiler_3.4.3    git2r_0.21.0     
 [7] R.methodsS3_1.7.1 R.utils_2.6.0     iterators_1.0.9  
[10] tools_3.4.3       digest_0.6.14     bit_1.1-12       
[13] tibble_1.4.1      gtable_0.2.0      evaluate_0.10.1  
[16] lattice_0.20-35   rlang_0.1.6       foreach_1.4.4    
[19] parallel_3.4.3    yaml_2.1.16       Rmpfr_0.6-1      
[22] ECOSolveR_0.3-2   stringr_1.2.0     knitr_1.18       
[25] rprojroot_1.3-2   bit64_0.9-7       grid_3.4.3       
[28] R6_2.2.2          rmarkdown_1.8     magrittr_1.5     
[31] scales_0.5.0      MASS_7.3-47       backports_1.1.2  
[34] codetools_0.2-15  htmltools_0.3.6   scs_1.1-1        
[37] colorspace_1.3-2  labeling_0.3      stringi_1.1.6    
[40] lazyeval_0.2.1    munsell_0.4.3     pscl_1.5.2       
[43] doParallel_1.0.11 truncnorm_1.0-7   R.oo_1.21.0

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