Last updated: 2020-10-05
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In supplementary of the manuscript, we show the derivation for multivariate SuSiE with missing data. We notice that we only need to compute \(\tilde{\mathbf{X}}_i\) and \(\sum_{i=1}^{N} \tilde{\mathbf{X}}_i \Gamma_i \Sigma_i^\dagger \Gamma_i \tilde{\mathbf{X}}_i\) once before the algorithm begins.
We simulate data with 100 samples, 100 SNPs, 2 conditions, half of the observation is missing.
library(mmbr)Loading required package: mashrLoading required package: ashrLoading required package: susieRsimulate_multivariate = function(n=100,p=100,r=2,center_scale=TRUE,y_missing=0) {
set.seed(1)
res = mmbr:::mmbr_sim1(n,p,r,4,center_scale=center_scale,y_missing=y_missing)
res$L = 10
return(res)
}
dat = simulate_multivariate(r=2, center_scale = F, y_missing = 0.5)
residual_var = cov(dat$y)# create data object
data_obj = mmbr:::DenseDataYMissing$new(dat$X, dat$y_missing)
# compute residual variance according to different missing pattern
data_obj$set_residual_variance(residual_var, quantities = 'residual_variance')
# compute \tilde{\mathbf{X}}_i, \tilde{\mathbf{y}}_i
data_obj$standardize(TRUE,FALSE)
# compute svs
data_obj$set_residual_variance(quantities = 'effect_variance')In Single Effect Model (BayesianSimpleRegression, BayesianMultivariateRegression, MashRegression), we only need bhat and sbhat2. The sbhat2 is precomputed in data object.
data_obj$svs[[1]] [,1] [,2]
[1,] 0.097968791 0.006018362
[2,] 0.006018362 0.136472648data_obj$svs[[2]] [,1] [,2]
[1,] 0.089531112 0.005459086
[2,] 0.005459086 0.149178188The bhat can be obtained using get_coef function:
head(data_obj$get_coef(F)) [,1] [,2]
[1,] 0.54061432 -0.472094111
[2,] 0.38118760 0.005747207
[3,] -0.01114687 0.383212746
[4,] 0.16990375 0.644584948
[5,] -0.07297641 -0.399183192
[6,] -0.29919993 0.322249929
sessionInfo()R version 3.6.3 (2020-02-29)
Platform: x86_64-apple-darwin15.6.0 (64-bit)
Running under: macOS Catalina 10.15.6
Matrix products: default
BLAS: /Library/Frameworks/R.framework/Versions/3.6/Resources/lib/libRblas.0.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/3.6/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] mmbr_0.0.1.0305 susieR_0.9.26 mashr_0.2.40 ashr_2.2-51
[5] workflowr_1.6.1
loaded via a namespace (and not attached):
[1] progress_1.2.2 tidyselect_1.0.0 xfun_0.13 purrr_0.3.4
[5] lattice_0.20-41 colorspace_1.4-1 vctrs_0.3.4 htmltools_0.4.0
[9] yaml_2.2.1 rlang_0.4.7 mixsqp_0.3-46 later_1.0.0
[13] pillar_1.4.6 glue_1.4.2 matrixStats_0.57.0 lifecycle_0.2.0
[17] plyr_1.8.6 stringr_1.4.0 munsell_0.5.0 gtable_0.3.0
[21] mvtnorm_1.1-1 evaluate_0.14 knitr_1.28 httpuv_1.5.2
[25] invgamma_1.1 irlba_2.3.3 Rcpp_1.0.5 promises_1.1.0
[29] backports_1.1.10 scales_1.1.1 rmeta_3.0 truncnorm_1.0-8
[33] abind_1.4-5 fs_1.4.1 hms_0.5.3 ggplot2_3.3.2
[37] digest_0.6.25 stringi_1.4.6 dplyr_0.8.5 grid_3.6.3
[41] rprojroot_1.3-2 tools_3.6.3 magrittr_1.5 tibble_3.0.3
[45] crayon_1.3.4 whisker_0.4 pkgconfig_2.0.3 ellipsis_0.3.1
[49] Matrix_1.2-18 prettyunits_1.1.1 SQUAREM_2020.4 assertthat_0.2.1
[53] rmarkdown_2.1 reshape_0.8.8 R6_2.4.1 git2r_0.26.1
[57] compiler_3.6.3