Set up the data

# Load required packages
library(mashr); library(ExtremeDeconvolution); library(flashr2)

Loading required package: ashr

# read data
data = readRDS('../data/ImmuneQTLSummary.4MASH.rds')
data$max$se = data$max$beta/data$max$z
data$null$se = data$null$beta / data$null$z

# set parameters
K = 10
P = 5

We estimate the covariance using column-centered Z scores

D.center = apply(as.matrix(data$max$z), 2, function(x) x - mean(x))
mash_data_center = mashr::set_mash_data(Bhat = as.matrix(D.center))

Generate covariance matrices

Here we create 3 type of data-driven covariance matrices:

• Flash (rank 5, previously computed): Flash \[ \tilde{Z}_{n\times 7} = LF' + E \] \[ U = \frac{1}{n} (LF')'(LF') \]
  • plus single rank Flashs for each factor The 5 matrices \(F_{q}L_{q}' L_{q} F_{q}'\)
• PCA (rank 5, to be computed)
  • plus single rank PCAs
• Optionally
  • Empirical covariance

and apply Extreme Deconvolution to refine these matrices. We observed that Extreme Deconvolution perserves rank.

Additionally we include 2 other types of covariance matrices:

• canonical configurations (aka bmalite)

• simple heterogeneity models

FlashResult = readRDS('../output/Immune.flash2.center.greedy.K10.rds')
Flash_res = flash_get_lf(FlashResult$f)

U.flash = c(mashr::cov_from_factors(t(as.matrix(FlashResult$F_flash[,1:5])), "Flash"), 
            list("tFlash" = t(Flash_res) %*% Flash_res / nrow(data$max$z)))

# PCA matrices
U.pca = cov_pca(mash_data_center, P)

# Emperical data matrices
# Denoised data-driven matrices
U.dd = c(U.flash, U.pca, list("XX" = t(D.center) %*% D.center / nrow(data$max$z)))

mash_data = mashr::set_mash_data(Bhat = as.matrix(data$max$beta), 
                                 Shat = as.matrix(data$max$se), alpha=0)

U.ed = cov_ed(mash_data, U.dd)

# Canonical
U.can = cov_canonical(mash_data) 

# save Covariance matrix
saveRDS(list(Ulist = c(U.ed, U.can), DD_raw = U.dd), 
        paste0('../output/ImmuneEE.U.center.xtx.K',K,'.P',P,'.rds'))

Session information

sessionInfo()

R version 3.4.2 (2017-09-28)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS High Sierra 10.13.1

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] flashr2_0.2-3            ExtremeDeconvolution_1.3
[3] mashr_0.2-4              ashr_2.1-27             

loaded via a namespace (and not attached):
 [1] Rcpp_0.12.13      compiler_3.4.2    git2r_0.19.0     
 [4] plyr_1.8.4        iterators_1.0.8   tools_3.4.2      
 [7] digest_0.6.12     evaluate_0.10.1   tibble_1.3.4     
[10] gtable_0.2.0      lattice_0.20-35   rlang_0.1.2      
[13] Matrix_1.2-11     foreach_1.4.3     yaml_2.1.14      
[16] parallel_3.4.2    mvtnorm_1.0-6     stringr_1.2.0    
[19] knitr_1.17        rprojroot_1.2     grid_3.4.2       
[22] rmarkdown_1.7     rmeta_2.16        ggplot2_2.2.1    
[25] magrittr_1.5      backports_1.1.1   scales_0.5.0     
[28] codetools_0.2-15  htmltools_0.3.6   MASS_7.3-47      
[31] assertthat_0.2.0  colorspace_1.3-2  stringi_1.1.5    
[34] lazyeval_0.2.1    pscl_1.5.2        doParallel_1.0.11
[37] munsell_0.4.3     truncnorm_1.0-7   SQUAREM_2017.10-1