[R] Question to NLME, ML vs. REML

[Klaus Thul]

Dear all,

I am planning to use nlme library for analysis of experiments in semiconductor 
industry. Currently I am using "lm" but plan to move to "lme" to handle 
within wafer / wafer-to-wafer and lot-to-lot variation correctly. 

So far everything is working well, but I have a fundamentel question: 

NLME offers "maximum likelihood" and "restricted maximum likelihood" for 
parameter estimation. ML has the advantage, that likelihood ratios can be 
computed even with changes in model structure. In addition, ML works with the 
stepAIC function from MASS-library which I am currently using for 
model-building.

I am wondering, why REML is the default setting in NLME and therefore somehow 
preferred by the authors. What is the main reason to use REML? 

Maybe I am lacking here statistical knowledge. Any hint, including reference 
to literature would be very helpful.

Best regards,
Klaus Thul