Package 'limpca' reference manual

Title:	An R package for the linear modeling of high-dimensional designed data based on ASCA/APCA family of methods
Description:	This package has for objectives to provide a method to make Linear Models for high-dimensional designed data. limpca applies a GLM (General Linear Model) version of ASCA and APCA to analyse multivariate sample profiles generated by an experimental design. ASCA/APCA provide powerful visualization tools for multivariate structures in the space of each effect of the statistical model linked to the experimental design and contrarily to MANOVA, it can deal with mutlivariate datasets having more variables than observations. This method can handle unbalanced design.
Authors:	Bernadette Govaerts [aut, ths], Sebastien Franceschini [ctb], Robin van Oirbeek [ctb], Michel Thiel [aut], Pascal de Tullio [dtc], Manon Martin [aut, cre] , Nadia Benaiche [ctb]
Maintainer:	Manon Martin <[email protected]>
License:	Artistic-2.0
Version:	1.3.0
Built:	2024-11-04 06:07:49 UTC
Source:	https://github.com/bioc/limpca

Converts data to a lmpDataList.

Description

Creates the lmpDataList from a SummarizedExperiment or by manually defining the design, the outcomes and the model formula. lmpDataList serves as an input for the lmpModelMatrix function to start the limpca modeling.

Usage

data2LmpDataList(
  se = NULL,
  assay_name = NULL,
  outcomes = NULL,
  design = NULL,
  formula = NULL,
  verbose = TRUE
)
data2LmpDataList(
  se = NULL,
  assay_name = NULL,
  outcomes = NULL,
  design = NULL,
  formula = NULL,
  verbose = TRUE
)

Arguments

`se`	A `SummarizedExperiment` object.
`assay_name`	If not `NULL` (default), a character string naming the assay from the `SummarizedExperiment` object `se`. If `NULL`, the first assay is selected.
`outcomes`	If not `NULL` (default), a numerical matrix with n observations and m response variables. The rownames needs to be non-NULL and match those of the design matrix.
`design`	If not `NULL` (default), a data.frame with the experimental design of n observations and q explanatory variables. The rownames of design has to match the rownames of outcomes.
`formula`	If not `NULL` (default), a character string with the formula that will be used to analyze the data. Only the right part of the formula is necessary, eg: `"~ A + B"`, The names of the formula should match the column names of the design
`verbose`	If `TRUE`, prints useful information about the outputted list.

Details

Data can be included as a SummarizedExperiment (SE) object or by manually defining one or multiple elements of outcomes, design and formula. If a SE is provided, the outcomes corresponds to a transposed assay of the SE (by default the first one), the design corresponds to the colData of the SE and the formula can be provided as a formula element in the S4Vectors::metadata of SE (metadata(se)$formula).

In the outputted list, the outcomes are structured in a standard statistical fashion, i.e. with observations in rows and the variables (features) in column. If the outcomes argument is not NULL, it has to be formatted that way (see Arguments).

Note that there is a priority to the outcomes, design and formula arguments if they are not NULL (e.g. if both se and outcomes arguments are provided, the resulting outcomes matrix will be from the outcomes argument). outcomes and design elements are mandatory.

Multiple checks are performed to ensure that the data are correctly formatted:

the rownames of design and outcomes should match
the names of the model terms in the formula should match column names from the design

Value

A list with the 3 following named elements:

outcomes: A nxm matrix with the m response variables.
design: A nxq data.frame with the experimental design.
formula: A character string with the model formula.

Examples


data(UCH)

### create manually the dataset

res <- data2LmpDataList(
  outcomes = UCH$outcomes,
  design = UCH$design[, 1, drop = FALSE], formula = "~ Hippurate"
)

### create the dataset from a SummarizedExperiment

library(SummarizedExperiment)

se <- SummarizedExperiment(
  assays = list(
    counts = t(UCH$outcomes),
    counts2 = t(UCH$outcomes * 2)
  ), colData = UCH$design,
  metadata = list(formula = "~ Hippurate + Citrate")
)

res <- data2LmpDataList(se, assay_name = "counts2")

# changing the formula:
res <- data2LmpDataList(se,
  assay_name = "counts2",
  formula = "~ Hippurate + Citrate + Time"
)

data(UCH)

### create manually the dataset

res <- data2LmpDataList(
  outcomes = UCH$outcomes,
  design = UCH$design[, 1, drop = FALSE], formula = "~ Hippurate"
)

### create the dataset from a SummarizedExperiment

library(SummarizedExperiment)

se <- SummarizedExperiment(
  assays = list(
    counts = t(UCH$outcomes),
    counts2 = t(UCH$outcomes * 2)
  ), colData = UCH$design,
  metadata = list(formula = "~ Hippurate + Citrate")
)

res <- data2LmpDataList(se, assay_name = "counts2")

# changing the formula:
res <- data2LmpDataList(se,
  assay_name = "counts2",
  formula = "~ Hippurate + Citrate + Time"
)

Linear modeling of high-dimensional designed data based on ASCA/APCA family of methods

Description

This package has for objectives to provide a method to make Linear Models for high-dimensional designed data. This method handles unbalanced design. More features should be included in the future (e.g. generalized linear models, random effects, ...).

The core functions of the package are:

data2LmpDataList: Converts data to a lmpDataList, the input argument for lmpModelMatrix.
lmpModelMatrix: Creates the model matrix $\mathbf{X}$ from the design matrix and the model formula.
lmpEffectMatrices: Estimates the model by OLS based on the outcomes and model matrices provided in the outputs of the lmpModelMatrix function and calculates the estimated effect matrices $\hat{\mathbf{M}}_0, \hat{\mathbf{M}}_1, ...\hat{\mathbf{M}}_F$ and residual matrix $\hat{\mathbf{E}}$ . It calculates also the type III percentage of variance explained by each effect.
lmpBootstrapTests: Tests the significance of one or a combination of the model effects using bootstrap. This function is based on the outputs of the lmpEffectMatrices function.
lmpPcaEffects: Performs a PCA on each of the effect matrices from the outputs of lmpEffectMatrices. It has an option to choose the method applied: ASCA, APCA or ASCA-E. Combined effects (i.e. linear combinations of original effect matrices) can also be created and decomposed by PCA.

The functions allowing the visualisation of the Linear Models results are:

lmpScreePlot: Provides a barplot of the percentage of variance associated to the PCs of the effect matrices ordered by importance based on the outputs of lmpContributions.
lmpContributions: This reports the contribution of each effect to the total variance, but also the contribution of each PC to the total variance per effect. Moreover, these contributions are summarized in a barplot.
lmpScorePlot: Draws the score plots of each effect matrix provided in the lmpPcaEffects function output.
lmpLoading1dPlot or lmpLoading2dPlot: Plots the loadings as a line plot (1D) or in 2D as a scatterplot.
lmpScoreScatterPlotM: Plots the scores of all model effects simultaneously in a scatterplot matrix. By default, the first PC only is kept for each model effect.
lmpEffectPlot: Plots the ASCA scores by effect levels for a given model effect and for one PC at a time. This graph is especially appealing to interpret interactions or combined effects.

Other useful functions to visualise and explore by PCA the multivariate data are:

plotDesign: Provides a graphical representation of the experimental design. It allows to visualize factor levels and check the design balance.
plotScatter: Produces a plot describing the relationship between two columns of the outcomes matrix $\mathbf{Y}$ . It allows to choose colors and symbols for the levels of the design factors. Ellipses, polygons or segments can be added to group different sets of points on the graph.
plotScatterM: Produces a scatter plot matrix between the selected columns of the outcomes matrix $\mathbf{Y}$ choosing specific colors and symbols for up to four factors from the design on the upper and lower diagonals.
plotMeans: Draws, for a given response variable, a plot of the response means by levels of up to three categorical factors from the design. When the design is balanced, it allows to visualize main effects or interactions for the response of interest. For unbalanced designs, this plot must be used with caution.
plotLine: Generates the response profile of one or more observations i.e. plots of one or more rows of the outcomes matrix on the y-axis against the m response variables on the x-axis. Depending on the response type (spectra, gene expression...), point, line or segment plots can be used.
pcaBySvd: Operates a principal component analysis on the $\mathbf{Y}$ outcome/response matrix by a singular value decomposition. Outputs are can be visulised with the functions pcaScorePlot, pcaLoading1dPlot, pcaLoading2dPlot and pcaScreePlot.
pcaScorePlot: Produces score plots from the pcaBySvd output.
pcaLoading1dPlot or pcaLoading2dPlot: Plots the PCA loadings as a line plot (1D) or in 2D as a scatterplot.
pcaScreePlot: Returns a bar plot of the percentage of variance explained by each Principal Component (PC) calculated by pcaBySvd.

Details

Package:	limpca
Type:	Package
License:	GPL-2

See the package vignettes (vignette(package = "limpca")) for detailed case studies.

References

Thiel, M., Benaiche, N., Martin, M., Franceschini, S., Van Oirbeek, R., Govaerts, B. (2023). limpca: An R package for the linear modeling of high-dimensional designed data based on ASCA/APCA family of methods. Journal of Chemometrics. e3482. https://doi.org/10.1002/cem.3482

Martin, M. (2020). Uncovering informative content in metabolomics data: from pre-processing of 1H NMR spectra to biomarkers discovery in multifactorial designs. Prom.: Govaerts, B. PhD thesis. Institut de statistique, biostatistique et sciences actuarielles, UCLouvain, Belgium. http://hdl.handle.net/2078.1/227671

Thiel M., Feraud B. and Govaerts B. (2017). ASCA+ and APCA+: Extensions of ASCA and APCA in the analysis of unbalanced multifactorial designs. Journal of Chemometrics. 31:e2895. https://doi.org/10.1002/cem.2895

Tests the significance of model effects by bootstrap.

