Package 'HDANOVA'

Title:	High-Dimensional Analysis of Variance
Description:	Functions and datasets to support Smilde, Marini, Westerhuis and Liland (2025, ISBN: 978-1-394-21121-0) "Analysis of Variance for High-Dimensional Data - Applications in Life, Food and Chemical Sciences". This implements and imports a collection of methods for HD-ANOVA data analysis with common interfaces, result- and plotting functions, multiple real data sets and four vignettes covering a range different applications.
Authors:	Kristian Hovde Liland [aut, cre]
Maintainer:	Kristian Hovde Liland <[email protected]>
License:	GPL (>= 2)
Version:	0.8.2
Built:	2025-01-20 21:19:40 UTC
Source:	https://github.com/khliland/hdanova

Help Index

ANOVA Principal Component Analysis - APCA

Description

APCA function for fitting ANOVA Principal Component Analysis models.

Usage

apca(formula, data, add_error = TRUE, contrasts = "contr.sum", ...)
apca(formula, data, add_error = TRUE, contrasts = "contr.sum", ...)

Arguments

`formula`	Model formula accepting a single response (block) and predictors.
`data`	The data set to analyse.
`add_error`	Add error to LS means (default = TRUE).
`contrasts`	Effect coding: "sum" (default = sum-coding), "weighted", "reference", "treatment".
`...`	Additional parameters for the asca_fit function.

Value

An object of class apca, inheriting from the general asca class. Further arguments and plots can be found in the asca documentation.

References

Harrington, P.d.B., Vieira, N.E., Espinoza, J., Nien, J.K., Romero, R., and Yergey, A.L. (2005) Analysis of variance–principal component analysis: A soft tool for proteomic discovery. Analytica chimica acta, 544 (1-2), 118–127.

Examples

data(candies)
ap <- apca(assessment ~ candy, data=candies)
scoreplot(ap)

# Numeric effects
candies$num <- eff <- 1:165
mod <- apca(assessment ~ candy + assessor + num, data=candies)
summary(mod)
scoreplot(mod, factor=3, gr.col=rgb(eff/max(eff), 1-eff/max(eff),0), pch.scores="x")
data(candies)
ap <- apca(assessment ~ candy, data=candies)
scoreplot(ap)

# Numeric effects
candies$num <- eff <- 1:165
mod <- apca(assessment ~ candy + assessor + num, data=candies)
summary(mod)
scoreplot(mod, factor=3, gr.col=rgb(eff/max(eff), 1-eff/max(eff),0), pch.scores="x")

Analysis of Variance Simultaneous Component Analysis - ASCA

Description

This is a quite general and flexible implementation of ASCA.

Usage

asca(formula, data, contrasts = "contr.sum", ...)
asca(formula, data, contrasts = "contr.sum", ...)

Arguments

`formula`	Model formula accepting a single response (block) and predictors. See Details for more information.
`data`	The data set to analyse.
`contrasts`	Effect coding: "sum" (default = sum-coding), "weighted", "reference", "treatment".
`...`	Additional arguments to `asca_fit`.

Details

ASCA is a method which decomposes a multivariate response according to one or more design variables. ANOVA is used to split variation into contributions from factors, and PCA is performed on the corresponding least squares estimates, i.e., Y = X1 B1 + X2 B2 + ... + E = T1 P1' + T2 P2' + ... + E. This version of ASCA encompasses variants of LiMM-PCA, generalized ASCA and covariates ASCA. It includes confidence ellipsoids for the balanced crossed-effect ASCA.

The formula interface is extended with the function r() to indicate random effects and comb() to indicate effects that should be combined. See Examples for use cases.

Value

An asca object containing loadings, scores, explained variances, etc. The object has associated plotting (asca_plots) and result (asca_results) functions.

References

Smilde, A., Jansen, J., Hoefsloot, H., Lamers,R., Van Der Greef, J., and Timmerman, M.(2005). ANOVA-Simultaneous Component Analysis (ASCA): A new tool for analyzing designed metabolomics data. Bioinformatics, 21(13), 3043–3048.
Liland, K.H., Smilde, A., Marini, F., and Næs,T. (2018). Confidence ellipsoids for ASCA models based on multivariate regression theory. Journal of Chemometrics, 32(e2990), 1–13.
Martin, M. and Govaerts, B. (2020). LiMM-PCA: Combining ASCA+ and linear mixed models to analyse high-dimensional designed data. Journal of Chemometrics, 34(6), e3232.

