Simulating Design Matrix \(X\): Correlation patterns

Introduction

Independent and normalized columns

Toeplitz column correlation

\(\text{SE}\left(\hat\beta_j\right)\)

Correlation among \(X_j\) and \(\hat\beta_j\)

Factor model column correlation

\(\text{SE}\left(\hat\beta_j\right)\)

Correlation among \(X_j\) and \(\hat\beta_j\).

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     

loaded via a namespace (and not attached):
 [1] compiler_3.4.3  backports_1.1.2 magrittr_1.5    rprojroot_1.3-2
 [5] tools_3.4.3     htmltools_0.3.6 yaml_2.1.16     Rcpp_0.12.14   
 [9] stringi_1.1.6   rmarkdown_1.8   knitr_1.19      git2r_0.21.0   
[13] stringr_1.2.0   digest_0.6.14   evaluate_0.10.1