Description

Tests the significance of the effects from the model using bootstrap. This function is based on the outputs of lmpEffectMatrices. Tests on combined effects are also provided.

Usage

lmpBootstrapTests(
  resLmpEffectMatrices,
  nboot = 100,
  nCores = 2,
  verbose = FALSE
)
lmpBootstrapTests(
  resLmpEffectMatrices,
  nboot = 100,
  nCores = 2,
  verbose = FALSE
)

Arguments

`resLmpEffectMatrices`	A list of 12 from `lmpEffectMatrices`.
`nboot`	An integer with the number of bootstrap sample to be drawn.
`nCores`	The number of cores to use for parallel execution.
`verbose`	If `TRUE`, will display a message with the duration of execution.

Value

A list with the following elements:

f.obs: A vector of size F (number of effects in the model) with the F statistics for each model term calculated on the initial data.
f.boot: b × F matrix with the F statistics calculated on the bootstrap samples.
p.values: A vector of size F with the p-value for each model effect.
resultsTable: A 2 × F matrix with the p-value and the percentage of variance for each model effect.

References

Thiel M.,Feraud B. and Govaerts B. (2017) ASCA+ and APCA+: Extensions of ASCA and APCA in the analysis of unbalanced multifactorial designs, Journal of Chemometrics

Thiel, M., Benaiche, N., Martin, M., Franceschini, S., Van Oirbeek, R., & Govaerts, B. (2023) limpca: an R package for the linear modeling of high dimensional designed data based on ASCA/APCA family of methods, Journal of Chemometrics

Examples

data("UCH")
resLmpModelMatrix <- lmpModelMatrix(UCH)
resLmpEffectMatrices <- lmpEffectMatrices(resLmpModelMatrix = resLmpModelMatrix)

res <- lmpBootstrapTests(
  resLmpEffectMatrices = resLmpEffectMatrices,
  nboot = 10, nCores = 2, verbose = TRUE
)

data("UCH")
resLmpModelMatrix <- lmpModelMatrix(UCH)
resLmpEffectMatrices <- lmpEffectMatrices(resLmpModelMatrix = resLmpModelMatrix)

res <- lmpBootstrapTests(
  resLmpEffectMatrices = resLmpEffectMatrices,
  nboot = 10, nCores = 2, verbose = TRUE
)

Summary of the contributions of each effect

Description

Reports the contribution of each effect to the total variance, but also the contribution of each PC to the total variance per effect. These contributions are also summarized in a barplot.

Usage

lmpContributions(resLmpPcaEffects, nPC = 5)
lmpContributions(resLmpPcaEffects, nPC = 5)

Arguments

`resLmpPcaEffects`	A list corresponding to the output value of `lmpPcaEffects`.
`nPC`	The number of Principal Components to display.

Value

A list of:

totalContribTable: Table of the percentage of contribution of each effect to the total variance.
effectTable: Table of the percentage of variance explained by each principal component in each model effect decomposition.
contribTable: Table of the percentage of variance explained by each principal component of each effect reported to the percentage contribution of the given effect to the total variance.
combinedEffectTable: Equivalent of the EffectTable for combined effects.
plotTotal: Plot of the ordered contributions of TotalContribTable.
plotContrib: Plot of the ordered contributions of ContribTable.

Examples

data("UCH")
resLmpModelMatrix <- lmpModelMatrix(UCH)
resLmpEffectMatrices <- lmpEffectMatrices(resLmpModelMatrix)
resLmpPcaEffects <- lmpPcaEffects(resLmpEffectMatrices, method = "ASCA-E")

lmpContributions(resLmpPcaEffects)

data("UCH")
resLmpModelMatrix <- lmpModelMatrix(UCH)
resLmpEffectMatrices <- lmpEffectMatrices(resLmpModelMatrix)
resLmpPcaEffects <- lmpPcaEffects(resLmpEffectMatrices, method = "ASCA-E")

lmpContributions(resLmpPcaEffects)

Computes the effect matrices

Description

Estimates the model by OLS based on the outcomes and model matrices provided in the outputs of lmpModelMatrix function and calculates the estimated effect matrices $\hat{\mathbf{M}}_0, \hat{\mathbf{M}}_1, ...\hat{\mathbf{M}}_F$ , ... and residual matrix $\hat{\mathbf{E}}$ . It calculates also the type III percentage of variance explained by each effect.

Usage

lmpEffectMatrices(resLmpModelMatrix, SS = TRUE, contrastList = NA)
lmpEffectMatrices(resLmpModelMatrix, SS = TRUE, contrastList = NA)

Arguments

`resLmpModelMatrix`	A list of 5 elements from `lmpModelMatrix`.
`SS`	Logical. If `FALSE`, won't compute the percentage of variance for each effect.
`contrastList`	A list of contrasts for each parameter. If `NA`, the function creates automatically the list by default.

Value

A list with the following elements:

lmpDataList: The initial object: a list with outcomes, design and formula.
modelMatrix: A nxp model matrix specifically encoded for the ASCA-GLM method.
modelMatrixByEffect: A list of F+1 model matrices for each effect.
effectsNamesUnique: A character vector with the F+1 names of the model effects, each repeated once.
effectsNamesAll: A character vector with the p names of the model effects ordered and repeated as the column names of the model matrix.
effectMatrices: A list of F+1 effect matrices for each model effect.
predictedvalues: The nxm matrix of predicted outcome values.
residuals: The nxm matrix of model residuals.
parameters: The pxm matrix of the estimated parameters.
type3SS: A vector with the type III sum of squares for each model effect (If SS = TRUE).
variationPercentages: A vector with the percentage of variance for each model effect (If SS = TRUE).
varPercentagesPlot: A ggplot bar plot of the contributions of each model effect to the total variance (If SS = TRUE).

References

Thiel M.,Feraud B. and Govaerts B. (2017) ASCA+ and APCA+: Extensions of ASCA and APCA in the analysis of unbalanced multifactorial designs, Journal of Chemometrics

Examples

data("UCH")
resLmpModelMatrix <- lmpModelMatrix(UCH)
reslmpEffectMatrices <- lmpEffectMatrices(resLmpModelMatrix)
reslmpEffectMatrices$varPercentagesPlot

data("UCH")
resLmpModelMatrix <- lmpModelMatrix(UCH)
reslmpEffectMatrices <- lmpEffectMatrices(resLmpModelMatrix)
reslmpEffectMatrices$varPercentagesPlot

Effect plot

Description

Plots the ASCA scores by effect levels for a given model effect and for one PC at a time. This graph is especially appealing to interpret interactions or combined effects. It is a wrapper of plotMeans.

Usage

lmpEffectPlot(
  resASCA,
  effectName,
  axes = 1,
  x,
  z = NULL,
  w = NULL,
  hline = 0,
  ...
)
lmpEffectPlot(
  resASCA,
  effectName,
  axes = 1,
  x,
  z = NULL,
  w = NULL,
  hline = 0,
  ...
)

Arguments

`resASCA`	A list corresponding to the ASCA output value of `lmpPcaEffects`.
`effectName`	Name of the effect to be used to plot the scores.
`axes`	A numerical vector with the Principal Components axes to be drawn.
`x`	A character string giving the `design` factor whose levels will form the x axis.
`z`	A character string giving the `design` factor whose levels will form the traces.
`w`	A character string giving the `design` factor whose levels will be used for the facet.
`hline`	If not `NULL`, draws one or several horizontal line(s) at values given in `hline`.
`...`	Additional arguments to be passed to `plotMeans`.

Details

lmpEffectPlot is a wrapper of plotMeans.

Value

An effect plot (ggplot).

Examples


data("UCH")
resLmpModelMatrix <- lmpModelMatrix(UCH)
resLmpEffectMatrices <- lmpEffectMatrices(resLmpModelMatrix)
resASCA <- lmpPcaEffects(
  resLmpEffectMatrices = resLmpEffectMatrices,
  method = "ASCA", combineEffects = list(c("Hippurate", "Time", "Hippurate:Time"))
)

# Effect plot for an interaction effect
lmpEffectPlot(resASCA, effectName = "Hippurate:Time", x = "Hippurate", z = "Time")
# Effect plot for a combined effect
lmpEffectPlot(resASCA, effectName = "Hippurate+Time+Hippurate:Time", x = "Hippurate", z = "Time")

data("UCH")
resLmpModelMatrix <- lmpModelMatrix(UCH)
resLmpEffectMatrices <- lmpEffectMatrices(resLmpModelMatrix)
resASCA <- lmpPcaEffects(
  resLmpEffectMatrices = resLmpEffectMatrices,
  method = "ASCA", combineEffects = list(c("Hippurate", "Time", "Hippurate:Time"))
)

# Effect plot for an interaction effect
lmpEffectPlot(resASCA, effectName = "Hippurate:Time", x = "Hippurate", z = "Time")
# Effect plot for a combined effect
lmpEffectPlot(resASCA, effectName = "Hippurate+Time+Hippurate:Time", x = "Hippurate", z = "Time")

Loadings represented on a line plot.

Description

Plots the loading vectors for each effect matrix from the lmpPcaEffects outputs with line plots. This is a wrapper of plotLine.

Usage

lmpLoading1dPlot(resLmpPcaEffects, effectNames = NULL, axes = c(1, 2), ...)
lmpLoading1dPlot(resLmpPcaEffects, effectNames = NULL, axes = c(1, 2), ...)