Examples

# Load candies data
data(candies)

# Basic ASCA model with two factors
mod <- asca(assessment ~ candy + assessor, data=candies)
print(mod)

# ASCA model with interaction
mod <- asca(assessment ~ candy * assessor, data=candies)
print(mod)

# Result plotting for first factor
loadingplot(mod, scatter=TRUE, labels="names")
scoreplot(mod)
# No backprojection
scoreplot(mod, projections=FALSE)
# Spider plot
scoreplot(mod, spider=TRUE, projections=FALSE)

# ASCA model with compressed response using 5 principal components
mod.pca <- asca(assessment ~ candy + assessor, data=candies, pca.in=5)

# Mixed Model ASCA, random assessor
mod.mix <- asca(assessment ~ candy + r(assessor), data=candies)
scoreplot(mod.mix)

# Mixed Model ASCA, REML estimation
mod.mix <- asca(assessment ~ candy + r(assessor), data=candies, REML=TRUE)
scoreplot(mod.mix)

# Load Caldana data
data(caldana)

# Combining effects in ASCA
mod.comb <- asca(compounds ~ time + comb(light + time:light), data=caldana)
summary(mod.comb)
timeplot(mod.comb, factor="light", time="time", comb=2)

# Permutation testing
mod.perm <- asca(assessment ~ candy * assessor, data=candies, permute=TRUE)
summary(mod.perm)

# Load candies data
data(candies)

# Basic ASCA model with two factors
mod <- asca(assessment ~ candy + assessor, data=candies)
print(mod)

# ASCA model with interaction
mod <- asca(assessment ~ candy * assessor, data=candies)
print(mod)

# Result plotting for first factor
loadingplot(mod, scatter=TRUE, labels="names")
scoreplot(mod)
# No backprojection
scoreplot(mod, projections=FALSE)
# Spider plot
scoreplot(mod, spider=TRUE, projections=FALSE)

# ASCA model with compressed response using 5 principal components
mod.pca <- asca(assessment ~ candy + assessor, data=candies, pca.in=5)

# Mixed Model ASCA, random assessor
mod.mix <- asca(assessment ~ candy + r(assessor), data=candies)
scoreplot(mod.mix)

# Mixed Model ASCA, REML estimation
mod.mix <- asca(assessment ~ candy + r(assessor), data=candies, REML=TRUE)
scoreplot(mod.mix)

# Load Caldana data
data(caldana)

# Combining effects in ASCA
mod.comb <- asca(compounds ~ time + comb(light + time:light), data=caldana)
summary(mod.comb)
timeplot(mod.comb, factor="light", time="time", comb=2)

# Permutation testing
mod.perm <- asca(assessment ~ candy * assessor, data=candies, permute=TRUE)
summary(mod.perm)

ASCA Fitting Workhorse Function

Description

This function is called by all ASCA related methods in this package. It is documented so that one can have access to a richer set of parameters from the various methods or call this function directly. The latter should be done with care as there are many possibilities and not all have been used in publications or tested thoroughly.

Usage

asca_fit(
  formula,
  data,
  subset,
  weights,
  na.action,
  family,
  permute = FALSE,
  perm.type = c("approximate", "exact"),
  unrestricted = FALSE,
  add_error = FALSE,
  aug_error = "denominator",
  use_ED = FALSE,
  pca.in = FALSE,
  contrasts = "contr.sum",
  coding,
  equal_baseline = FALSE,
  SStype = "II",
  REML = NULL
)
asca_fit(
  formula,
  data,
  subset,
  weights,
  na.action,
  family,
  permute = FALSE,
  perm.type = c("approximate", "exact"),
  unrestricted = FALSE,
  add_error = FALSE,
  aug_error = "denominator",
  use_ED = FALSE,
  pca.in = FALSE,
  contrasts = "contr.sum",
  coding,
  equal_baseline = FALSE,
  SStype = "II",
  REML = NULL
)

Arguments

`formula`	Model formula accepting a single response (block) and predictors. See Details for more information.
`data`	The data set to analyse.
`subset`	Expression for subsetting the data before modelling.
`weights`	Optional object weights.
`na.action`	How to handle NAs (no action implemented).
`family`	Error distributions and link function for Generalized Linear Models.
`permute`	Perform approximate permutation testing, default = FALSE (numeric or TRUE = 1000 permutations).
`perm.type`	Type of permutation: "approximate" (default) or "exact".
`unrestricted`	Use unrestricted ANOVA decomposition (default = FALSE).
`add_error`	Add error to LS means, e.g., for APCA.
`aug_error`	Augment score matrices in backprojection. Default = "denominator" (of F test), "residual" (force error term), nueric value (alpha-value in LiMM-PCA).
`use_ED`	Use "effective dimensions" for score rescaling in LiMM-PCA.
`pca.in`	Compress response before ASCA (number of components).
`contrasts`	Effect coding: "sum" (default = sum-coding), "weighted", "reference", "treatment".
`coding`	Defunct. Use 'contrasts' instead.
`equal_baseline`	Experimental: Set to `TRUE` to let interactions, where a main effect is missing, e.g., a nested model, be handled with the same baseline as a cross effect model. If `TRUE` the corresponding interactions will be put in quotation marks and included in the `model.frame`.
`SStype`	Type of sum-of-squares: "I" = sequential, "II" (default) = last term, obeying marginality, "III" = last term, not obeying marginality.
`REML`	Parameter to mixlm: NULL (default) = sum-of-squares, TRUE = REML, FALSE = ML.

