An example of non-biological, unwanted variance is the batch effect, but we have already taken care of this effect by adding it to a linear model. But more noise needs to be removed to obtain the expected clustering of the samples. The source of this variation is unknown. We therefore resort to factor analysis and infer the factors from the data and incorporate into the linear model for differential expression analysis. There are several reports that use factor analysis for normalization, but care must be taken to separate biological factors from unwanted variation. This is not possible in a rigorous way, but we believe that using the knowledge of sample identities will limit the effect of removing biological information together with non-biological factors. We start with a log-linear regression model.