Last updated: 2020-03-30
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Knit directory: causal-TWAS/
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\[Y = \tilde{X}\gamma + G\theta + \epsilon\] \(Y\): quantitative traits, \(N\) x 1 vector, \(N\) is number of individuals
\(\tilde{X}\): cis-gene expression (the genetic component of expression). \(N\) x \(J\) matrix, \(J\) is number of genes.
\(G\): genotype (standardized). \(N\) x \(M\) matrix, \(M\) is number of SNPs.
\(\gamma\): effect sizes for \(\tilde{X}\), \(\gamma_j\), effect size for gene \(j\).
\[ \gamma_j \sim N(0, \sigma_\gamma^2)\] \(\theta\): effect sizes for \(G\), \(\theta_m\), effect size for SNP \(m\).
\[ \theta_m \sim N(0, \sigma_\theta^2)\]
The above model is equivalent to this: \[Y \sim N(0,\sigma_\gamma^2XX^T + \sigma_\theta^2GG^T + \sigma_e^2I) \] This is REML with multiple (more than 2) variance components. Use HE regression function from GEMMA software.
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_1.6.0 Rcpp_1.0.0 digest_0.6.18 later_0.7.5
[5] rprojroot_1.3-2 R6_2.3.0 backports_1.1.2 git2r_0.26.1
[9] magrittr_1.5 evaluate_0.12 stringi_1.3.1 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_1.3.0 httpuv_1.4.5 yaml_2.2.0
[21] compiler_3.5.1 htmltools_0.3.6 knitr_1.20