Value

An asca object containing loadings, scores, explained variances, etc. The object has associated plotting (asca_plots) and result (asca_results) functions.

ASCA Plot Methods

Description

Various plotting procedures for asca objects.

Usage

## S3 method for class 'asca'
loadingplot(object, factor = 1, comps = 1:2, ...)

## S3 method for class 'asca'
scoreplot(
  object,
  factor = 1,
  comps = 1:2,
  within_level = "all",
  pch.scores = 19,
  pch.projections = 1,
  gr.col = NULL,
  projections = TRUE,
  spider = FALSE,
  ellipsoids,
  confidence,
  xlim,
  ylim,
  xlab,
  ylab,
  legendpos,
  ...
)

permutationplot(object, factor = 1, xlim, xlab = "SSQ", main, ...)
## S3 method for class 'asca'
loadingplot(object, factor = 1, comps = 1:2, ...)

## S3 method for class 'asca'
scoreplot(
  object,
  factor = 1,
  comps = 1:2,
  within_level = "all",
  pch.scores = 19,
  pch.projections = 1,
  gr.col = NULL,
  projections = TRUE,
  spider = FALSE,
  ellipsoids,
  confidence,
  xlim,
  ylim,
  xlab,
  ylab,
  legendpos,
  ...
)

permutationplot(object, factor = 1, xlim, xlab = "SSQ", main, ...)

Arguments

`object`	`asca` object.
`factor`	`integer/character` for selecting a model factor. If factor <= 0 or "global", the PCA of the input is used (negativ factor to include factor level colouring with global PCA).
`comps`	`integer` vector of selected components.
`...`	additional arguments to underlying methods.
`within_level`	MSCA parameter for chosing plot level (default = "all").
`pch.scores`	`integer` plotting symbol.
`pch.projections`	`integer` plotting symbol.
`gr.col`	`integer` vector of colours for groups.
`projections`	Include backprojections in score plot (default = TRUE).
`spider`	Draw lines between group centers and backprojections (default = FALSE).
`ellipsoids`	`character` "confidence" or "data" ellipsoids for balanced fixed effect models.
`confidence`	`numeric` vector of ellipsoid confidences, default = c(0.4, 0.68, 0.95).
`xlim`	`numeric` x limits.
`ylim`	`numeric` y limits.
`xlab`	`character` x label.
`ylab`	`character` y label.
`legendpos`	`character` position of legend.
`main`	Plot title.

Details

Usage of the functions are shown using generics in the examples in asca. Plot routines are available as scoreplot.asca and loadingplot.asca.

Value

The plotting routines have no return.

References

Smilde, A., Jansen, J., Hoefsloot, H., Lamers,R., Van Der Greef, J., and Timmerman, M.(2005). ANOVA-Simultaneous Component Analysis (ASCA): A new tool for analyzing designed metabolomics data. Bioinformatics, 21(13), 3043–3048.
Liland, K.H., Smilde, A., Marini, F., and Næs,T. (2018). Confidence ellipsoids for ASCA models based on multivariate regression theory. Journal of Chemometrics, 32(e2990), 1–13.
Martin, M. and Govaerts, B. (2020). LiMM-PCA: Combining ASCA+ and linear mixed models to analyse high-dimensional designed data. Journal of Chemometrics, 34(6), e3232.

ASCA Result Methods

Description

Standard result computation and extraction functions for ASCA (asca).

Usage

## S3 method for class 'asca'
print(x, ...)

## S3 method for class 'asca'
summary(object, extended = TRUE, df = FALSE, ...)

## S3 method for class 'summary.asca'
print(x, digits = 2, ...)

## S3 method for class 'asca'
loadings(object, factor = 1, ...)

## S3 method for class 'asca'
scores(object, factor = 1, ...)

projections(object, ...)

## S3 method for class 'asca'
projections(object, factor = 1, ...)
## S3 method for class 'asca'
print(x, ...)

## S3 method for class 'asca'
summary(object, extended = TRUE, df = FALSE, ...)

## S3 method for class 'summary.asca'
print(x, digits = 2, ...)

## S3 method for class 'asca'
loadings(object, factor = 1, ...)

## S3 method for class 'asca'
scores(object, factor = 1, ...)

projections(object, ...)

