I have data from a incomplete factorial experiment with repeated measures and potential nesting and am trying to figure out 1) the right way to design the mixed model to analyze the data, and 2) how to code with either lmer or lme.

1: Model design - I have treatment Till with three levels (N,C,O) and treatment Rot with two levels (W,F). Each of the Rot treatments only occur in one year, so only W occurred in 2013 and only F occurred in 2014. This is not an ideal design of course, but it's what I have to work with - I'd like to still call the treatment Rot but explain in the manuscript's text the link with year and related caveats. The design is full factorial between Till and Rot except that one combination (W X O) is missing. There are three replicate Plot#s for each Till level that were measured at 5 unequally spaced Timepoint#s each of the two growing seasons (i.e., under each Rot level). There are a number of response variables I'd like to predict based on those elements of experiment design (Fixed = Till, Rot; Random = Plot#, Timepoint).

My thought is that this design is appropriate but I want to check with those who are more knowledgeable:

Fixed effects = Till crossed with Rot

Random effects = Plot# nested within Till; Timepoint# nested within Rot or just Timepoint# as a random effect on it's own

*Image of Experimental Design*

2: Model syntax - I plan to test for auto-correlation over Timepoint# using lme or lmer in R. I know how to do that in lme but I don't think there's functionality to do so in lmer. I've read a bit about model syntax for both those functions but am still not certain I'm coding my models correctly so a suggestion of how to code the correct model design in either of those functions would be extremely helpful, too.

I have read through a number of Cross-validated and Stack Overflow posts and have read a bit of Zuur 2009 but haven't been able to confidently determine the right model structure or R syntax.


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