Arguments

`resLmpPcaEffects`	A list corresponding to the output value of `lmpPcaEffects`.
`effectNames`	Names of the effects to be plotted. if `NULL`, all the effects are plotted.
`axes`	A numerical vector with the Principal Components axes to be drawn.
`...`	Additional arguments to be passed to `plotLine` such as `xaxis_type`, `type` or `ang_x_axis`.

Details

lmpLoading1dPlot is a wrapper of plotLine. See ?plotLine for more information on the additional arguments.

Value

A list of ggplot objects representing the loading plots.

Examples


# Example of "spectral" type loadings (line and numerical x-axis)
data("UCH")
resLmpModelMatrix <- lmpModelMatrix(UCH)
resLmpEffectMatrices <- lmpEffectMatrices(resLmpModelMatrix)
resASCA <- lmpPcaEffects(resLmpEffectMatrices,
  combineEffects = list(c("Time", "Hippurate:Time"))
)
lmpLoading1dPlot(resASCA)
lmpLoading1dPlot(resASCA, effectNames = c("Hippurate", "Citrate"))

# Example of "segment" and discrete type loadings (segments and character x-axis)
data("trout")
resLmpModelMatrix <- lmpModelMatrix(trout)
resLmpEffectMatrices <- lmpEffectMatrices(resLmpModelMatrix)
resASCA <- lmpPcaEffects(resLmpEffectMatrices)
lmpLoading1dPlot(resASCA,
  effectNames = "Day",
  xaxis_type = "character", type = "s", ang_x_axis = 90
)
# Example of "spectral" type loadings (line and numerical x-axis)
data("UCH")
resLmpModelMatrix <- lmpModelMatrix(UCH)
resLmpEffectMatrices <- lmpEffectMatrices(resLmpModelMatrix)
resASCA <- lmpPcaEffects(resLmpEffectMatrices,
  combineEffects = list(c("Time", "Hippurate:Time"))
)
lmpLoading1dPlot(resASCA)
lmpLoading1dPlot(resASCA, effectNames = c("Hippurate", "Citrate"))

# Example of "segment" and discrete type loadings (segments and character x-axis)
data("trout")
resLmpModelMatrix <- lmpModelMatrix(trout)
resLmpEffectMatrices <- lmpEffectMatrices(resLmpModelMatrix)
resASCA <- lmpPcaEffects(resLmpEffectMatrices)
lmpLoading1dPlot(resASCA,
  effectNames = "Day",
  xaxis_type = "character", type = "s", ang_x_axis = 90
)

Loading plots on a 2D scatter plot

Description

Draws a 2D loading plot of each effect matrix provided in lmpPcaEffects outputs. As a wrapper of the plotScatter function, it allows the visualization of effect loading matrices for two components at a time with all options available in plotScatter.

Usage

lmpLoading2dPlot(
  resLmpPcaEffects,
  effectNames = NULL,
  axes = c(1, 2),
  addRownames = FALSE,
  pl_n = 10,
  metadata = NULL,
  drawOrigin = TRUE,
  ...
)
lmpLoading2dPlot(
  resLmpPcaEffects,
  effectNames = NULL,
  axes = c(1, 2),
  addRownames = FALSE,
  pl_n = 10,
  metadata = NULL,
  drawOrigin = TRUE,
  ...
)

Arguments

`resLmpPcaEffects`	A list corresponding to the output value of `lmpPcaEffects`.
`effectNames`	Names of the effects to be plotted. If `NULL`, all the effects are plotted.
`axes`	A numerical vector with the 2 Principal Components axes to be drawn.
`addRownames`	Boolean indicating if the labels should be plotted. By default, uses the column names of the outcome matrix but it can be manually specified with the `points_labs` argument from `plotScatter`.
`pl_n`	The number of labels that should be plotted, based on the distance measure $d$ (see Details).
`metadata`	A nxk "free encoded" data.frame corresponding to `design` in `plotScatter`.
`drawOrigin`	if `TRUE`, draws horizontal and vertical intercepts at (0,0) based on the `plotScatter` function.
`...`	Additional arguments to be passed to `plotScatter`.

Details

lmpLoading2dPlot is a wrapper of plotScatter. See ?plotScatter for more information on the additional arguments.

The distance measure $d$ that is used to rank the variables is based on the following formula:

$d = \sqrt(P_{ab}^2*\lambda_{ab}^2)$

where $a$ and $b$ are two selected Principal Components, $P_{ab}$ represents their loadings and $\lambda_{ab}$ their singular values.

Value

A list of loading plots (ggplot).

Examples


data("UCH")
resLmpModelMatrix <- lmpModelMatrix(UCH)
resLmpEffectMatrices <- lmpEffectMatrices(resLmpModelMatrix)
resASCA <- lmpPcaEffects(resLmpEffectMatrices)

lmpLoading2dPlot(resASCA, effectNames = "Hippurate")

# adding color, shape and labels to points
id_hip <- c(seq(126, 156), seq(362, 375))
peaks <- rep("other", ncol(UCH$outcomes))
peaks[id_hip] <- "hip"
metadata <- data.frame(peaks)

lmpLoading2dPlot(resASCA,
  effectNames = "Hippurate",
  metadata = metadata, addRownames = TRUE, color = "peaks",
  shape = "peaks"
)

# changing max.overlaps of ggrepel
options(ggrepel.max.overlaps = 30)
lmpLoading2dPlot(resASCA,
  effectNames = "Hippurate",
  metadata = metadata, addRownames = TRUE, color = "peaks",
  shape = "peaks", pl_n = 20
)

data("UCH")
resLmpModelMatrix <- lmpModelMatrix(UCH)
resLmpEffectMatrices <- lmpEffectMatrices(resLmpModelMatrix)
resASCA <- lmpPcaEffects(resLmpEffectMatrices)

lmpLoading2dPlot(resASCA, effectNames = "Hippurate")

# adding color, shape and labels to points
id_hip <- c(seq(126, 156), seq(362, 375))
peaks <- rep("other", ncol(UCH$outcomes))
peaks[id_hip] <- "hip"
metadata <- data.frame(peaks)

lmpLoading2dPlot(resASCA,
  effectNames = "Hippurate",
  metadata = metadata, addRownames = TRUE, color = "peaks",
  shape = "peaks"
)

# changing max.overlaps of ggrepel
options(ggrepel.max.overlaps = 30)
lmpLoading2dPlot(resASCA,
  effectNames = "Hippurate",
  metadata = metadata, addRownames = TRUE, color = "peaks",
  shape = "peaks", pl_n = 20
)

Creates the model matrix `X`

Description

Creates the model matrix X from the design matrix and the model formula.

Usage

lmpModelMatrix(lmpDataList)
lmpModelMatrix(lmpDataList)

Arguments

lmpDataList

A list containing the outcomes, the experimental design and the formula.

Details

In typical ASCA-GLM (ASCA+) analysis, the effects of the GLM model must first be used to transform the design matrix to a model matrix where the design factors encoded usign sum coding commonly used in industrial experimental design. Suppose the design matrix is nxk with n observations and k factors. After the transformation, the model matrix will be of size nxp. For a fator with a levels, the sum coding creates a-1 columns in the model matrix with 0 and 1 for the a-1 first levels and -1 for the last one. p is the total number parameter for each response (outcome) in the ASCA model. More information is available in the article (Thiel et al, 2017) Note that at the moment, only factors can be used as explanatory variables.

Value

A list with the 5 following named elements :

lmpDataList: The initial object: a list with outcomes, design and formula, as outputted by data2LmpDataList.
modelMatrix: A nxK model matrix specifically encoded for the ASCA-GLM method.
modelMatrixByEffect: A list of p model matrices for each model effect.
effectsNamesUnique: A character vector with the p names of the model effects, each repeated once.
effectsNamesAll: A character vector with the K names of the model effects ordered and repeated as the column names of the model matrix.

References

Thiel M.,Feraud B. and Govaerts B. (2017) ASCA+ and APCA+: Extensions of ASCA and APCA in the analysis of unbalanced multifactorial designs, Journal of Chemometrics

Examples


data("UCH")
resLmpModelMatrix <- lmpModelMatrix(UCH)

head(resLmpModelMatrix$modelMatrix)

data("UCH")
resLmpModelMatrix <- lmpModelMatrix(UCH)

head(resLmpModelMatrix$modelMatrix)

PCA on the effect matrices

Description

Performs a PCA on each of the effect matrices from the outputs of lmpEffectMatrices. It has an option to choose the method applied: ASCA, APCA or ASCA-E. Combined effects (i.e. linear combinations of original effect matrices) can also be created and decomposed by PCA.

Usage

lmpPcaEffects(
  resLmpEffectMatrices,
  method = c("ASCA", "APCA", "ASCA-E"),
  combineEffects = NULL,
  verbose = FALSE
)
lmpPcaEffects(
  resLmpEffectMatrices,
  method = c("ASCA", "APCA", "ASCA-E"),
  combineEffects = NULL,
  verbose = FALSE
)

Arguments

`resLmpEffectMatrices`	A resLmpEffectMatrices list resulting of `lmpEffectMatrices`.
`method`	The method used to compute the PCA. One of `c("ASCA","APCA","ASCA-E")`.
`combineEffects`	If not `NULL`, a list of vectors containing the names of the effects to be combined.
`verbose`	If `TRUE`, will display a message with the duration of execution.

Details

The function allows 3 different methods :

ASCA: PCA is applied directly on each pure effect matrix $\hat{\mathbf{M}}_f, f=1...F$ .
ASCA-E: PCA is applied on each pure effect matrix but then the augmented effect matrix is projected in the space of the ASCA components.
APCA: PCA is applied on each augmented effect matrix : $\hat{\mathbf{M}}_f+\hat{\mathbf{E}}$ .

