limpca 1.0.0

This package was created to analyse models with high-dimensional data and a multi-factor design of experiment. `limpca`

stands for **li**near **m**odeling of high-dimensional designed data based on the ASCA (ANOVA-Simultaneous Component Analysis) and A**PCA** (ANOVA-Principal Component Analysis) family of methods. These methods combine ANOVA with a General Linear Model (GLM) decomposition and PCA. They provide powerful visualization tools for multivariate structures in the space of each effect of the statistical model linked to the experimental design. Details on the methods used and the package implementation can be found in the articles of Thiel, Féraud, and Govaerts (2017), Guisset, Martin, and Govaerts (2019) and Thiel et al. (2023).

Therefore, ASCA/APCA are highly informative modeling and visualisation tools to analyse -omics data tables in a multivariate framework and act as a complement to differential expression analyses methods such as `limma`

(Ritchie et al. (2015)).

`Get started with limpca`

(this vignette): This vignette is a short application of`limpca`

on the`UCH`

dataset with data visualisation, exploration (PCA), GLM decomposition and ASCA modelling. The ASCA model used in this example is a three-way ANOVA with fixed effects.Analysis of the UCH dataset with limpca: This vignette is an extensive application of

`limpca`

on the`UCH`

dataset with data visualisation, exploration (PCA), GLM decomposition and ASCA/APCA/ASCA-E modelling. The applied model is a three-way ANOVA with fixed effects. This document presents all the usual steps of the analysis, from importing the data to visualising the results.Analysis of the Trout dataset with limpca: This vignette is an extensive application of

`limpca`

on the`Trout`

dataset with data visualisation, exploration (PCA), GLM decomposition and ASCA/APCA/ASCA-E modelling. The applied model involves three main effects and their two-way interaction terms. It also compares the results of ASCA to a univariate ANOVA modeling.

`limpca`

package`limpca`

can be installed from Bioconductor:

```
if (!requireNamespace("BiocManager", quietly = TRUE))
install.packages("BiocManager")
BiocManager::install("limpca")
```

And then loaded into your R session:

`library("limpca")`

For any enquiry, you can send an email to the package authors: bernadette.govaerts@uclouvain.be ; michel.thiel@uclouvain.be or manon.martin@uclouvain.be

`UCH`

datasetIn order to use the limpca core functions, the data need to be formatted as a list (informally called an lmpDataList) with the following elements: `outcomes`

(multivariate matrix), `design`

(data.frame) and `formula`

(character string).
The `UCH`

data set is already formatted appropriately and can be loaded from `limpca`

with the `data`

function.

```
data("UCH")
str(UCH)
#> List of 3
#> $ design :'data.frame': 34 obs. of 5 variables:
#> ..$ Hippurate: Factor w/ 3 levels "0","1","2": 1 1 1 1 1 1 2 2 2 2 ...
#> ..$ Citrate : Factor w/ 3 levels "0","2","4": 1 1 2 2 3 3 1 1 2 2 ...
#> ..$ Dilution : Factor w/ 1 level "diluted": 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ Day : Factor w/ 2 levels "2","3": 1 1 1 1 1 1 1 1 1 1 ...
#> ..$ Time : Factor w/ 2 levels "1","2": 1 2 1 2 1 2 1 2 1 2 ...
#> $ outcomes: num [1:34, 1:600] 0.0312 0.0581 0.027 0.0341 0.0406 ...
#> ..- attr(*, "dimnames")=List of 2
#> .. ..$ : chr [1:34] "M2C00D2R1" "M2C00D2R2" "M2C02D2R1" "M2C02D2R2" ...
#> .. ..$ X1: chr [1:600] "9.9917004" "9.9753204" "9.9590624" "9.9427436" ...
#> $ formula : chr "outcomes ~ Hippurate + Citrate + Time + Hippurate:Citrate + Time:Hippurate + Time:Citrate + Hippurate:Citrate:Time"
```

Alternatively, the lmpDataList can be created with the function `data2LmpDataList`

:

- from scratch:

```
UCH2 <- data2LmpDataList(
outcomes = UCH$outcomes,
design = UCH$design,
formula = UCH$formula
)
#> | dim outcomes: 34x600
#> | formula: ~ Hippurate + Citrate + Time + Hippurate:Citrate + Time:Hippurate + Time:Citrate + Hippurate:Citrate:Time
#> | design variables (5):
#> * Hippurate (factor)
#> * Citrate (factor)
#> * Dilution (factor)
#> * Day (factor)
#> * Time (factor)
```

- or from a
`SummarizedExperiment`

:

```
se <- SummarizedExperiment(
assays = list(
counts = t(UCH$outcomes)), colData = UCH$design,
metadata = list(formula = UCH$formula)
)
UCH3 <- data2LmpDataList(se, assay_name = "counts")
#> | dim outcomes: 34x600
#> | formula: ~ Hippurate + Citrate + Time + Hippurate:Citrate + Time:Hippurate + Time:Citrate + Hippurate:Citrate:Time
#> | design variables (5):
#> * Hippurate (factor)
#> * Citrate (factor)
#> * Dilution (factor)
#> * Day (factor)
#> * Time (factor)
```

`SummarizedExperiment`

is a generic data container that stores rectangular matrices of experimental results. See Morgan et al. (2023) for more information.

The design can be visualised with `plotDesign()`

.

```
# design
plotDesign(
design = UCH$design, x = "Hippurate",
y = "Citrate", rows = "Time",
title = "Design of the UCH dataset"
)
```

```
# row 3 of outcomes
plotLine(
Y = UCH$outcomes,
title = "H-NMR spectrum",
rows = c(3),
xlab = "ppm",
ylab = "Intensity"
)
```

```
ResPCA <- pcaBySvd(UCH$outcomes)
pcaScreePlot(ResPCA, nPC = 6)
```

```
pcaScorePlot(
resPcaBySvd = ResPCA, axes = c(1, 2),
title = "PCA scores plot: PC1 and PC2",
design = UCH$design,
color = "Hippurate", shape = "Citrate",
points_labs_rn = FALSE
)
```