lmdme-Class: lmdme S4 class: Linear Model decomposition for Designed... In lmdme: 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=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:

1. The intercept is estimated using X=μ+E_1

2. The first factor (A) using E_1=A+E_2

3. The second factor (B) using E_2=B+E_3

4. 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).

Features

1. Flexible formula type interface,

2. Fast limma based implementation based on `lmFit`,

3. p values for each estimated coefficient levels in each factor

4. F values for factor effects

5. 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

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.

Author(s)

Cristobal Fresno and Elmer A Fernandez

References

1. 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

2. 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

3. 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

`lmdme`, `decomposition`, `biplot`, `loadingplot` and additional related lmdme class functions.