## S3 method for class 'asca'
projections(object, factor = 1, ...)

Arguments

`x`	`asca` object.
`...`	additional arguments to underlying methods.
`object`	`asca` object.
`extended`	Extended output in summary (default = TRUE).
`df`	Show degrees of freedom in summary (default = FALSE).
`digits`	`integer` number of digits for printing.
`factor`	`integer/character` for selecting a model factor.

Details

Usage of the functions are shown using generics in the examples in asca. Explained variances are available (block-wise and global) through blockexpl and print.rosaexpl. Object printing and summary are available through: print.asca and summary.asca. Scores and loadings have their own extensions of scores() and loadings() through scores.asca and loadings.asca. Special to ASCA is that scores are on a factor level basis, while back-projected samples have their own function in projections.asca.

Value

Returns depend on method used, e.g. projections.asca returns projected samples, scores.asca return scores, while print and summary methods return the object invisibly.

References

Smilde, A., Jansen, J., Hoefsloot, H., Lamers,R., Van Der Greef, J., and Timmerman, M.(2005). ANOVA-Simultaneous Component Analysis (ASCA): A new tool for analyzing designed metabolomics data. Bioinformatics, 21(13), 3043–3048.
Liland, K.H., Smilde, A., Marini, F., and Næs,T. (2018). Confidence ellipsoids for ASCA models based on multivariate regression theory. Journal of Chemometrics, 32(e2990), 1–13.
Martin, M. and Govaerts, B. (2020). LiMM-PCA: Combining ASCA+ and linear mixed models to analyse high-dimensional designed data. Journal of Chemometrics, 34(6), e3232.

Block-wise indexable data.frame

Description

This is a convenience function for making data.frames that are easily indexed on a block-wise basis.

Usage

block.data.frame(X, block_inds = NULL, to.matrix = TRUE)
block.data.frame(X, block_inds = NULL, to.matrix = TRUE)

Arguments

`X`	Either a single `data.frame` to index or a `list` of matrices/data.frames
`block_inds`	Named `list` of indexes if `X` is a single `data.frame`, otherwise `NULL`.
`to.matrix`	`logical` indicating if input list elements should be converted to matrices.

Value

A data.frame which can be indexed block-wise.

Examples

# Random data
M <- matrix(rnorm(200), nrow = 10)
# .. with dimnames
dimnames(M) <- list(LETTERS[1:10], as.character(1:20))

# A named list for indexing
inds <- list(B1 = 1:10, B2 = 11:20)

X <- block.data.frame(M, inds)
str(X)

# Random data
M <- matrix(rnorm(200), nrow = 10)
# .. with dimnames
dimnames(M) <- list(LETTERS[1:10], as.character(1:20))

# A named list for indexing
inds <- list(B1 = 1:10, B2 = 11:20)

X <- block.data.frame(M, inds)
str(X)

Arabidopsis thaliana growth experiment

Description

A dataset containing 67 metabolites from plants grown under different light and temperature conditions. This subset of the data contains only the light effect and time effect for limited conditions, while the full data also contains gene expressions.

Usage

data(caldana)
data(caldana)

Format

A data.frame having 140 rows and 3 variables:

light: Light levels
time: Time of measurement
compound: Metabolic compounds

References

Caldana C, Degenkolbe T, Cuadros-Inostroza A, Klie S, Sulpice R, Leisse A, et al. High-density kinetic analysis of the metabolomic and transcriptomic response of Arabidopsis to eight environmental conditions. Plant J. 2011;67(5):869-884.

Sensory assessment of candies.

Description

A dataset containing 9 sensory attributes for 5 candies assessed by 11 trained assessors.

Usage

data(candies)
data(candies)

Format

A data.frame having 165 rows and 3 variables:

assessment: Matrix of sensory attributes
assessor: Factor of assessors
candy: Factor of candies

References

Luciano G, Næs T. Interpreting sensory data by combining principal component analysis and analysis of variance. Food Qual Prefer. 2009;20(3):167-175.

Dummy-coding of a single vector

Description

Flexible dummy-coding allowing for all R's built-in types of contrasts and optional dropping of a factor level to reduce rank defficiency probability.

Usage

dummycode(Y, contrast = "contr.sum", drop = TRUE)
dummycode(Y, contrast = "contr.sum", drop = TRUE)

Arguments

`Y`	`vector` to dummy code.
`contrast`	Contrast type, default = "contr.sum".
`drop`	`logical` indicating if one level should be dropped (default = TRUE).

Value

matrix made by dummy-coding the input vector.

Examples

vec <- c("a","a","b","b","c","c")
dummycode(vec)
vec <- c("a","a","b","b","c","c")
dummycode(vec)

Extracting the Extended Model Frame from a Formula or Fit

Description

This function attempts to apply model.frame and extend the result with columns of interactions.

