Dear everyone,
I am trying to obtain linear regression details for my linear mixed model (LMM) created with the lme4 package in R.
I have a regression-based environmental variance model (EVM) based on a LMM with Yield as response variable and four levels of Treatments (fixed effect) and Year is considered a random effect as it reflects the environment.
model2
R A Fisher published this problem solution in 1925 see the attachment. Google the paper and you can download it from several places. This is at best only a regression analysis with one covariate. If you really want to understand your research and experimental design work your problem this way. Best wishes and good luck with your research, David Booth ps Douglas Montgomery Design and analysis of experiments is a good thing to have as you deal with this problem and can be downloaded from the z-library. BTW. Fisher's collected works are available from a a library in Australia. DB
Looking at the table ---- but not at the original paper ---- it's not clear to me how you would have an intercept and a slope for each level of a treatment. In context of the paper, does a regression of "maize yield" on "environmental yield" make sense ? Is this is a similar design to your experiment ?
Dear Salvatore,
Thank you for your reply.
Indeed it might sound strange first to think of a intercept and a slope for each level of treatment. I can explain it a bit better, but otherwise I suggest you to take a look at the original paper. The authors use a regression-based environmental variance modelling approach to elucidate yield stability of each treatment. This is often used in plant breeding and ecological analysis and even in long-term crop genotype analysis field trials (see this paper for more details: Article Methods of yield stability analysis in long-term field exper...
). Hence, the intercept and slope is derived from this linear mixed model created for each treatment level, where Year = environment and Treatment = genotype. My question is: How can I re-create the analysis in R, that the authors conduct in SAS to obtain: Intercept with std.error., slope with std.error., RMSE etc. for each treatment level.Thank you
Note also that this question is asked here: https://stats.stackexchange.com/questions/563707/environmental-variance-model-how-to-obtain-slope-rmse-and-regression-p-values
Hi Sal Mangiafico ,
Thank you. I have not tried with SAS because I am not familiar with SAS and my original intention was alway to use R. Would you be able to try it out in SAS?
Sorry, I'm not familiar with kind of analysis. From what you explained,
"the intercept and slope is derived from this linear mixed model created for each treatment level, where Year = environment and Treatment = genotype",
it still doesn't make sense to me. However, I suspect that the table you present corresponds to this description in the Methods section of the paper,
"A simple linear regression of treatment means on the environmental means for each data set was conducted using PROC GLM of SAS (SAS Institute, 2008)."
Yes exactly! That is the description from the Methods section of the paper. So I am trying to build a model where environmental mean yields are the fixed effect and Treatment are the random effect. See the example of Figure 1 in this article Article Fertilizer Rate Effects on Forage Yield Stability and Nutrie...
where they use the same approach as in the original paper from where my data comes from. What I struggle with is to obtain the intercept and slope of the individual treatments, basically the regression equation and the accommodating std.error and RMSE.
I have proceeded by using the ggpmisc package (https://docs.r4photobiology.info/ggpmisc/) and adding regression formulas for each of the treatments e.g. see this post: https://stackoverflow.com/questions/61357383/label-ggplot-with-group-names-and-their-equation-possibly-with-ggpmisc However, I still need the RMSEs any suggestions? Also, I would prefer to have my results in a table.
For a model, RMSE is just the square root of (the sum of (the squared differences of each predicted value and actual value)). The calculation is easy. Sometimes getting the predicted and actual values out of the model object in R is a little tricky.