In LIMMA for gene expression data normalization, offset is used to correct background and quantile for between array normalization. How same works and setting different offset values like 16 or 50, means what ?. It will be easy for me to understand in words rather than in equations..
The lower values you chose for your offset, the broader the background you get, which means it is more like a threshold that define your cut off for the odds in your data, if you chose 16, this will get rid off the most awful 16% of the odd values that distort your curves and data... If you chose 50%, this means you tell the program to narrow the curve and remove 50% of any odd values that can disturb the normality of the curves. Which means more strengincy. I wish I understand your question and wish this unswerving it...
However, if you read my answer, you will find the same info you said yet with simple words... i did not use the log equations or the gene expresion words... but i told him that the odds (in your words should be the low expressed genes) are going to be taken off...and if he used 50% offset...it means more stringency. .. which means more sever portion of his dots are going to be tsken away... in conclusion ... your answer is more technical while mine is more simple... but yours is much informative ...to me... thanks again...
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