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I have very big experiment with 70 places around country. In each place there are several experimental plots where measures have been done. There were several measurement occasions during last 50 years. The whole experiment is unbalanced as the number of plots within experiment varies. My task is to analyze experiment. As it is unbalanced I'd like to use linear mixed model and R as a software. As far as I understand the concept of mixed models I'd like to use following:

dependent variable ~ (1|experiment_location) + (1|plot) 
                     +(1|measurement_time) + independent_variables

Can someone answer me if it is the right way to study the experiment? I read several posts at CrossValidated but I'm not a statistician and I have hard to understand them. Thus, I will be grateful for all kind of comments. BR

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The question is what do you want to estimate. Your model definition says that you want random intercepts for location, time and plot and a fixed intercept and slope for independent variables. What could be defined differently:

  • Is there any hierarchical structure? If you want to model changes across different locations through the time then locations are nested in time i.e. (1|time:location)
  • If you want to model what is the impact of independent variables in different locations then you could change your model definition to include e.g. (1 + variable|location)

there are also other possibilities that depend on your data structure and the questions you want to ask.

I personally would recommend you few (very readable) books:

  • Snijders, T.A.B. and Bosker, R.J. (2012). Multilevel Analysis: An Introduction to Basic and Advanced Multilevel Modeling. London: Sage Publishers.
  • Hox, J. (2010). Multilevel Analysis: Techniques and Applications. New York: Routledge.
  • Gelman, A. and Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models. Cambridge: Cambridge University Press.
  • Pinheiro, J.C. and Bates, D.M. (2000). Mixed-Effects Models in S and S-PLUS. New York: Springer.

There is also an online book on lme4 and an in press paper by authors of the package you could check.

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  • $\begingroup$ I went ahead with the question and realized that probably need more explanation. The final goal of the project is to create model which will predict dependent variable on a basis of independent variables. One of the problems is that plot is equal to the treatment which is defined by several independent variables. So far I’ve used the model with only “location” as random effect because I think that inclusion of plot as random can take some part of the variance due to the treatment. Moreover, my model so far gives strange results as there is no effect of independent variable which Id like to see $\endgroup$ – Legionista Feb 2 '15 at 14:37
  • $\begingroup$ If you have additional questions maybe ask them as a new question..? $\endgroup$ – Tim Feb 2 '15 at 14:43
  • $\begingroup$ Ok I do this. I just did not want to multiplicate similar question. $\endgroup$ – Legionista Feb 2 '15 at 14:48
  • $\begingroup$ It is not the same if you made some research and have some specific questions considering the problems you encounter now. I had an impression that your initial question is rather general and now you have a specific one. $\endgroup$ – Tim Feb 2 '15 at 14:52
  • $\begingroup$ Understood, I will re-submit it. $\endgroup$ – Legionista Feb 2 '15 at 14:54

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