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I am currently analyzing data from a field experiment originally designed for a two-way ANOVA. The experiment involves two factors—SOIL (2 levels) and PLANT (2 levels)—with 6 replicates in a block design. The experiment includes three sampling times and data from two soil depths.

Given the repeated measures over time and at different depths, I am concerned about the independence assumption required for a two-way ANOVA. While conducting separate two-way ANOVAs for each sampling and depth is an option, it would result in a loss of statistical power and hinder cross-comparison between different samplings and depths, which is crucial for my study.

To address these challenges, I am considering using a Linear Mixed Model with the following structure:

soil_carbon ~ (SOIL*PLANT*DEPTH*SAMPLING) + (1|BLOCK) + (1|PLOT) + (1|PLOT:SAMPLING) + (1|PLOT:DEPTH)

Model Explanation:

  • (SOIL*PLANT*DEPTH*SAMPLING): This term represents the interaction between the fixed effects of the study.
  • (1|BLOCK): Random effect of blocking
  • 1|PLOT): Random effect of different plots
  • (1|PLOT:SAMPLING): SAMPLING nested within the PLOT. Account for the fact that the sampling were done always in the same plot.
  • (1|PLOT:DEPTH): DEPTH nested within the PLOT. Account for the fact that the different depths are sampled within each plot.

Specific Questions: a) Given that SAMPLING and DEPTH are nested within PLOT in the random effects, can these factors also be included as fixed effects in the model? My goal is to compare the different levels of depth and sampling with each other. Should they be included in both the random and fixed effects, or only in the random effects?

b) To test the significance of the fixed effects, I am considering using a likelihood ratio test to simplify the model. Is this approach appropriate for Linear Mixed Models?

If you have any alternative suggestions or recommendations for analyzing this data, I would greatly appreciate your insights.

Edit: I named SAMPLING wrongly in one of the descriptions. Now should be fine.

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  • $\begingroup$ are TIME and SAMPLING the same? $\endgroup$ Commented Aug 20, 2024 at 0:44
  • $\begingroup$ Sampling and time are the same. I edited the original post to correct it. PS: I really like your book for Ecological Modeling. Can't believe that you are really answering me here. Thanks for your help. $\endgroup$ Commented Aug 20, 2024 at 6:59

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Hello fellow soil enthusiast!

a) For DEPTH, depending on your questions, you may want to be a fixed effect - if you are specifically interested in understanding effects of depth. Keep in mind that if you have more than 2 levels of depth, you may need an approach that treats it as an ordered factor.

It is not clear to me what SAMPLING means in this example. Is this something to do with repeat measures on the same trial? Also not clear what the difference between BLOCK and PLOT is.

b) see some discussion here: Likelihood ratio tests on linear mixed effect models

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  • $\begingroup$ Hi Jacob, always good to talk with a fellow soil scientist, specially one that understand of statistics (lol) a) I have only two depths. So, I guess that this dows not applies to my case. But, anyway, this is really good to know, I was not aware. Yes, SAMPLING corresponds to repeated measures on the same Plot. BLOCK is the experimental design of the experiment. Each of the 6 replicates of the study is arranged in a block, like in the classical frequentists studies. PLOT is the identification of the field plot, which in my case is 2 plants*2soils*6 replicates on block design = 24 $\endgroup$ Commented Aug 20, 2024 at 7:22

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