Value

A list with first,the PCA results from pcaBySvd for each effect matrix. Those results contain :

scores: Scores from the PCA for each principal component.
loadings: Loadings from the PCA for each principal component.
eigval: Eigenvalues of each principal component.
singvar: Singular values of each principal component.
var: Explained variances of each principal component.
cumvar: Cumulated explained variances of each principal component.
original.dataset: Original dataset.

There are also others outputs :

lmpDataList: The initial object: a list of outcomes, design and formula.
effectsNamesUnique: A character vector with the F+1 names of the model terms, each repeated once.
method: The dimension reduction method used: c("ASCA","APCA","ASCA-E").
type3SS: A vector with the type III SS for each model term.
variationPercentages: A vector with the percentage of variance explained by each model term.

References

Thiel M.,Feraud B. and Govaerts B. (2017) ASCA+ and APCA+: Extensions of ASCA and APCA in the analysis of unbalanced multifactorial designs. Journal of Chemometrics. 31:e2895. https://doi.org/10.1002/cem.2895

Examples

data("UCH")
resLmpModelMatrix <- lmpModelMatrix(UCH)
resLmpEffectMatrices <- lmpEffectMatrices(resLmpModelMatrix)
resLmpPcaEffects <- lmpPcaEffects(resLmpEffectMatrices, method = "ASCA-E")

data("UCH")
resLmpModelMatrix <- lmpModelMatrix(UCH)
resLmpEffectMatrices <- lmpEffectMatrices(resLmpModelMatrix)
resLmpPcaEffects <- lmpPcaEffects(resLmpEffectMatrices, method = "ASCA-E")

Score plots of effect matrices

Description

Draws the score plots of each (augmented) effect matrix provided in lmpPcaEffects. As a wrapper of the plotScatter function, it allows to visualize the scores of the effect matrices for two components at a time with all the available options in plotScatter.

Usage

lmpScorePlot(resLmpPcaEffects, effectNames = NULL, axes = c(1, 2), ...)
lmpScorePlot(resLmpPcaEffects, effectNames = NULL, axes = c(1, 2), ...)

Arguments

`resLmpPcaEffects`	A list corresponding to the output value of `lmpPcaEffects`.
`effectNames`	Names of the effects to be plotted. If `NULL`, all the effects are plotted.
`axes`	A numerical vector with the 2 Principal Components axes to be drawn.
`...`	Additional arguments to be passed to `plotScatter`.

Details

lmpScorePlot is a wrapper of plotScatter.

Value

A list of score plots (ggplot).

Examples


data("UCH")
resLmpModelMatrix <- lmpModelMatrix(UCH)
resLmpEffectMatrices <- lmpEffectMatrices(resLmpModelMatrix)

# PCA decomposition of effect matrices (ASCA)
resASCA <- lmpPcaEffects(resLmpEffectMatrices)
# Score plot of Hippurate effect matrix
lmpScorePlot(resASCA,
  effectNames = "Hippurate",
  color = "Hippurate", shape = "Hippurate"
)

# PCA decomposition of augmented effect matrices (APCA)
resASCA <- lmpPcaEffects(resLmpEffectMatrices, method = "APCA")
# Score plot of Hippurate augmented effect matrix
lmpScorePlot(resASCA,
  effectNames = "Hippurate",
  color = "Hippurate", shape = "Hippurate", drawShapes = "ellipse"
)
data("UCH")
resLmpModelMatrix <- lmpModelMatrix(UCH)
resLmpEffectMatrices <- lmpEffectMatrices(resLmpModelMatrix)

# PCA decomposition of effect matrices (ASCA)
resASCA <- lmpPcaEffects(resLmpEffectMatrices)
# Score plot of Hippurate effect matrix
lmpScorePlot(resASCA,
  effectNames = "Hippurate",
  color = "Hippurate", shape = "Hippurate"
)

# PCA decomposition of augmented effect matrices (APCA)
resASCA <- lmpPcaEffects(resLmpEffectMatrices, method = "APCA")
# Score plot of Hippurate augmented effect matrix
lmpScorePlot(resASCA,
  effectNames = "Hippurate",
  color = "Hippurate", shape = "Hippurate", drawShapes = "ellipse"
)

Scatterplot matrix of effect matrices scores

Description

Plots the scores of all model effects simultaneously in a scatterplot matrix. By default, the first PC only is kept for each model effect and, as a wrapper of plotScatterM, the choice of symbols and colors to distinguish factor levels allows an enriched visualization of the factors’ effect on the responses.

Usage

lmpScoreScatterPlotM(
  resLmpPcaEffects,
  effectNames = NULL,
  PCdim = NULL,
  modelAbbrev = FALSE,
  ...
)
lmpScoreScatterPlotM(
  resLmpPcaEffects,
  effectNames = NULL,
  PCdim = NULL,
  modelAbbrev = FALSE,
  ...
)

Arguments

`resLmpPcaEffects`	A list corresponding to the output value of `lmpPcaEffects`.
`effectNames`	A character vector with the name of the effects to plot.
`PCdim`	A numeric vector with the same length than effectNames and indicating the number of component to plot.
`modelAbbrev`	A logical whether to abbreviate the interaction terms or not.
`...`	Additional arguments to be passed to `plotScatterM`.

Details

lmpScoreScatterPlotM is a wrapper of plotScatterM.

Value

A matrix of graphs

Examples


data("UCH")
resLmpModelMatrix <- lmpModelMatrix(UCH)
ResLmpEffectMatrices <- lmpEffectMatrices(resLmpModelMatrix)
resLmpPcaEffects <- lmpPcaEffects(ResLmpEffectMatrices, method = "ASCA-E")

lmpScoreScatterPlotM(resLmpPcaEffects,
  varname.colorup = "Citrate",
  varname.pchup = "Hippurate",
  varname.pchdown = "Day",
  varname.colordown = "Time"
)

# advanced setting
lmpScoreScatterPlotM(resLmpPcaEffects,
  modelAbbrev = FALSE,
  effectNames = c("Citrate", "Hippurate", "Hippurate:Citrate"),
  PCdim = c(2, 2, 2),
  varname.colorup = "Citrate",
  vec.colorup = c("red", "blue", "green"),
  varname.pchup = "Hippurate",
  vec.pchup = c(1, 2, 3),
  varname.pchdown = "Day",
  vec.pchdown = c(4, 5),
  varname.colordown = "Time",
  vec.colordown = c("brown", "grey")
)

data("UCH")
resLmpModelMatrix <- lmpModelMatrix(UCH)
ResLmpEffectMatrices <- lmpEffectMatrices(resLmpModelMatrix)
resLmpPcaEffects <- lmpPcaEffects(ResLmpEffectMatrices, method = "ASCA-E")

lmpScoreScatterPlotM(resLmpPcaEffects,
  varname.colorup = "Citrate",
  varname.pchup = "Hippurate",
  varname.pchdown = "Day",
  varname.colordown = "Time"
)

# advanced setting
lmpScoreScatterPlotM(resLmpPcaEffects,
  modelAbbrev = FALSE,
  effectNames = c("Citrate", "Hippurate", "Hippurate:Citrate"),
  PCdim = c(2, 2, 2),
  varname.colorup = "Citrate",
  vec.colorup = c("red", "blue", "green"),
  varname.pchup = "Hippurate",
  vec.pchup = c(1, 2, 3),
  varname.pchdown = "Day",
  vec.pchdown = c(4, 5),
  varname.colordown = "Time",
  vec.colordown = c("brown", "grey")
)

Scree Plot

Description

Provides a barplot of the percentage of variance associated to the PCs of the effect matrices ordered by importance based on the outputs of lmpContributions.

Usage

lmpScreePlot(
  resLmpContributions,
  effectNames = NULL,
  nPC = 5,
  theme = theme_bw()
)
lmpScreePlot(
  resLmpContributions,
  effectNames = NULL,
  nPC = 5,
  theme = theme_bw()
)

Arguments

`resLmpContributions`	A resLmpContributions list from the function `lmpContributions`.
`effectNames`	Names of the effects to be plotted. if `NULL`, all the effects are plotted.
`nPC`	An integer with the number of components to plot.
`theme`	`ggplot` theme

Value

A scree plot (ggplot).

Examples


data("UCH")
resLmpModelMatrix <- lmpModelMatrix(UCH)
resLmpEffectMatrices <- lmpEffectMatrices(resLmpModelMatrix)
resASCAE <- lmpPcaEffects(resLmpEffectMatrices, method = "ASCA-E")
resLmpContributions <- lmpContributions(resASCAE)
lmpScreePlot(resLmpContributions, effectNames = "Hippurate:Citrate", nPC = 4)

data("UCH")
resLmpModelMatrix <- lmpModelMatrix(UCH)
resLmpEffectMatrices <- lmpEffectMatrices(resLmpModelMatrix)
resASCAE <- lmpPcaEffects(resLmpEffectMatrices, method = "ASCA-E")
resLmpContributions <- lmpContributions(resASCAE)
lmpScreePlot(resLmpContributions, effectNames = "Hippurate:Citrate", nPC = 4)

Singular Value Decomposition for PCA analysis

Description

Operates a Principal Component Analysis on the Y outcome/response matrix by a singular Value Decomposition (the pre-processing involves the mean-centering of Y). Outputs are represented with the functions pcaScorePlot, pcaLoading1dPlot, pcaLoading2dPlot and pcaScreePlot.

Usage

pcaBySvd(Y = NULL, lmpDataList = NULL, nPC = min(dim(Y)))
pcaBySvd(Y = NULL, lmpDataList = NULL, nPC = min(dim(Y)))

Arguments

`Y`	The $n \times m$ matrix with $n$ observations and $m$ (response) variables.
`lmpDataList`	A list with outcomes, design and formula, as outputted by `data2LmpDataList`.
`nPC`	Number of Principal Components to extract.

