Last updated: 2020-03-30

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options(stringsAsFactors = FALSE)

Simulation 1 – Shared effects, independent variables

dat1 <- readRDS("output/fit_mr_mash_n600_p1000_p_caus50_r5_pve0.5_sigmaoffdiag1_sigmascale0.8_gammaoffdiag0_gammascale0.8_Voffdiag0.2_Vscale0_updatew0TRUE_updatew0TRUE_updatew0methodmixsqp_updateVTRUE.rds")
n1 <- dat1$params$n
p1 <- dat1$params$p
p_causal1 <- dat1$params$p_causal
r1 <- dat1$params$r
pve1 <- dat1$params$pve
prop_testset1 <- dat1$params$prop_testset
progress_dat1 <- dat1$fit$progress
V1 <- dat1$inputs$V
Sigma1 <- dat1$inputs$Sigma
Gamma1 <- dat1$inputs$Gamma

The results below are based on simulation with 600 samples, 1000 variables of which 50 were causal, 5 responses with a per-response proportion of variance explained (PVE) of 0.5. Variables, X, were drawn from MVN(0, Gamma), causal effects, B, were drawn from MVN(0, Sigma). The responses, Y, were drawn from MN(XB, I, V).

cat("Gamma (First 5 elements)")
Gamma (First 5 elements)
Gamma1[1:5, 1:5]
     [,1] [,2] [,3] [,4] [,5]
[1,]  0.8  0.0  0.0  0.0  0.0
[2,]  0.0  0.8  0.0  0.0  0.0
[3,]  0.0  0.0  0.8  0.0  0.0
[4,]  0.0  0.0  0.0  0.8  0.0
[5,]  0.0  0.0  0.0  0.0  0.8
cat("Sigma")
Sigma
Sigma1
     [,1] [,2] [,3] [,4] [,5]
[1,]  0.8  0.8  0.8  0.8  0.8
[2,]  0.8  0.8  0.8  0.8  0.8
[3,]  0.8  0.8  0.8  0.8  0.8
[4,]  0.8  0.8  0.8  0.8  0.8
[5,]  0.8  0.8  0.8  0.8  0.8
cat("V")
V
V1
         [,1]     [,2]     [,3]     [,4]     [,5]
[1,] 25.55836  0.00000  0.00000  0.00000  0.00000
[2,]  0.00000 25.55836  0.00000  0.00000  0.00000
[3,]  0.00000  0.00000 25.55836  0.00000  0.00000
[4,]  0.00000  0.00000  0.00000 25.55836  0.00000
[5,]  0.00000  0.00000  0.00000  0.00000 25.55836

mr.mash was fitted to the training data (80% of the data) updating V and updating the prior weights using mixSQP.

Here, we investigate convergence.

plot(progress_dat1$iter, progress_dat1$ELBO_diff, xlab="Iteration", ylab="log Difference in ELBO", main="ELBO vs iteration", type="b", pch=16, cex.lab=1.5, cex.axis=1.5, log="y")
Warning in xy.coords(x, y, xlabel, ylabel, log): 7 y values <= 0 omitted
from logarithmic plot

Version Author Date
8621d7d fmorgante 2020-03-30
d5773c9 fmorgante 2020-03-30

Simulation 2 – Independent effects, independent variables

dat2 <- readRDS("output/fit_mr_mash_n600_p1000_p_caus50_r5_pve0.5_sigmaoffdiag0_sigmascale0.8_gammaoffdiag0_gammascale0.8_Voffdiag0.2_Vscale0_updatew0TRUE_updatew0TRUE_updatew0methodmixsqp_updateVTRUE.rds")
n2 <- dat2$params$n
p2 <- dat2$params$p
p_causal2 <- dat2$params$p_causal
r2 <- dat2$params$r
pve2 <- dat2$params$pve
prop_testset2 <- dat2$params$prop_testset
progress_dat2 <- dat2$fit$progress
V2 <- dat2$inputs$V
Sigma2 <- dat2$inputs$Sigma
Gamma2 <- dat2$inputs$Gamma

The results below are based on simulation with 600 samples, 1000 variables of which 50 were causal, 5 responses with a per-response proportion of variance explained (PVE) of 0.5. Variables, X, were drawn from MVN(0, Gamma), causal effects, B, were drawn from MVN(0, Sigma). The responses, Y, were drawn from MN(XB, I, V).

cat("Gamma (First 5 elements)")
Gamma (First 5 elements)
Gamma2[1:5, 1:5]
     [,1] [,2] [,3] [,4] [,5]
[1,]  0.8  0.0  0.0  0.0  0.0
[2,]  0.0  0.8  0.0  0.0  0.0
[3,]  0.0  0.0  0.8  0.0  0.0
[4,]  0.0  0.0  0.0  0.8  0.0
[5,]  0.0  0.0  0.0  0.0  0.8
cat("Sigma")
Sigma
Sigma2
     [,1] [,2] [,3] [,4] [,5]
[1,]  0.8  0.0  0.0  0.0  0.0
[2,]  0.0  0.8  0.0  0.0  0.0
[3,]  0.0  0.0  0.8  0.0  0.0
[4,]  0.0  0.0  0.0  0.8  0.0
[5,]  0.0  0.0  0.0  0.0  0.8
cat("V")
V
V2
         [,1]     [,2]     [,3]     [,4]     [,5]
[1,] 39.87305  0.00000  0.00000  0.00000  0.00000
[2,]  0.00000 24.41042  0.00000  0.00000  0.00000
[3,]  0.00000  0.00000 27.69452  0.00000  0.00000
[4,]  0.00000  0.00000  0.00000 25.53166  0.00000
[5,]  0.00000  0.00000  0.00000  0.00000 29.00472

mr.mash was fitted to the training data (80% of the data) updating V and updating the prior weights using mixSQP.

