HDANOVA (version 0.8.4)

apls: Analysis of Variance Partial Least Squares - APLS

Description

This is a quite general and flexible implementation of APLS.

Usage

apls(
  formula,
  data,
  add_error = TRUE,
  contrasts = "contr.sum",
  permute = FALSE,
  perm.type = c("approximate", "exact"),
  ...
)

Value

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

Arguments

formula

Model formula accepting a single response (block) and predictors. See Details for more information.

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".

permute

Number of permutations to perform (default = 1000).

perm.type

Type of permutation to perform, either "approximate" or "exact" (default = "approximate").

...

Additional arguments to hdanova.

Details

APLS 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 PLS is performed on the corresponding least squares estimates, i.e., Y = X1 B1 + X2 B2 + ... + E = T1 P1' + T2 P2' + ... + E. For balanced designs, the PLS components are equivalent to PCA components, i.e., APLS and APCA are equivalent. This version of APLS encompasses variants of LiMM-PLS, generalized APLS and covariates APLS.

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.

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.

See Also

Main methods: asca, apca, limmpca, msca, pcanova, prc and permanova. Workhorse function underpinning most methods: hdanova. Extraction of results and plotting: asca_results, asca_plots, pcanova_results and pcanova_plots

Examples

# Load candies data
data(candies)

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

# APLS model with interaction
mod <- apls(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)

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

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

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

# Load Caldana data
data(caldana)

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

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