lmdme-class: 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 i-th observation (gene) can be written: $X=\mu+A+B+AB+\epsilon$ where

X stands for the observed value
The intercept $\mu$
A, B and AB are the first, second and interaction terms respectively
The error term $\epsilon ~ N(0,\sigma^2)$.

The model is iterative decomposed in a step by step fashion decomposing one term at each time:

The intercept is estimated using $X=\mu+E_1$
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, p-values and F-values are stored in a list container, so their corresponding length is equal to the number of model terms + 1 (the intercept).

Arguments

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 (arrays-designed 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 p-value matrices.
F.p.values: list with corresponding F-p-values 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 ANOVA-PCA or "asca" for ANOVA-SCA) and scale ("none", "row" or "column")

lmdme-general-functions

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.

ANOVA-linear-decomposition-functions

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 p-values 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.

variance-covariance-decomposition-functions

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 ANOVA-PCA (APCA) but, if it is performed on the coefficients it is referred to, as ANOVA-SCA (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 co-variance 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.

References

Smilde AK, Jansen JJ, Hoefsloot HCJ, Lamer RAN, Van der Greef J, Timmerman ME (2005) ANOVA-simultaneaus component analysis (ASCA): a new tool for analyzing designed metabolomics data, Bioinformatics 21,13,3043 DOI:/10.1093/bioinformatics/bti476
Zwanenburg G, Hoefsloot HCJ, Westerhuis JA, Jansen JJ, Smilde AK (2011) ANOVA.Principal component analysis and ANOVA-simultaneaus component analysis: a comparison J. Chemometrics 25:561-567 DOI:10.1002/cem.1400
Tarazona S, Prado-Lopez S, Dopazo J, Ferrer A, Conesa A (2012) Variable Selection for Multifactorial Genomic Data, Chemometrics and Intelligent Laboratory Systems, 110:113-122