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 iteratively decomposed in a step by step fashion decomposing one term 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, p-values and F-value are stored in a list container, so their corresponding length is equal to the number of model terms + 1 (the intercept).

`model` |
formula object to carry out the decomposition. |

`data` |
matrix or data.frame with individuals/genes (per rows) and samples/conditions (per columns). |

`design` |
data.frame with the design of the experiment, (rows) samples/conditions as in data columns and as many columns to indicate the factors present in each sample. |

`Bayes` |
Should limma estimate empirical Bayes statistics, i. e., moderated t-statistics? Default value is FALSE. |

`verbose` |
Should the process progress be printed? Default value is FALSE. |

`...` |
Additional parameters for |

`lmdme` |
lmdme class object with the corresponding completed slots according to the given model |

use ** lmdme** high level constructor for
the creation of the class instead of directly calling its
constructor by means of new.

Cristobal Fresno and Elmer A Fernandez

Smyth, G. K. (2005). Limma: linear models for microarray data. In: Bioinformatics and Computational Biology Solutions using R and Bioconductor. R. Gentleman, V. Carey, S. Dudoit, R. Irizarry, W. Huber (eds), Springer, New York, pages 397–420.

Cristobal Fresno, Monica G. Balzarini, Elmer A. Fernandez (2014) lmdme: Linear Models on Designed Multivariate Experiments in R, Journal of Statistical Software, 56(7), 1-16, http://www.jstatsoft.org/v56/i07/.

`decomposition`

, `lmFit`

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 | ```
{
data(stemHypoxia)
##Just to make a balanced dataset in the Fisher sense (2 samples per
## time*oxygen levels)
design<-design[design$time %in% c(0.5,1,5) & design$oxygen %in% c(1,5,21), ]
design$time<-as.factor(design$time)
design$oxygen<-as.factor(design$oxygen)
rownames(M)<-M[, 1]
#Keeping appropriate samples only
M<-M[, colnames(M) %in% design$samplename]
##ANOVA decomposition
fit<-lmdme(model=~time+oxygen+time:oxygen, data=M, design=design)
}
``` |

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