Usage

extended.model.frame(formula, data, ..., sep = ".")
extended.model.frame(formula, data, ..., sep = ".")

Arguments

`formula`	a model formula or terms object or an R object.
`data`	a data.frame, list or environment (see `model.frame`).
`...`	further arguments to pass to `model.frame`.
`sep`	separator in contraction of names for interactions (default = ".").

Value

A data.frame that includes everything a model.frame does plus interaction terms.

Examples

dat <- data.frame(Y = c(1,2,3,4,5,6),
                  X = factor(LETTERS[c(1,1,2,2,3,3)]),
                  W = factor(letters[c(1,2,1,2,1,2)]))
extended.model.frame(Y ~ X*W, dat)
dat <- data.frame(Y = c(1,2,3,4,5,6),
                  X = factor(LETTERS[c(1,1,2,2,3,3)]),
                  W = factor(letters[c(1,2,1,2,1,2)]))
extended.model.frame(Y ~ X*W, dat)

Linear Mixed Model PCA

Description

This function mimics parts of the LiMM-PCA framework, combining ASCA+ and linear mixed models to analyse high-dimensional designed data. The default is to use REML estimation and scaling of the backprojected errors. See examples for alternatives.

Usage

limmpca(
  formula,
  data,
  pca.in = 5,
  aug_error = 0.05,
  use_ED = FALSE,
  REML = TRUE,
  contrasts = "contr.sum",
  ...
)
limmpca(
  formula,
  data,
  pca.in = 5,
  aug_error = 0.05,
  use_ED = FALSE,
  REML = TRUE,
  contrasts = "contr.sum",
  ...
)

Arguments

`formula`	Model formula accepting a single response (block) and predictors. See Details for more information.
`data`	The data set to analyse.
`pca.in`	Compress response before ASCA (number of components), default = 5.
`aug_error`	Error term of model ("denominator", "residual", numeric alpha-value). The latter implies the first with a scaling factor.
`use_ED`	Use Effective Dimensions instead of degrees of freedom when scaling.
`REML`	Use restricted maximum likelihood estimation. Alternatives: TRUE (default), FALSE (ML), NULL (least squares).
`contrasts`	Effect coding: "sum" (default = sum-coding), "weighted", "reference", "treatment".
`...`	Additional arguments to `asca_fit`.

Value

An object of class limmpca, inheriting from the general asca class.

References

Martin, M. and Govaerts, B. (2020). LiMM-PCA: Combining ASCA+ and linear mixed models to analyse high-dimensional designed data. Journal of Chemometrics, 34(6), e3232.

Examples

# Load candies data
data(candies)

# Default LiMM-PCA model with two factors and interaction, 5 PCA components
mod <- limmpca(assessment ~ candy*r(assessor), data=candies)
summary(mod)
scoreplot(mod, factor = "candy")

# LiMM-PCA with least squares estimation and 8 PCA components
modLS <- limmpca(assessment ~ candy*r(assessor), data=candies, REML=NULL, pca.in=8)
summary(modLS)
scoreplot(modLS, factor = "candy")

# Load Caldana data
data(caldana)

# Combining effects in LiMM-PCA (assuming light is a random factor)
mod.comb <- limmpca(compounds ~ time + comb(r(light) + r(time:light)), data=caldana, pca.in=8)
summary(mod.comb)
# Load candies data
data(candies)

# Default LiMM-PCA model with two factors and interaction, 5 PCA components
mod <- limmpca(assessment ~ candy*r(assessor), data=candies)
summary(mod)
scoreplot(mod, factor = "candy")

# LiMM-PCA with least squares estimation and 8 PCA components
modLS <- limmpca(assessment ~ candy*r(assessor), data=candies, REML=NULL, pca.in=8)
summary(modLS)
scoreplot(modLS, factor = "candy")

# Load Caldana data
data(caldana)

# Combining effects in LiMM-PCA (assuming light is a random factor)
mod.comb <- limmpca(compounds ~ time + comb(r(light) + r(time:light)), data=caldana, pca.in=8)
summary(mod.comb)

Model Frame and Model Matrix for ASCA-like Models

Description

Extraction functions to retrieve the model.frame and model.matrix of an asca object.

Usage

## S3 method for class 'asca'
model.frame(formula, ...)

## S3 method for class 'asca'
model.matrix(object, ...)
## S3 method for class 'asca'
model.frame(formula, ...)

## S3 method for class 'asca'
model.matrix(object, ...)

Arguments

`formula`	The `asca` object.
`...`	Not implemented
`object`	The `asca` object.

Value

A data.frame or matrix object.

