Last updated: 2018-05-12

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    html 4491358 LSun 2018-01-30 linear regression
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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

Expand here to see past versions of avg-1.png:
Version Author Date
4491358 LSun 2018-01-30

Expand here to see past versions of avg-2.png:
Version Author Date
4491358 LSun 2018-01-30

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

No id variables; using all as measure variables

Expand here to see past versions of 500-1.png:
Version Author Date
4491358 LSun 2018-01-30 
No id variables; using all as measure variables

Expand here to see past versions of 500-2.png:
Version Author Date
4491358 LSun 2018-01-30 
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

Expand here to see past versions of 500-3.png:
Version Author Date
4491358 LSun 2018-01-30

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

No id variables; using all as measure variables

Expand here to see past versions of 100-1.png:
Version Author Date
4491358 LSun 2018-01-30 
No id variables; using all as measure variables

Expand here to see past versions of 100-2.png:
Version Author Date
4491358 LSun 2018-01-30 
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

Expand here to see past versions of 100-3.png:
Version Author Date
4491358 LSun 2018-01-30

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 10.13.4

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_0.95        
 [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_0.12.16      pillar_1.0.1     
 [4] plyr_1.8.4        compiler_3.4.3    git2r_0.21.0     
 [7] workflowr_1.0.1   R.methodsS3_1.7.1 R.utils_2.6.0    
[10] iterators_1.0.9   tools_3.4.3       digest_0.6.15    
[13] bit_1.1-12        tibble_1.4.1      gtable_0.2.0     
[16] evaluate_0.10.1   lattice_0.20-35   rlang_0.1.6      
[19] foreach_1.4.4     parallel_3.4.3    yaml_2.1.18      
[22] Rmpfr_0.6-1       ECOSolveR_0.4     stringr_1.3.0    
[25] knitr_1.20        rprojroot_1.3-2   bit64_0.9-7      
[28] grid_3.4.3        R6_2.2.2          rmarkdown_1.9    
[31] magrittr_1.5      whisker_0.3-2     scales_0.5.0     
[34] MASS_7.3-47       codetools_0.2-15  backports_1.1.2  
[37] htmltools_0.3.6   scs_1.1-1         colorspace_1.3-2 
[40] labeling_0.3      stringi_1.1.6     lazyeval_0.2.1   
[43] munsell_0.4.3     pscl_1.5.2        doParallel_1.0.11
[46] truncnorm_1.0-7   R.oo_1.21.0

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