Value

A list containing the following elements:

scores: Scores
loadings: Loadings
eigval: Eigenvalues
singvar: Singular values
var: Explained variances
cumvar: Cumulated explained variances
original.dataset: Original dataset
design: Design of the study

Examples


data("UCH")

PCA.res1 <- pcaBySvd(Y = UCH$outcomes)

PCA.res2 <- pcaBySvd(lmpDataList = UCH)

identical(PCA.res1, PCA.res2)
data("UCH")

PCA.res1 <- pcaBySvd(Y = UCH$outcomes)

PCA.res2 <- pcaBySvd(lmpDataList = UCH)

identical(PCA.res1, PCA.res2)

Loadings represented on a line plot.

Description

Plots the loading vectors from pcaBySvd output with different available line types.

Usage

pcaLoading1dPlot(resPcaBySvd, axes = c(1, 2), title = "PCA loading plot", ...)
pcaLoading1dPlot(resPcaBySvd, axes = c(1, 2), title = "PCA loading plot", ...)

Arguments

`resPcaBySvd`	A list corresponding to the output value of `pcaBySvd`.
`axes`	A numerical vector of length 2 with the Principal Components axes to be drawn.
`title`	Plot title.
`...`	Additional arguments to be passed to `plotLine`.

Details

pcaLoading1dPlot is a wrapper of plotLine. See ?plotLine for more information on the additional arguments.

Value

A ggplot2 object with the PCA loading plot.

Examples


data("UCH")
ResPCA <- pcaBySvd(UCH$outcomes)

pcaLoading1dPlot(
  resPcaBySvd = ResPCA, axes = c(1, 2),
  title = "PCA loading plot UCH", xlab = "ppm", ylab = "Values"
)
data("UCH")
ResPCA <- pcaBySvd(UCH$outcomes)

pcaLoading1dPlot(
  resPcaBySvd = ResPCA, axes = c(1, 2),
  title = "PCA loading plot UCH", xlab = "ppm", ylab = "Values"
)

Loading plots on a 2D scatter plot

Description

Produces 2D loading plots from pcaBySvd with the same graphical options as plotScatter as this is a wrapper of this function.

Usage

pcaLoading2dPlot(
  resPcaBySvd,
  axes = c(1, 2),
  title = "PCA loading plot",
  addRownames = FALSE,
  pl_n = 10,
  metadata = NULL,
  drawOrigin = TRUE,
  ...
)
pcaLoading2dPlot(
  resPcaBySvd,
  axes = c(1, 2),
  title = "PCA loading plot",
  addRownames = FALSE,
  pl_n = 10,
  metadata = NULL,
  drawOrigin = TRUE,
  ...
)

Arguments

`resPcaBySvd`	A list corresponding to the output value of `pcaBySvd`.
`axes`	A numerical vector of length 2 with the Principal Components axes to be drawn.
`title`	Plot title.
`addRownames`	Boolean indicating if the labels should be plotted. By default, uses the row names of the loadings matrix but it can be manually specified with the `points_labs` argument from `plotScatter`.
`pl_n`	The number of labels that should be plotted, based on a distance measure (see Details).
`metadata`	A $n \times k$ "freely encoded" data.frame corresponding to the `design` argument in `plotScatter`.
`drawOrigin`	if `TRUE`, draws horizontal and vertical intercepts at (0,0) based on the `plotScatter` function.
`...`	Additional arguments to be passed to `plotScatter`.

Details

pcaLoading2dPlot is a wrapper of plotScatter. See ?plotScatter for more information on the additional arguments.

The distance measure $d$ that is used to rank the variables is based on the following formula:

$d = \sqrt(P_{ab}^2*\lambda_{ab}^2)$

where $a$ and $b$ are two selected Principal Components, $P_{ab}$ represents their loadings and $\lambda_{ab}$ their singular values.

Value

A ggplot2 object with the PCA loading plot.

Examples


data("UCH")
ResPCA <- pcaBySvd(UCH$outcomes)

pcaLoading2dPlot(
  resPcaBySvd = ResPCA, axes = c(1, 2),
  title = "PCA loading plot UCH"
)

# adding color,  shape and labels to points
id_cit <- seq(446, 459)
id_hip <- c(seq(126, 156), seq(362, 375))
peaks <- rep("other", ncol(UCH$outcomes))
peaks[id_hip] <- "hip"
peaks[id_cit] <- "cit"
metadata <- data.frame(peaks)

pcaLoading2dPlot(
  resPcaBySvd = ResPCA, axes = c(1, 2),
  title = "PCA loading plot UCH", metadata = metadata,
  color = "peaks", shape = "peaks", addRownames = TRUE
)

# changing max.overlaps of ggrepel
options(ggrepel.max.overlaps = 30)
pcaLoading2dPlot(
  resPcaBySvd = ResPCA, axes = c(1, 2),
  title = "PCA loading plot UCH", metadata = metadata,
  color = "peaks", shape = "peaks", addRownames = TRUE,
  pl_n = 35
)

data("UCH")
ResPCA <- pcaBySvd(UCH$outcomes)

pcaLoading2dPlot(
  resPcaBySvd = ResPCA, axes = c(1, 2),
  title = "PCA loading plot UCH"
)

# adding color,  shape and labels to points
id_cit <- seq(446, 459)
id_hip <- c(seq(126, 156), seq(362, 375))
peaks <- rep("other", ncol(UCH$outcomes))
peaks[id_hip] <- "hip"
peaks[id_cit] <- "cit"
metadata <- data.frame(peaks)

pcaLoading2dPlot(
  resPcaBySvd = ResPCA, axes = c(1, 2),
  title = "PCA loading plot UCH", metadata = metadata,
  color = "peaks", shape = "peaks", addRownames = TRUE
)

# changing max.overlaps of ggrepel
options(ggrepel.max.overlaps = 30)
pcaLoading2dPlot(
  resPcaBySvd = ResPCA, axes = c(1, 2),
  title = "PCA loading plot UCH", metadata = metadata,
  color = "peaks", shape = "peaks", addRownames = TRUE,
  pl_n = 35
)

Score plots

Description

Produces score plots from pcaBySvd output with the same graphical options as plotScatter as this is a wrapper of this function..

Usage

pcaScorePlot(
  resPcaBySvd,
  design = NULL,
  axes = c(1, 2),
  title = "PCA score plot",
  points_labs_rn = FALSE,
  ...
)
pcaScorePlot(
  resPcaBySvd,
  design = NULL,
  axes = c(1, 2),
  title = "PCA score plot",
  points_labs_rn = FALSE,
  ...
)

Arguments

`resPcaBySvd`	A list corresponding to the output value of `pcaBySvd`.
`design`	A $n \times k$ "freely encoded" experimental design data.frame.
`axes`	A numerical vector of length 2 with the Principal Components axes to be drawn.
`title`	Plot title.
`points_labs_rn`	Boolean indicating if the rownames of the scores matrix should be plotted.
`...`	Additional arguments to be passed to `plotScatter`.

Details

pcaScorePlot is a wrapper of plotScatter. See ?plotScatter for more information on the additional arguments.

Value

A ggplot2 PCA score plot.

Examples


data("UCH")

# design is explicitly defined
ResPCA <- pcaBySvd(Y = UCH$outcomes)

pcaScorePlot(
  resPcaBySvd = ResPCA, axes = c(1, 2),
  title = "PCA score plot UCH", design = UCH$design,
  color = "Hippurate", shape = "Citrate"
)

# design is recovered from lmpDataList through pcaBySvd()
ResPCA <- pcaBySvd(lmpDataList = UCH)

pcaScorePlot(
  resPcaBySvd = ResPCA, axes = c(1, 2),
  title = "PCA score plot UCH",
  color = "Hippurate", shape = "Citrate"
)

data("UCH")

# design is explicitly defined
ResPCA <- pcaBySvd(Y = UCH$outcomes)

pcaScorePlot(
  resPcaBySvd = ResPCA, axes = c(1, 2),
  title = "PCA score plot UCH", design = UCH$design,
  color = "Hippurate", shape = "Citrate"
)

# design is recovered from lmpDataList through pcaBySvd()
ResPCA <- pcaBySvd(lmpDataList = UCH)

pcaScorePlot(
  resPcaBySvd = ResPCA, axes = c(1, 2),
  title = "PCA score plot UCH",
  color = "Hippurate", shape = "Citrate"
)

Scree Plot

Description

Returns a bar plot of the percentage of variance explained by each Principal Component calculated by pcaBySvd.

Usage

pcaScreePlot(
  resPcaBySvd,
  nPC = 5,
  title = "PCA scree plot",
  theme = theme_bw()
)
pcaScreePlot(
  resPcaBySvd,
  nPC = 5,
  title = "PCA scree plot",
  theme = theme_bw()
)

Arguments

`resPcaBySvd`	A list corresponding to the output value of `pcaBySvd`.
`nPC`	An integer with the number of Principal Components to plot.
`title`	Plot title.
`theme`	`ggplot2` theme, see `?ggtheme` for more info.

Value

A ggplot2 PCA scree plot

Examples


data("UCH")
resPCA <- pcaBySvd(UCH$outcomes)
pcaScreePlot(resPCA, nPC = 4)

data("UCH")
resPCA <- pcaBySvd(UCH$outcomes)
pcaScreePlot(resPCA, nPC = 4)

Plot of the design matrix

Description

Provides a graphical representation of the experimental design. It allows to visualize factors levels and check the design balance.