Examples

# Load candies data
data(candies)

# Basic ASCA model with two factors
mod <- asca(assessment ~ candy + assessor, data=candies)

# Extract model frame and model matrix
mf <- model.frame(mod)
head(mf)
mm <- model.matrix(mod)
par.old <- par(mar=c(3,3,3,1), mgp=c(1,0.7,0))
image(t(mm[seq(165,1,-1),]), main="Model Matrix", xlab="dummy values", ylab="samples",
     axes=FALSE)
par(par.old)
# Load candies data
data(candies)

# Basic ASCA model with two factors
mod <- asca(assessment ~ candy + assessor, data=candies)

# Extract model frame and model matrix
mf <- model.frame(mod)
head(mf)
mm <- model.matrix(mod)
par.old <- par(mar=c(3,3,3,1), mgp=c(1,0.7,0))
image(t(mm[seq(165,1,-1),]), main="Model Matrix", xlab="dummy values", ylab="samples",
     axes=FALSE)
par(par.old)

Multilevel Simultaneous Component Analysis - MSCA

Description

This MSCA implementation assumes a single factor to be used as between-individuals factor.

Usage

msca(formula, data, contrasts = "contr.sum", ...)
msca(formula, data, contrasts = "contr.sum", ...)

Arguments

`formula`	Model formula accepting a single response (block) and predictors. See Details for more information.
`data`	The data set to analyse.
`contrasts`	Effect coding: "sum" (default = sum-coding), "weighted", "reference", "treatment".
`...`	Additional arguments to `asca_fit`.

Value

An asca object containing loadings, scores, explained variances, etc. The object has associated plotting (asca_plots) and result (asca_results) functions.

References

Smilde, A., Jansen, J., Hoefsloot, H., Lamers,R., Van Der Greef, J., and Timmerman, M.(2005). ANOVA-Simultaneous Component Analysis (ASCA): A new tool for analyzing designed metabolomics data. Bioinformatics, 21(13), 3043–3048.
Liland, K.H., Smilde, A., Marini, F., and Næs,T. (2018). Confidence ellipsoids for ASCA models based on multivariate regression theory. Journal of Chemometrics, 32(e2990), 1–13.

Examples

# Load candies data
data(candies)

# Basic MSCA model with a single factor
mod <- msca(assessment ~ candy, data=candies)
print(mod)
summary(mod)

# Result plotting for first factor
loadingplot(mod, scatter=TRUE, labels="names")
scoreplot(mod)

# Within scores
scoreplot(mod, factor="within")

# Within scores per factor level
par.old <- par(mfrow=c(3,2), mar=c(4,4,2,1), mgp=c(2,0.7,0))
for(i in 1:length(mod$scores.within))
  scoreplot(mod, factor="within", within_level=i,
            main=paste0("Level: ", names(mod$scores.within)[i]),
            panel.first=abline(v=0,h=0,col="gray",lty=2))
par(par.old)

# Permutation testing
mod.perm <- asca(assessment ~ candy * assessor, data=candies, permute=TRUE)
summary(mod.perm)

# Load candies data
data(candies)

# Basic MSCA model with a single factor
mod <- msca(assessment ~ candy, data=candies)
print(mod)
summary(mod)

# Result plotting for first factor
loadingplot(mod, scatter=TRUE, labels="names")
scoreplot(mod)

# Within scores
scoreplot(mod, factor="within")

# Within scores per factor level
par.old <- par(mfrow=c(3,2), mar=c(4,4,2,1), mgp=c(2,0.7,0))
for(i in 1:length(mod$scores.within))
  scoreplot(mod, factor="within", within_level=i,
            main=paste0("Level: ", names(mod$scores.within)[i]),
            panel.first=abline(v=0,h=0,col="gray",lty=2))
par(par.old)

# Permutation testing
mod.perm <- asca(assessment ~ candy * assessor, data=candies, permute=TRUE)
summary(mod.perm)

Principal Components Analysis of Variance Simultaneous Component Analysis - PC-ANOVA

Description

This is a quite general and flexible implementation of PC-ANOVA.

Usage

pcanova(formula, data, ncomp = 0.9, contrasts = "contr.sum", ...)
pcanova(formula, data, ncomp = 0.9, contrasts = "contr.sum", ...)

Arguments

`formula`	Model formula accepting a single response (block) and predictor names separated by + signs.
`data`	The data set to analyse.
`ncomp`	The number of components to retain, proportion of variation or default = minimum cross-validation error.
`contrasts`	Effect coding: "sum" (default = sum-coding), "weighted", "reference", "treatment".
`...`	Additional parameters for the asca_fit function.

Details

PC-ANOVA works in the opposite order of ASCA. First the response matrix is decomposed using ANOVA. Then the components are analysed using ANOVA with respect to a design or grouping in the data. The latter can be ordinary fixed effects modelling or mixed models.

