Beta value

Beta matrix

There exists a transformation between M value (analyzed here, and first introduced in this paper) and the Beta value (formula for transformation is also described here):

beta=2^M/(2^M+1); M=log2(M/U); beta=M/(M+U+offset)

Data distribution based on the expression used for measuring DNA methylation (beta vs M value):
 

I used the matrix of M values and transformed them into beta values. Here are the plots of the first eigengene, first eigenarray (colored by the probe dye) and the outliers identified in the first eigengene:

Density plots by the color of the dye of the first 3 eigenarrays:
 
Consultation with Brig and Justin: don't split the data, keep all probes together.

Correlation with adjustment and biological variables:

since we already know from the analyses of the M value that batch, center, plate row and plate column have effect on the data, I will skip the preliminary steps and remove these factors. Also, the dataset will exclude batch number 0652.

> X<-model.matrix(~factor(batch[mask]) + adj$plate_row[mask] + adj$plate_column[mask] + factor(center[mask]))
> Xmod<-solve(t(X) %*% X) %*% t(X) %*% t(beta[,mask])
> betaRes<- beta[,mask] - t(X %*% Xmod)

Correlation with adjustment and biological variables:

It seems that with beta value I see a stronger correlation with age. First eigengene, first and second eigenarrays and the outliers:

We can proceed with building a comethylation network although the outliers look terrible.