Usage

plotDesign(
  design = NULL,
  lmpDataList = NULL,
  x = NULL,
  y = NULL,
  rows = NULL,
  cols = NULL,
  title = "Plot of the design",
  theme = theme_bw()
)
plotDesign(
  design = NULL,
  lmpDataList = NULL,
  x = NULL,
  y = NULL,
  rows = NULL,
  cols = NULL,
  title = "Plot of the design",
  theme = theme_bw()
)

Arguments

`design`	A data.frame representing the $n \times k$ "freely encoded" experimental design. Can be `NULL` if `lmpDataList` is defined.
`lmpDataList`	If not `NULL`, a list with outcomes, design and formula, as outputted by `data2LmpDataList`.
`x`	By default, the first column of `design` ; otherwise if not `NULL`, a character string giving the column name of `design` to be used for the x-axis. The column needs to be a factor.
`y`	By default, the second column of `design` if present ; otherwise if not `NULL`, a character string giving the column name of `design` to be used for the y-axis.
`rows`	By default, the fourth column of `design` if present ; otherwise if not `NULL`, a character vector with one or several column name(s) of `design` to be used for faceting along the rows. The column needs to be a factor.
`cols`	By default, the third column of `design` if present ; otherwise if not `NULL`, a character vector with one or several column name(s) of `design` to be used for faceting along the columns. The column needs to be a factor.
`title`	Plot title.
`theme`	The `ggplot2` theme, see `?ggtheme` for more info.

Details

Either design or lmpDataList need to be defined. If both are given, the priority goes to design. The default behavior (parameters x, y, cols and rows are NULL) uses the first four columns of df. If at least one of these arguments is not NULL, the function will only use the non NULL parameters to be displayed.

Value

A ggplot2 plot of the design matrix.

Examples

### trout data
data(trout)

plotDesign(design = trout$design, x = "Day", y = "Treatment")

# equivalent to:
plotDesign(lmpDataList = trout, x = "Day", y = "Treatment")

### mtcars
data(mtcars)
library(tidyverse)
df <- mtcars %>%
  dplyr::select(cyl, vs, am, gear, carb) %>%
  as.data.frame() %>%
  dplyr::mutate(across(everything(), as.factor))

# Default behavior: display the 4 first factors in the design
plotDesign(design = df)

# 2 factors
plotDesign(
  design = df, x = "cyl", y = "vs",
  cols = NULL, rows = NULL
)
# 3 factors
plotDesign(
  design = df, x = "cyl", y = "vs",
  cols = NULL, rows = c("am")
)
# 4 factors
plotDesign(
  design = df, x = "cyl", y = "vs",
  cols = c("gear"), rows = c("am")
)
# 5 factors
plotDesign(
  design = df, x = "cyl", y = "vs",
  cols = c("gear"), rows = c("am", "carb")
)

plotDesign(
  design = df, x = "cyl", y = "vs",
  cols = c("vs"), rows = c("am", "carb")
)

### UCH
data("UCH")
plotDesign(design = UCH$design, x = "Hippurate", y = "Citrate", rows = "Day")

### trout data
data(trout)

plotDesign(design = trout$design, x = "Day", y = "Treatment")

# equivalent to:
plotDesign(lmpDataList = trout, x = "Day", y = "Treatment")

### mtcars
data(mtcars)
library(tidyverse)
df <- mtcars %>%
  dplyr::select(cyl, vs, am, gear, carb) %>%
  as.data.frame() %>%
  dplyr::mutate(across(everything(), as.factor))

# Default behavior: display the 4 first factors in the design
plotDesign(design = df)

# 2 factors
plotDesign(
  design = df, x = "cyl", y = "vs",
  cols = NULL, rows = NULL
)
# 3 factors
plotDesign(
  design = df, x = "cyl", y = "vs",
  cols = NULL, rows = c("am")
)
# 4 factors
plotDesign(
  design = df, x = "cyl", y = "vs",
  cols = c("gear"), rows = c("am")
)
# 5 factors
plotDesign(
  design = df, x = "cyl", y = "vs",
  cols = c("gear"), rows = c("am", "carb")
)

plotDesign(
  design = df, x = "cyl", y = "vs",
  cols = c("vs"), rows = c("am", "carb")
)

### UCH
data("UCH")
plotDesign(design = UCH$design, x = "Hippurate", y = "Citrate", rows = "Day")

Line plot

Description

Generates the response profile of one or more observations i.e. plots of one or more rows of the outcomes matrix on the y-axis against the $m$ response variables on the x-axis. Depending on the response type (spectra, gene expression...), point, line or segment plots can be used.

Usage

plotLine(
  Y = NULL,
  lmpDataList = NULL,
  rows = 1,
  type = c("l", "p", "s"),
  title = "Line plot",
  xlab = NULL,
  ylab = NULL,
  xaxis_type = c("numeric", "character"),
  stacked = FALSE,
  ncol = 1,
  nrow = NULL,
  facet_label = NULL,
  hline = 0,
  size = 0.5,
  color = NULL,
  shape = 1,
  theme = theme_bw(),
  ang_x_axis = NULL
)
plotLine(
  Y = NULL,
  lmpDataList = NULL,
  rows = 1,
  type = c("l", "p", "s"),
  title = "Line plot",
  xlab = NULL,
  ylab = NULL,
  xaxis_type = c("numeric", "character"),
  stacked = FALSE,
  ncol = 1,
  nrow = NULL,
  facet_label = NULL,
  hline = 0,
  size = 0.5,
  color = NULL,
  shape = 1,
  theme = theme_bw(),
  ang_x_axis = NULL
)

Arguments

`Y`	A numerical matrix containing the rows to be drawn. Can be `NULL` if `lmpDataList` is defined.
`lmpDataList`	If not `NULL`, a list with outcomes, design and formula, as outputted by `data2LmpDataList`.
`rows`	A vector with either the row name(s) of the $Y$ matrix to plot (character) or the row index position(s) (integer). Default to 1.
`type`	Type of graph to be drawn: `"p"` for point, `"l"` for line (default) or `"s"` for segment.
`title`	Plot title.
`xlab`	If not `NULL`, label for the x-axis.
`ylab`	If not `NULL`, label for the y-axis.
`xaxis_type`	The data type of the x-axis: either `"numeric"` (default) or `"character"`.
`stacked`	Logical. If `TRUE`, will draw stacked plots, otherwise will draw separate plots.
`ncol`	If `stacked` is `FALSE`, the number of columns to represent the separate plots. Default to `1`.
`nrow`	If `stacked` is `FALSE`, the number of rows to represent the separate plots.
`facet_label`	If `stacked` is `FALSE`, the labels of the separate plots.
`hline`	If not `NULL`, draws (a) horizontal line(s), by default at y intercept = 0.
`size`	Argument of length 1 giving the points size (if `type` == `"p"`) or the line size (if `type` == `"l"` or `"s"`).
`color`	If not `NULL`, argument of length 1 with possible values: `"rows"`, a color name (character) or a numeric value representing a color.
`shape`	The points shape (default = `1`) if `type` == `"p"`.
`theme`	The `ggplot2` theme (default: `theme_bw()`), see `?ggtheme` for more info.
`ang_x_axis`	If not `NULL`, rotation angle to rotate the x-axis text (based on the argument `axis.text.x` from `ggplot2::theme()`)

Details

Either Y or lmpDataList need to be defined. If both are given, the priority goes to Y.

Value

A ggplot2 line plot.

Examples


data("UCH")
plotLine(Y = UCH$outcomes)

plotLine(lmpDataList = UCH)

# separate plots
plotLine(Y = UCH$outcomes, rows = seq(1, 8), hline = NULL)
plotLine(Y = UCH$outcomes, rows = seq(1, 8), color = 2)
plotLine(Y = UCH$outcomes, rows = seq(1, 8), ncol = 2)
plotLine(
  Y = UCH$outcomes, type = "p",
  rows = seq(1, 8), ncol = 2
)

# stacked plots
library(ggplot2)
plotLine(
  Y = UCH$outcomes, rows = seq(1, 1),
  stacked = TRUE, color = "rows"
) +
  scale_color_brewer(palette = "Set1")

data("UCH")
plotLine(Y = UCH$outcomes)

plotLine(lmpDataList = UCH)

# separate plots
plotLine(Y = UCH$outcomes, rows = seq(1, 8), hline = NULL)
plotLine(Y = UCH$outcomes, rows = seq(1, 8), color = 2)
plotLine(Y = UCH$outcomes, rows = seq(1, 8), ncol = 2)
plotLine(
  Y = UCH$outcomes, type = "p",
  rows = seq(1, 8), ncol = 2
)

# stacked plots
library(ggplot2)
plotLine(
  Y = UCH$outcomes, rows = seq(1, 1),
  stacked = TRUE, color = "rows"
) +
  scale_color_brewer(palette = "Set1")

Means plot

Description

For a given response variable, draws a plot of the response means by levels of up to three categorical factors from the design. When the design is balanced, it allows to visualize main effects or interactions for the response of interest. For unbalanced designs, this plot must be used with caution.