Value

A pcanova object containing loadings, scores, explained variances, etc. The object has associated plotting (pcanova_plots) and result (pcanova_results) functions.

References

Luciano G, Næs T. Interpreting sensory data by combining principal component analysis and analysis of variance. Food Qual Prefer. 2009;20(3):167-175.

Examples

# Load candies data
data(candies)

# Basic PC-ANOVA model with two factors, cross-validated opt. of #components
mod <- pcanova(assessment ~ candy + assessor, data = candies)
print(mod)

# PC-ANOVA model with interaction, minimum 90% explained variance
mod <- pcanova(assessment ~ candy * assessor, data = candies, ncomp = 0.9)
print(mod)
summary(mod)

# Tukey group letters for 'candy' per component
lapply(mod$models, function(x)
       mixlm::cld(mixlm::simple.glht(x,
                                     effect = "candy")))

# Result plotting
loadingplot(mod, scatter=TRUE, labels="names")
scoreplot(mod)

# Mixed Model PC-ANOVA, random assessor
mod.mix <- pcanova(assessment ~ candy + r(assessor), data=candies, ncomp = 0.9)
scoreplot(mod.mix)
# Fixed effects
summary(mod.mix)

# Load candies data
data(candies)

# Basic PC-ANOVA model with two factors, cross-validated opt. of #components
mod <- pcanova(assessment ~ candy + assessor, data = candies)
print(mod)

# PC-ANOVA model with interaction, minimum 90% explained variance
mod <- pcanova(assessment ~ candy * assessor, data = candies, ncomp = 0.9)
print(mod)
summary(mod)

# Tukey group letters for 'candy' per component
lapply(mod$models, function(x)
       mixlm::cld(mixlm::simple.glht(x,
                                     effect = "candy")))

# Result plotting
loadingplot(mod, scatter=TRUE, labels="names")
scoreplot(mod)

# Mixed Model PC-ANOVA, random assessor
mod.mix <- pcanova(assessment ~ candy + r(assessor), data=candies, ncomp = 0.9)
scoreplot(mod.mix)
# Fixed effects
summary(mod.mix)

PC-ANOVA Result Methods

Description

Various plotting procedures for pcanova objects.

Usage

## S3 method for class 'pcanova'
scoreplot(object, factor = 1, comps = 1:2, col = "factor", ...)
## S3 method for class 'pcanova'
scoreplot(object, factor = 1, comps = 1:2, col = "factor", ...)

Arguments

`object`	`pcanova` object.
`factor`	`integer/character` for selecting a model factor.
`comps`	`integer` vector of selected components.
`col`	`character` for selecting a factor to use for colouring (default = first factor) or ordinary colour specifications.
`...`	additional arguments to underlying methods.

Details

Usage of the functions are shown using generics in the examples in pcanova. Plot routines are available as scoreplot.pcanova and loadingplot.pcanova.

Value

The plotting routines have no return.

References

Luciano G, Næs T. Interpreting sensory data by combining principal component analysis and analysis of variance. Food Qual Prefer. 2009;20(3):167-175.

PC-ANOVA Result Methods

Description

Standard result computation and extraction functions for ASCA (pcanova).

Usage

## S3 method for class 'pcanova'
summary(object, ...)

## S3 method for class 'summary.pcanova'
print(x, digits = 2, ...)

## S3 method for class 'pcanova'
print(x, ...)

## S3 method for class 'pcanova'
summary(object, ...)
## S3 method for class 'pcanova'
summary(object, ...)

## S3 method for class 'summary.pcanova'
print(x, digits = 2, ...)

## S3 method for class 'pcanova'
print(x, ...)

## S3 method for class 'pcanova'
summary(object, ...)

Arguments

`object`	`pcanova` object.
`...`	additional arguments to underlying methods.
`x`	`pcanova` object.
`digits`	`integer` number of digits for printing.

Details

Usage of the functions are shown using generics in the examples in pcanova. Explained variances are available (block-wise and global) through blockexpl and print.rosaexpl. Object printing and summary are available through: print.pcanova and summary.pcanova. Scores and loadings have their own extensions of scores() and loadings() through scores.pcanova and loadings.pcanova. Special to ASCA is that scores are on a factor level basis, while back-projected samples have their own function in projections.pcanova.

Value

Returns depend on method used, e.g. projections.pcanova returns projected samples, scores.pcanova return scores, while print and summary methods return the object invisibly.

References

Luciano G, Næs T. Interpreting sensory data by combining principal component analysis and analysis of variance. Food Qual Prefer. 2009;20(3):167-175.

Permutation Based MANOVA - PERMANOVA

Description

Wrapper for the adonis2 function to allow ordinary formula input.

