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| File | Version | Author | Date | Message |
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| Rmd | 565210c | Dave Tang | 2025-01-10 | TL;DR section |
| html | cc5ada7 | Dave Tang | 2025-01-08 | Build site. |
| Rmd | 2e3db9a | Dave Tang | 2025-01-08 | Regression model for covariates |
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| Rmd | abe2d86 | Dave Tang | 2025-01-08 | Design matrices for gene expression experiments |
A guide to creating design matrices for gene expression experiments.
Understand:
A design matrix is used to define the form of a statistical model and
to store observed values of the explanatory variable(s). It is used in
the computation process to estimate model parameters. The
model.matrix() function from the base R {stats} package can
be used to construct design matrices.
group <- as.factor(c(1,1,1,2,2,2))
design <- model.matrix(~0+group)
design group1 group2
1 1 0
2 1 0
3 1 0
4 0 1
5 0 1
6 0 1
attr(,"assign")
[1] 1 1
attr(,"contrasts")
attr(,"contrasts")$group
[1] "contr.treatment"In the design matrix, rows are associated with samples and columns are associated with model parameters.
Contrasts can be created using
limma::makeContrasts().
contrasts <- limma::makeContrasts(group1-group2, levels=colnames(design))
contrasts Contrasts
Levels group1 - group2
group1 1
group2 -1In the matrix, rows are associated with model parameters and columns represent a contrast of interest. A contrast matrix is used in conjunction with a design matrix to calculate specific values of interest between estimated parameters.
Gene expression will be the response variable, i.e., dependent variable, which is the variable that we are trying to predict or explain. The variables that influence the expression will be the explanatory variables, i.e., independent variables.
The modelling process requires the use of a design matrix (or model matrix) that has two roles:
In the modelling process, a single design matrix is defined and then simultaneously applied to each and every gene in the dataset.
Consider two types of explanatory variables: “covariates” and “factors”. Covariates contain numerical values that are quantitative measurements associated with samples in the experiment. These can be the age or weight of an individual. For covariates, it is generally of interest to know the rate of change between the response and the covariate, such as “how much does the expression of a particular gene increase/decrease per unit increase in age?”. We can use a straight line to model, or describe, this relationship, which takes the form of
\[expression = \beta_0 + \beta_1age\]
where the line is defined by \(\beta_0\) the y-intercept and \(\beta_1\) the slope. In this model, the age covariate takes continuous, numerical values such as 0.8, 1.3, 2.0, 5.6, and so on. We refer to this model generally as a regression model, where the slope indicates the rate of change, or how much gene expression is expected to increase/decrease by per unit increase of the covariate.
The y-intercept and slope of the line, or the \(\beta\)s (\(\beta_0\) and \(\beta_1\)), are referred to as the model parameters. The true values of the parameters are unknown, but are estimated in the modelling process. A positive estimate of a model parameter indicates that an explanatory variable has a positive influence on gene expression (an increasing slope), whilst a negative value indicates that the explanatory variable has a negative influence on gene expression (a decreasing slope). In some cases, one may convert the age covariate into a factor by categorising the smaller values as “young” and larger values as “mature”, and instead use the models described below.
Install {limma} using BiocManager::install().
if (!require("BiocManager", quietly = TRUE))
install.packages("BiocManager")
BiocManager::install("limma")
sessionInfo()R version 4.4.1 (2024-06-14)
Platform: x86_64-pc-linux-gnu
Running under: Ubuntu 22.04.5 LTS
Matrix products: default
BLAS: /usr/lib/x86_64-linux-gnu/openblas-pthread/libblas.so.3
LAPACK: /usr/lib/x86_64-linux-gnu/openblas-pthread/libopenblasp-r0.3.20.so; LAPACK version 3.10.0
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
time zone: Etc/UTC
tzcode source: system (glibc)
attached base packages:
[1] stats graphics grDevices utils datasets methods base
other attached packages:
[1] lubridate_1.9.3 forcats_1.0.0 stringr_1.5.1 dplyr_1.1.4
[5] purrr_1.0.2 readr_2.1.5 tidyr_1.3.1 tibble_3.2.1
[9] ggplot2_3.5.1 tidyverse_2.0.0 workflowr_1.7.1
loaded via a namespace (and not attached):
[1] sass_0.4.9 utf8_1.2.4 generics_0.1.3 stringi_1.8.4
[5] hms_1.1.3 digest_0.6.37 magrittr_2.0.3 timechange_0.3.0
[9] evaluate_1.0.1 grid_4.4.1 fastmap_1.2.0 rprojroot_2.0.4
[13] jsonlite_1.8.9 processx_3.8.4 whisker_0.4.1 limma_3.62.1
[17] ps_1.8.1 promises_1.3.0 httr_1.4.7 fansi_1.0.6
[21] scales_1.3.0 jquerylib_0.1.4 cli_3.6.3 rlang_1.1.4
[25] munsell_0.5.1 withr_3.0.2 cachem_1.1.0 yaml_2.3.10
[29] tools_4.4.1 tzdb_0.4.0 colorspace_2.1-1 httpuv_1.6.15
[33] vctrs_0.6.5 R6_2.5.1 lifecycle_1.0.4 git2r_0.35.0
[37] fs_1.6.4 pkgconfig_2.0.3 callr_3.7.6 pillar_1.9.0
[41] bslib_0.8.0 later_1.3.2 gtable_0.3.6 glue_1.8.0
[45] Rcpp_1.0.13 statmod_1.5.0 xfun_0.48 tidyselect_1.2.1
[49] rstudioapi_0.17.1 knitr_1.48 htmltools_0.5.8.1 rmarkdown_2.28
[53] compiler_4.4.1 getPass_0.2-4