Here, we investigate convergence.

plot(progress_dat2$iter, progress_dat2$ELBO_diff, xlab="Iteration", ylab="log Difference in ELBO", main="ELBO vs iteration", type="b", pch=16, cex.lab=1.5, cex.axis=1.5, log="y")
Warning in xy.coords(x, y, xlabel, ylabel, log): 13 y values <= 0 omitted
from logarithmic plot

Version Author Date
4f5c291 fmorgante 2020-03-30

Simulation 3 – Independent effects, correlated variables

dat3 <- readRDS("output/fit_mr_mash_n600_p1000_p_caus50_r5_pve0.5_sigmaoffdiag0_sigmascale0.8_gammaoffdiag0_gammascale0.8_Voffdiag0.2_Vscale0_updatew0TRUE_updatew0TRUE_updatew0methodmixsqp_updateVTRUE.rds")
n3 <- dat3$params$n
p3 <- dat3$params$p
p_causal3 <- dat3$params$p_causal
r3 <- dat3$params$r
pve3 <- dat3$params$pve
prop_testset3 <- dat3$params$prop_testset
progress_dat3 <- dat3$fit$progress
V3 <- dat3$inputs$V
Sigma3 <- dat3$inputs$Sigma
Gamma3 <- dat3$inputs$Gamma

The results below are based on simulation with 600 samples, 1000 variables of which 50 were causal, 5 responses with a per-response proportion of variance explained (PVE) of 0.5. Variables, X, were drawn from MVN(0, Gamma), causal effects, B, were drawn from MVN(0, Sigma). The responses, Y, were drawn from MN(XB, I, V).

cat("Gamma (First 5 elements)")
Gamma (First 5 elements)
Gamma3[1:5, 1:5]
     [,1] [,2] [,3] [,4] [,5]
[1,]  0.8  0.0  0.0  0.0  0.0
[2,]  0.0  0.8  0.0  0.0  0.0
[3,]  0.0  0.0  0.8  0.0  0.0
[4,]  0.0  0.0  0.0  0.8  0.0
[5,]  0.0  0.0  0.0  0.0  0.8
cat("Sigma")
Sigma
Sigma3
     [,1] [,2] [,3] [,4] [,5]
[1,]  0.8  0.0  0.0  0.0  0.0
[2,]  0.0  0.8  0.0  0.0  0.0
[3,]  0.0  0.0  0.8  0.0  0.0
[4,]  0.0  0.0  0.0  0.8  0.0
[5,]  0.0  0.0  0.0  0.0  0.8
cat("V")
V
V3
         [,1]     [,2]     [,3]     [,4]     [,5]
[1,] 39.87305  0.00000  0.00000  0.00000  0.00000
[2,]  0.00000 24.41042  0.00000  0.00000  0.00000
[3,]  0.00000  0.00000 27.69452  0.00000  0.00000
[4,]  0.00000  0.00000  0.00000 25.53166  0.00000
[5,]  0.00000  0.00000  0.00000  0.00000 29.00472

mr.mash was fitted to the training data (80% of the data) updating V and updating the prior weights using mixSQP.

Here, we investigate convergence.

plot(progress_dat3$iter, progress_dat3$ELBO_diff, xlab="Iteration", ylab="log Difference in ELBO", main="ELBO vs iteration", type="b", pch=16, cex.lab=1.5, cex.axis=1.5, log="y")
Warning in xy.coords(x, y, xlabel, ylabel, log): 13 y values <= 0 omitted
from logarithmic plot

Version Author Date
7a2afe7 fmorgante 2020-03-30 

sessionInfo()
R version 3.5.1 (2018-07-02)
Platform: x86_64-pc-linux-gnu (64-bit)
Running under: Scientific Linux 7.4 (Nitrogen)

Matrix products: default
BLAS/LAPACK: /software/openblas-0.2.19-el7-x86_64/lib/libopenblas_haswellp-r0.2.19.so

locale:
 [1] LC_CTYPE=en_US.UTF-8       LC_NUMERIC=C              
 [3] LC_TIME=en_US.UTF-8        LC_COLLATE=en_US.UTF-8    
 [5] LC_MONETARY=en_US.UTF-8    LC_MESSAGES=en_US.UTF-8   
 [7] LC_PAPER=en_US.UTF-8       LC_NAME=C                 
 [9] LC_ADDRESS=C               LC_TELEPHONE=C            
[11] LC_MEASUREMENT=en_US.UTF-8 LC_IDENTIFICATION=C       

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

loaded via a namespace (and not attached):
 [1] workflowr_1.6.1 Rcpp_1.0.3      digest_0.6.23   later_0.7.5    
 [5] rprojroot_1.3-2 R6_2.4.1        backports_1.1.5 git2r_0.26.1   
 [9] magrittr_1.5    evaluate_0.12   stringi_1.4.3   fs_1.3.1       
[13] promises_1.0.1  whisker_0.3-2   rmarkdown_1.10  tools_3.5.1    
[17] stringr_1.4.0   glue_1.3.1      httpuv_1.4.5    yaml_2.2.0     
[21] compiler_3.5.1  htmltools_0.3.6 knitr_1.20