Need help defining terms for mixed model nested ANOVA

#1
Hello - I am looking at the effects of restoration practices on a suite of environmental soil parameters through time. I am having trouble defining the terms of my model. My experimental design is as follows:

  • 3 restoration categories: F, G, I.
  • On each treatment, there is a fertilization treatment: +/-
  • Because I am interested in the main effects of both restoration, fertilization, and the interaction, I believe this is 3x2 design.
  • Three randomly selected sites were sampled for each restoration+fertilization treatment, for a total of 18 sites.
  • These 18 sites were sampled immediately following the restoration implementation, and then the same sites were sampled repeatedly over a year, for a total of 5 sampling events.
  • Samples were sediment cores that were divided into depth horizons; I am treating sediment depth as a covariable
.

Whereas the site factor is not my primary interest, I would like to know if there are significant site effects.

I am having difficulty in defining the model terms and in particular any nesting that should involve site and/or time. I have seen repeated sampling designs with terms of time, treatment, and site nested in treatment, but I haven't been able to find examples of a 4-way example.

I am using Primer/Permanova for multivariate hypothesis testing, modeling, and ordination.

Many thanks for any advice!
 

noetsi

Fortran must die
#3
I have worked with nesting in the context of multiway analysis which is different than the design you are using, but I have a question. If you have found examples of nesting for 3 factors inside another, why do you assume that four factors nesting inside another would be done any different? And what are your four factors (I only see 3 in your model)?
 
#4
Hello - thanks for the response. I believe I have four factors: Restoration, Fertilization, Site, and Time. I believe Restoration and Fertilization are crossed. I have seen examples that nest site and or time into a single "treatment" type factor. However, I think that my design is different in that I have two "treatment" type factors: restoration (3 levels) and fertilization (2 levels). I visited the same sites through multiple sampling events. This is why I thought I needed to nest site in another factor, because sites across sampling events are not independent. But I don't know how to do that if I have two treatment factors. I have also seen designs with Site and Time that are not nested. I hope I am explaining this properly and I appreciate any additional advice you may have. Thanks!
 

noetsi

Fortran must die
#5
I am not enough of an expert in design of experiment to help. To me what you might consider is Confirmatory Factor Analysis which allows multiple factors to nest inside multiple factors and which allows lower level factors to nest inside more than one higher level factor (although this adds signficant complexity to the design). It can also address change over time, although that too adds complexity.

But this is entirely different than using ANOVA/DOE. And your question is probably, in honesty, beyond my level of expertise.