# Using ML or REML when comparing factor levels with Wald test?

I have finished my model reduction of a linear mixed model (and have used ML for this) and have found which factors that are significant in my final model.

I am aware of that using ML is necessary when performing model reduction with likelhood ratio test and using REML is preferable when I need to get the estimates out for the final model.

But what if I want to compare the levels of the significant factors against each other (such as either summary or LSmeans pairwise comparison), should I then fit the model with REML or ML? As far as I understand, both summary() and pairs() in R uses a Wald (not a likelyhood ratio test) when making factor level comparisons.

• If you're asking about lsmeans::summary() and lsmeans::pairs(), then yes, Wald tests are conducted. I think that now you've selected your model, you're better off using the REML fit for post-hoc comparisons. – Russ Lenth Aug 24 '17 at 17:30
• Thank you. The normal summary (outside of lsmeans) is also using a Wald test to compare the other treatments against the control, right? I could not find the answer to this in the help function for summary. – Ditlev Reventlow Aug 28 '17 at 8:10
• summary is a generic function, and there are methods for it for all manner of fitted models. You have not said what kind of model you fitted, so I have no idea what kind of tests it displays. You need to look at the documentation for the class of model that you fitted. – Russ Lenth Aug 28 '17 at 13:08
• I have used linear mixed effect models and generalised linear mixed effect models. I can see that the results are the same whether I make the summary outside of lsmeans or inside lsmeans, so it must be wald tests that are conducted in both cases. – Ditlev Reventlow Aug 29 '17 at 13:42