Usage

permanova(formula, data, ...)
permanova(formula, data, ...)

Arguments

`formula`	Model formula accepting a single response matrix and predictors. See details in `adonis2`.
`data`	The data set to analyse.
`...`	Additional arguments to `adonis2`.

Value

An ANOVA table with permutation-based p-values.

Examples

data(caldana)
(pr <- permanova(compounds ~ light * time, caldana))
data(caldana)
(pr <- permanova(compounds ~ light * time, caldana))

Principal Response Curves

Description

Wrapper for the prc function to allow for formula input.

Usage

prc(formula, data, ...)
prc(formula, data, ...)

Arguments

`formula`	Model formula accepting a single response (block) and predictors. If no predictor is called 'time', time is assumed to be the second predictor.
`data`	The data set to analyse.
`...`	Additional arguments to `prc`.

Value

An object of class prc.

Examples

data(caldana)
(pr <- prc(compounds ~ light * time, caldana))
summary(pr)
data(caldana)
(pr <- prc(compounds ~ light * time, caldana))
summary(pr)

Timeplot for Combined Effects

Description

Timeplot for Combined Effects

Usage

timeplot(
  object,
  factor,
  time,
  comb,
  comp = 1,
  ylim,
  x_time = FALSE,
  xlab = time,
  ylab = paste0("Score ", comp),
  lwd = 2,
  ...
)
timeplot(
  object,
  factor,
  time,
  comb,
  comp = 1,
  ylim,
  x_time = FALSE,
  xlab = time,
  ylab = paste0("Score ", comp),
  lwd = 2,
  ...
)

Arguments

`object`	`asca` object.
`factor`	`integer/character` main factor.
`time`	`integer/character` time factor.
`comb`	`integer/character` combined effect factor.
`comp`	`integer` component number.
`ylim`	`numeric` y limits.
`x_time`	`logical` use time levels as non-equispaced x axis (default = FALSE).
`xlab`	`character` x label.
`ylab`	`character` y label.
`lwd`	`numeric` line width.
`...`	additional arguments to `plot`.

Value

Nothing

Examples

data("caldana")
mod.comb <- asca(compounds ~ time + comb(light + light:time), data=caldana)

# Default time axis
timeplot(mod.comb, factor="light", time="time", comb=2)

# Non-equispaced time axis (using time levels)
timeplot(mod.comb, factor="light", time="time", comb=2, x_time=TRUE)

# Second component
timeplot(mod.comb, factor="light", time="time", comb=2, comp=2, x_time=TRUE)
data("caldana")
mod.comb <- asca(compounds ~ time + comb(light + light:time), data=caldana)

# Default time axis
timeplot(mod.comb, factor="light", time="time", comb=2)

# Non-equispaced time axis (using time levels)
timeplot(mod.comb, factor="light", time="time", comb=2, x_time=TRUE)

# Second component
timeplot(mod.comb, factor="light", time="time", comb=2, comp=2, x_time=TRUE)

Update a Model without Factor

Description

Perform a model update while removing a chosen factor. Hierarchical corresponds to type "II" sum-of-squares, i.e., obeying marginality, while non-hierarchical corresponds to type "III" sum-of-squares.

Usage

update_without_factor(model, fac, hierarchical = TRUE)
update_without_factor(model, fac, hierarchical = TRUE)

Arguments

`model`	`model` object to update.
`fac`	`character` factor to remove.
`hierarchical`	`logical` obey hierarchy when removing factor (default = TRUE).

Value

An updated model object is returned. If the supplied model is of type lmerMod and no random effects are left, the model is automatically converted to a linear model before updating.

Package 'HDANOVA'

Help Index

ANOVA Principal Component Analysis - APCA

Description

Usage

Arguments

Value

References

See Also

Examples

Analysis of Variance Simultaneous Component Analysis - ASCA

Description

Usage

Arguments

Details

Value

References

See Also

Examples

ASCA Fitting Workhorse Function

Description

Usage

Arguments

Value

ASCA Plot Methods

Description

Usage

Arguments

Details

Value

References

See Also

ASCA Result Methods

Description

Usage

Arguments

Details

Value

References

See Also

Block-wise indexable data.frame

Description

Usage

Arguments

Value

See Also

Examples

Arabidopsis thaliana growth experiment

Description

Usage

Format

References

Sensory assessment of candies.

Description

Usage

Format

References

Dummy-coding of a single vector

Description

Usage

Arguments

Value

Examples

Extracting the Extended Model Frame from a Formula or Fit

Description

Usage

Arguments

Value

See Also

Examples

Linear Mixed Model PCA

Description

Usage

Arguments

Value

References

See Also

Examples

Model Frame and Model Matrix for ASCA-like Models

Description