Usage

plotMeans(
  Y = NULL,
  design = NULL,
  lmpDataList = NULL,
  cols = NULL,
  x,
  z = NULL,
  w = NULL,
  title = NULL,
  xlab = NULL,
  ylab = NULL,
  color = NULL,
  shape = NULL,
  linetype = NULL,
  size = 2,
  hline = NULL,
  theme = theme_bw()
)
plotMeans(
  Y = NULL,
  design = NULL,
  lmpDataList = NULL,
  cols = NULL,
  x,
  z = NULL,
  w = NULL,
  title = NULL,
  xlab = NULL,
  ylab = NULL,
  color = NULL,
  shape = NULL,
  linetype = NULL,
  size = 2,
  hline = NULL,
  theme = theme_bw()
)

Arguments

`Y`	A numerical matrix containing the columns to be drawn. Can be `NULL` if `lmpDataList` is defined.
`design`	A $n \times k$ "freely encoded" experimental design data.frame. Can be `NULL` if `lmpDataList` is defined.
`lmpDataList`	If not `NULL`, a list with outcomes, design and formula, as outputted by `data2LmpDataList`.
`cols`	A vector with either the column name(s) of the $Y$ matrix to plot (character) or the column index position(s) (integer).
`x`	A character string giving the `design` factor whose levels will form the x-axis.
`z`	A character string giving the `design` factor whose levels will form the traces.
`w`	A character string giving the `design` factor whose levels will be used for the facet.
`title`	Plot title.
`xlab`	If not `NULL`, the label for the x-axis.
`ylab`	If not `NULL`, the label for the y-axis.
`color`	If not `NULL`, the color of the points and the line.
`shape`	If not `NULL`, the points shape.
`linetype`	If not `NULL`, the line type.
`size`	Points size.
`hline`	If not `NULL`, draws (a) horizontal line(s).
`theme`	The `ggplot2` theme, see `?ggtheme` for more info.

Details

Either Y or lmpDataList need to be defined. If both are given, the priority goes to Y. The same rule applies for design or lmpDataList.

Value

A list of ggplot2 means plot(s).

Examples


data("UCH")
# 1 factor
plotMeans(
  Y = UCH$outcomes, design = UCH$design, cols = "4.0628702",
  x = "Hippurate", color = "blue"
)

# equivalent to:
plotMeans(
  lmpDataList = UCH, cols = "4.0628702",
  x = "Hippurate", color = "blue"
)

# 2 factors
plotMeans(
  Y = UCH$outcomes, design = UCH$design, cols = c(364, 365),
  x = "Hippurate", z = "Time", shape = c(15, 1)
)

# 3 factors
plotMeans(
  Y = UCH$outcomes, design = UCH$design, cols = c(364, 365),
  x = "Hippurate", z = "Time", w = "Citrate", linetype = c(3, 3)
)

data("UCH")
# 1 factor
plotMeans(
  Y = UCH$outcomes, design = UCH$design, cols = "4.0628702",
  x = "Hippurate", color = "blue"
)

# equivalent to:
plotMeans(
  lmpDataList = UCH, cols = "4.0628702",
  x = "Hippurate", color = "blue"
)

# 2 factors
plotMeans(
  Y = UCH$outcomes, design = UCH$design, cols = c(364, 365),
  x = "Hippurate", z = "Time", shape = c(15, 1)
)

# 3 factors
plotMeans(
  Y = UCH$outcomes, design = UCH$design, cols = c(364, 365),
  x = "Hippurate", z = "Time", w = "Citrate", linetype = c(3, 3)
)

Scatter plot

Description

Produces a plot describing the relationship between two columns of the outcomes matrix $Y$ . Colors and symbols can be chosen for the levels of the design factors. Ellipses, polygons or segments can be added to group different sets of points on the graph.

Usage

plotScatter(
  Y = NULL,
  design = NULL,
  lmpDataList = NULL,
  xy,
  color = NULL,
  shape = NULL,
  points_labs = NULL,
  title = "Scatter plot",
  xlab = NULL,
  ylab = NULL,
  size = 2,
  size_lab = 3,
  drawShapes = c("none", "ellipse", "polygon", "segment"),
  typeEl = c("norm", "t", "euclid"),
  levelEl = 0.9,
  alphaPoly = 0.4,
  theme = theme_bw(),
  drawOrigin = FALSE
)
plotScatter(
  Y = NULL,
  design = NULL,
  lmpDataList = NULL,
  xy,
  color = NULL,
  shape = NULL,
  points_labs = NULL,
  title = "Scatter plot",
  xlab = NULL,
  ylab = NULL,
  size = 2,
  size_lab = 3,
  drawShapes = c("none", "ellipse", "polygon", "segment"),
  typeEl = c("norm", "t", "euclid"),
  levelEl = 0.9,
  alphaPoly = 0.4,
  theme = theme_bw(),
  drawOrigin = FALSE
)

Arguments

`Y`	A $n \times m$ matrix with $n$ observations and $m$ variables. Can be `NULL` if `lmpDataList` is defined.
`design`	A $n \times k$ "freely encoded" experimental design data.frame. Can be `NULL` if `lmpDataList` is defined.
`lmpDataList`	If not `NULL`, a list with outcomes, design and formula, as outputted by `data2LmpDataList`.
`xy`	x- and y-axis values: a vector of length 2 with either the column name(s) of the $Y$ matrix to plot (character) or the index position(s) (integer).
`color`	If not `NULL`, a character string giving the column name of `design` to be used as color. Currently treated as a discrete variable.
`shape`	If not `NULL`, a character string giving the column name of `design` to be used as shape. Currently treated as a discrete variable.
`points_labs`	If not `NULL`, a character vector with point labels.
`title`	Plot title.
`xlab`	If not `NULL`, label for the x-axis.
`ylab`	If not `NULL`, label for the y-axis.
`size`	The points size, by default `2`.
`size_lab`	The size of points labels, by default `3`.
`drawShapes`	Multiple shapes can be drawn based on the `color`: `"none"` for no shape (default), `"ellipse"` (ellipses with `ggplot2::stat_ellipse()`), `"polygon"` (polygons with `ggplot2::geom_polygon()`) or `"segment"` (segment from the centroids with `ggplot2::geom_segment()`).
`typeEl`	The type of ellipse, either `"norm"` (multivariate normal distribution, the default), `"t"` (multivariate t-distribution) or `"euclid"` (draws a circle with the radius equal to level, representing the euclidean distance from the center).
`levelEl`	The confidence level at which to draw an ellipse, by default `0.9`.
`alphaPoly`	The degree of transparency for polygons, by default `0.4`.
`theme`	The `ggplot2` theme (default: `theme_bw()`), see `?ggtheme` for more info.
`drawOrigin`	If `TRUE`, draws horizontal and vertical intercepts at (0,0).

Details

Either Y or lmpDataList need to be defined. If both are given, the priority goes to Y. The same rule applies for design or lmpDataList.

Value

A ggplot2 scatter plot.

Examples


data("UCH")

# Without the design info
plotScatter(Y = UCH$outcomes, xy = c(453, 369))

# equivalent to:
plotScatter(lmpDataList = UCH, xy = c(453, 369))

# With color and shape
plotScatter(
  lmpDataList = UCH,
  xy = c(453, 369), color = "Hippurate",
  shape = "Citrate"
)

# equivalent to:
plotScatter(
  Y = UCH$outcomes, design = UCH$design,
  xy = c(453, 369), color = "Hippurate",
  shape = "Citrate"
)

# With color and shapes
plotScatter(
  Y = UCH$outcomes, design = UCH$design,
  xy = c(453, 369), color = "Hippurate",
  drawShapes = "ellipse"
)

plotScatter(
  Y = UCH$outcomes, design = UCH$design,
  xy = c(453, 369), color = "Hippurate",
  drawShapes = "polygon"
)

plotScatter(
  Y = UCH$outcomes, design = UCH$design,
  xy = c(453, 369), color = "Hippurate",
  drawShapes = "segment"
)

# With customized shapes
library(ggplot2)
plotScatter(
  Y = UCH$outcomes, design = UCH$design,
  xy = c(453, 369), shape = "Hippurate", size = 3
) +
  scale_discrete_identity(
    aesthetics = "shape",
    guide = "legend"
  )

plotScatter(
  Y = UCH$outcomes, design = UCH$design,
  xy = c(453, 369), shape = "Hippurate"
) +
  scale_shape_discrete(solid = FALSE)

plotScatter(
  Y = UCH$outcomes, design = UCH$design,
  xy = c(453, 369), shape = "Hippurate"
) +
  scale_shape_manual(values = c(15, 16, 17))

# With labels
plotScatter(
  Y = UCH$outcomes, design = UCH$design,
  xy = c(453, 369), points_labs = rownames(UCH$design)
)

data("UCH")

# Without the design info
plotScatter(Y = UCH$outcomes, xy = c(453, 369))

# equivalent to:
plotScatter(lmpDataList = UCH, xy = c(453, 369))

# With color and shape
plotScatter(
  lmpDataList = UCH,
  xy = c(453, 369), color = "Hippurate",
  shape = "Citrate"
)

# equivalent to:
plotScatter(
  Y = UCH$outcomes, design = UCH$design,
  xy = c(453, 369), color = "Hippurate",
  shape = "Citrate"
)

# With color and shapes
plotScatter(
  Y = UCH$outcomes, design = UCH$design,
  xy = c(453, 369), color = "Hippurate",
  drawShapes = "ellipse"
)

plotScatter(
  Y = UCH$outcomes, design = UCH$design,
  xy = c(453, 369), color = "Hippurate",
  drawShapes = "polygon"
)

plotScatter(
  Y = UCH$outcomes, design = UCH$design,
  xy = c(453, 369), color = "Hippurate",
  drawShapes = "segment"
)

# With customized shapes
library(ggplot2)
plotScatter(
  Y = UCH$outcomes, design = UCH$design,
  xy = c(453, 369), shape = "Hippurate", size = 3
) +
  scale_discrete_identity(
    aesthetics = "shape",
    guide = "legend"
  )

plotScatter(
  Y = UCH$outcomes, design = UCH$design,
  xy = c(453, 369), shape = "Hippurate"
) +
  scale_shape_discrete(solid = FALSE)

plotScatter(
  Y = UCH$outcomes, design = UCH$design,
  xy = c(453, 369), shape = "Hippurate"
) +
  scale_shape_manual(values = c(15, 16, 17))

# With labels
plotScatter(
  Y = UCH$outcomes, design = UCH$design,
  xy = c(453, 369), points_labs = rownames(UCH$design)
)

Scatter plot matrix

Description

Produces a scatter plot matrix between the selected columns of the outcomes matrix $Y$ choosing specific colors and symbols for up to four factors from the design on the upper and lower diagonals.

