lmdme S4 class: Linear Model decomposition for Designed Multivariate Experiments.
Description
Linear Model ANOVA decomposition of Designed Multivariate
Experiments based on limma lmFit
implementation. For example in a two factor experimental
design with interaction, the linear model of the ith
observation (gene) can be written:
X=μ+A+B+AB+ε
where
X stands for the observed value
The intercept μ
A, B and AB are the first, second and interaction terms respectively
The error term ε ~ N(0,σ^2).
The model is iterative decomposed in a step by step fashion decomposing one term at each time:
The intercept is estimated using X=μ+E_1
The first factor (A) using E_1=A+E_2
The second factor (B) using E_2=B+E_3
The interaction (AB) using E_3=AB+E_4.
For each decomposed step the model, residuals, coefficients, pvalues and Fvalues are stored in a list container, so their corresponding length is equal to the number of model terms + 1 (the intercept).
Features
Flexible formula type interface,

Fast limma based implementation based on
lmFit
, p values for each estimated coefficient levels in each factor
F values for factor effects
Plotting functions for PCA and PLS.
Slots
design: data.frame with experimental design.
model: formula with the designed model to be decomposed.
modelDecomposition: list with the model formula obtained for each decomposition step.

residuals: list of residual matrices G rows(genes) x N columns (arraysdesigned measurements).

coefficients: list of coefficient matrices. Each matrix will have G rows(genes) x k columns(levels of the corresponding model term).
p.values: list of pvalue matrices.
F.p.values: list with corresponding Fpvalues vectors for each individual.
components: list with corresponding PCA or PLS components for the selected term/s.
componentsType: name character vector to keep process trace of the variance/covariance components slot: decomposition ("pca" or "pls"), type ("apca" for ANOVAPCA or "asca" for ANOVASCA) and scale ("none", "row" or "column")
lmdmegeneralfunctions
 print, show
Basic output for lmdme class
 summary
Basic statistics for lmdme class
 design, model, modelDecomposition, residuals and coefficients
Getters for their respective slots.
 p.values, F.p.values, components and componentsType
Getters for their respective slots.
ANOVAlineardecompositionfunctions
 lmdme
Function that produces the complete ANOVA decomposition based on model specification through a formula interface. Technically it's a high level wrapper of the initialize function.
 modelDecomposition
Getter for the used decomposed formula in each step
 p.adjust
Adjust coefficients pvalues for the Multiple Comparison Tests.
 Fpvalues, pvalues
Getters for the corresponding associated decomposed model coefficient statistics in each step, for each observation.
 residuals, resid, coef, coefficients, fitted.values, fitted
Getters for the corresponding decomposed model in each step.
 permutation
Produces the specified lmdme in addition to the required permuted objects (sampling the columns of data), using the same parameters to fit the model.
variancecovariancedecompositionfunctions
 decomposition
Function to perform PCA or PLS on the ANOVA decomposed terms. PCA can be performed on E_1, E_2 or E_3 and it is referred to, as ANOVAPCA (APCA) but, if it is performed on the coefficients it is referred to, as ANOVASCA (ASCA). On the other hand PLSR is based on pls library and if it is performed on coefficients (ASCA like) it uses the identity matrix for output covariance maximization or can be carried out on the E_{1,2 or 3} (APCA like) using the design matrix as the output.
 components
Getter for PCA or PLS decomposed models.
 componentsType
Getter for componentsType slot.
 leverage
Leverage calculation on PCA (APCA or ASCA) terms.
 biplot
Biplots for PCA or PLSR decomposed terms.
 screeplot
Screeplot on each PCA decomposed term.
 loadingplot
Loadingplot for PCA interaction terms.
Author(s)
Cristobal Fresno and Elmer A Fernandez
References
Smilde AK, Jansen JJ, Hoefsloot HCJ, Lamer RAN, Van der Greef J, Timmerman ME (2005) ANOVAsimultaneaus component analysis (ASCA): a new tool for analyzing designed
metabolomics data, Bioinformatics 21,13,3043 DOI:/10.1093/bioinformatics/bti476Zwanenburg G, Hoefsloot HCJ, Westerhuis JA, Jansen JJ, Smilde AK (2011) ANOVA.Principal component analysis and ANOVAsimultaneaus component analysis: a comparison J.
Chemometrics 25:561567 DOI:10.1002/cem.1400Tarazona S, PradoLopez S, Dopazo J, Ferrer A, Conesa A (2012) Variable Selection for Multifactorial Genomic Data, Chemometrics and Intelligent Laboratory Systems, 110:113122
See Also
lmdme
, decomposition
,
biplot
, loadingplot
and
additional related lmdme class functions.