Usage

plotScatterM(
  Y = NULL,
  design = NULL,
  lmpDataList = NULL,
  cols,
  labelVector = NULL,
  title = "Scatterplot matrix",
  varname.colorup = NULL,
  varname.colordown = NULL,
  varname.pchup = NULL,
  varname.pchdown = NULL,
  vec.colorup = NULL,
  vec.colordown = NULL,
  vec.pchup = NULL,
  vec.pchdown = NULL
)
plotScatterM(
  Y = NULL,
  design = NULL,
  lmpDataList = NULL,
  cols,
  labelVector = NULL,
  title = "Scatterplot matrix",
  varname.colorup = NULL,
  varname.colordown = NULL,
  varname.pchup = NULL,
  varname.pchdown = NULL,
  vec.colorup = NULL,
  vec.colordown = NULL,
  vec.pchup = NULL,
  vec.pchdown = NULL
)

Arguments

`Y`	$n \times m$ matrix with $n$ observations and $m$ variables. Can be `NULL` if `lmpDataList` is defined.
`design`	A $n \times k$ "freely encoded" experimental design data.frame. Can be `NULL` if `lmpDataList` is defined.
`lmpDataList`	If not `NULL`, a list with outcomes, design and formula, as outputted by `data2LmpDataList`.
`cols`	A vector with either the column names of the $Y$ matrix to plot (character) or the column index positions.
`labelVector`	Labels to display on the diagonal. If `NULL`, the column names are deduced from `cols`.
`title`	Title of the graph.
`varname.colorup`	A character string with the name of the variable used to color the upper triangle.
`varname.colordown`	A character string with the name of the variable used to color the lower triangle.
`varname.pchup`	A character string with the name of the variable used to mark points for the upper triangle.
`varname.pchdown`	A character string with the name of the variable used to mark points for the lower triangle.
`vec.colorup`	A color vector (character or numeric) with a length equal to the number of levels of `varname.colorup`.
`vec.colordown`	A color vector (character or numeric) with a length equal to the number of levels of `varname.colordown`.
`vec.pchup`	A symbol vector (character or numeric) with a length equal to the number of levels of `varname.pchup`.
`vec.pchdown`	A symbol vector (character or numeric) with a length equal to the number of levels of `varname.pchdown`.

Details

Either Y or lmpDataList need to be defined. If both are given, the priority goes to Y. The same rule applies for design or lmpDataList.

Value

A matrix of scatter plots.

Examples


data("UCH")

# basic usage
plotScatterM(
  Y = UCH$outcomes, design = UCH$design, cols = c(1:4)
)

# equivalent to:
plotScatterM(
  lmpDataList = UCH, cols = c(1:4)
)

# with optionnal arguments
plotScatterM(
  Y = UCH$outcomes, design = UCH$design, cols = c(1:4),
  varname.colorup = "Hippurate", varname.colordown = "Citrate",
  varname.pchup = "Time", varname.pchdown = "Day",
  vec.colorup = c(2, 4, 1),
  vec.colordown = c("orange", "purple", "green"),
  vec.pchup = c(1, 2), vec.pchdown = c("a", "b")
)

data("UCH")

# basic usage
plotScatterM(
  Y = UCH$outcomes, design = UCH$design, cols = c(1:4)
)

# equivalent to:
plotScatterM(
  lmpDataList = UCH, cols = c(1:4)
)

# with optionnal arguments
plotScatterM(
  Y = UCH$outcomes, design = UCH$design, cols = c(1:4),
  varname.colorup = "Hippurate", varname.colordown = "Citrate",
  varname.pchup = "Time", varname.pchdown = "Day",
  vec.colorup = c(2, 4, 1),
  vec.colordown = c("orange", "purple", "green"),
  vec.pchup = c(1, 2), vec.pchdown = c("a", "b")
)

trout: the Rainbow trouts transcriptomic dataset

Description

This dataset comes from the study of the modulation of immunity in rainbow trout (Oncorhynchus mykiss) by exposure to cadmium (Cd) combined with polyunsaturated fatty acids (PUFAs) enriched diets [Cornet et al., 2018].

The responses were quantified by measuring the modification of the expression of 15 immune-related genes (m = 15) by RT-qPCR (reverse transcription quantita- tive polymerase chain reaction). The experiment was carried out on 72 trouts and 3 factors were considered in the experimental design:

Day: Measurements on trouts were collected on days 28, 70 and 72
Treatment: Four polyunsaturated fatty acid diets: alpha-linolenic acid (ALA), linoleic acid (LA), eicosapentaenoic acid (EPA) and docosahexaenoic acid (DHA)
Exposure: Trouts were exposed (level = 2) or not (level = 0) to high cadmium concentrations.

This gives a 3 × 4 × 2 factorial design. Each of the 24 trials corresponds to a different aquarium. Three fish were analysed (3 replicates) for each condition, giving a total of 72 observations.

In the limpca vignette, some outliers are first detected and removed from the dataset. The data of each aquarium are then transformed in log10 and mean aggregated in order to avoid the use of an aquarium random factor in the statictical model. Data are then centered and scaled by column. The ASCA+/APCA+ analysis is then applyed on the transformed data.

Usage

data("trout")data("trout")

Format

A list of 3 : the experimental design, the outcomes for every observation and the formula considered to analyze the data. Caution ! Here, the data must first be aggregated before being analyzed with ASCA+ (see details in related vignette)

outcomes: A dataset with 72 observations and 15 response variables
formula: The suggested formula to analyze the data
design: The experimental design of 72 observations and 4 explanatory variables

Details

The data must first be aggregated before being analyzed with limpca. This will remove the hierarchy in the design and allow to apply a classical fixed effect general linear model to the data. See more details in the trout vignette (print(vignette(topic = "Trout", package = "limpca"))).

Source

Cornet, V., Ouaach, A., Mandiki, S., Flamion, E., Ferain, A., Van Larebeke, M., Lemaire, B., Reyes Lopez F., Tort, L., Larondelle, Y. and Kestemont, P. (2018). Environmentally-realistic concentration of cadmium combined with polyunsaturated fatty acids enriched diets modulated non-specific immunity in rainbow trout. Aquatic Toxicology, 196, 104–116. https://doi.org/10.1016/j.aquatox.2018.01.012

Benaiche, N. (2022). Stabilisation of the R package LMWiRe – Linear Models for Wide Responses. Prom. : Govaerts, B. Master thesis. Institut de statistique, biostatistique et sciences actuarielles, UCLouvain, Belgium. http://hdl.handle.net/2078.1/thesis:33996

Examples

  data("trout")data("trout")

UCH: the Urine Citrate-Hippurate metabolomic dataset

Description

This dataset comes from a 1H NMR analysis of urine of female rats with hippuric and citric acid were added to the samples in different known concentrations.

Usage

data("UCH")data("UCH")

Format

A list of length 3: the experimental design ('design'), the outcomes for every observations ('outcomes') and the formula considered to analyze the data ('formula').

design: A data.frame with the experimental design of 34 observations and 5 explanatory variables: Hippurate: concentration of hippuric acid; Citrate: concentration of citric acid; Dilution: dilution, here all the samples are diluted with a dilution rate of 50 %; Day: for each medium, the preparation of the mixtures were performed in two series; Time: each mixture or experimental condition was repeated twice.
outcomes: A numerical matrix with 34 observations and 600 response variables
formula: A character string with the suggested formula to analyze the data

Details

The UCH vignette can be accessed with: (print(vignette(topic = "UCH", package = "limpca"))).

The database has been experimentally created in order to control the spectral locations of the biomarkers to find (i.e. Hippurate and Citrate). This property allows us to evaluate the performances of the data analysis of various statistical methods. This urine experimental database is also designed in order to explore the influence on spectra of intra-sample 1H NMR replications (Time), and inter-day 1H NMR measurements (Day).

The model formula is:

outcomes = Hippurate + Citrate + Time + Hippurate:Citrate + Time:Hippurate + Time:Citrate + Hippurate:Citrate:Time

Source

Examples

data("UCH")
str(UCH)
data("UCH")
str(UCH)

Package 'limpca'

Help Index

Converts data to a lmpDataList.

Description

Usage

Arguments

Details

Value

See Also

Examples

Linear modeling of high-dimensional designed data based on ASCA/APCA family of methods

Description

Details

References

Tests the significance of model effects by bootstrap.

Description

Usage

Arguments

Value

References

Examples

Summary of the contributions of each effect

Description

Usage

Arguments

Value

Examples

Computes the effect matrices

Description

Usage

Arguments

Value

References

Examples

Effect plot

Description

Usage

Arguments

Details

Value

Examples

Loadings represented on a line plot.

Description

Usage

Arguments

Details

Value

Examples

Loading plots on a 2D scatter plot

Description

Usage

Arguments

Details

Value

Examples

Creates the model matrix X

Description

Usage

Arguments

Details

Value

References

See Also

Examples

PCA on the effect matrices

Description

Usage

Arguments

Details

Value

References

Examples

Score plots of effect matrices

Description

Usage

Arguments

Details

Value

Examples

Scatterplot matrix of effect matrices scores

Creates the model matrix `X`