Parresol 1999 and Parresol 2001 pointed out that biomass equations should be additive. He introduced two types of additive biomass equations: weighted seemingly unrelated regression (SUR) and nonlinear seemingly unrelated regression (NSUR). Although, there are some examples in the articles, but the whole procedure remained unclear for use. SUR can be calculated using systemfit r package. But I don't know how to calculate NSUR. Can I define the formula in r codes as nonlinear so I can calculate NSUR?
For NSUR you have to write nonlinear equations in the initial system, but I recommend you to make a previous analysis. Have a look at the variance of each biomass fraction by diameter class, in direct units. If a horizontal trend is showed, and you have a lot of data(> 300 data for example), try to fit the system wit nonlinear equations.
If you have only a few data, or a varying variance for each diameter class has been showed, you will need to fit the linearized (logarithm) system.
There is a lack of capability in the nlsystemfit R function. Also, you won't be able to fit a weighted regression, as there is no option in the function.
The solution is to develop o modify the function manually (statisticians do it better)
Dear García-Villabrille
Thank you for your response. You answered my question. As I found out, if I write a nonlinear formula in the initial system, the result will be NSUR. I have a couple of more question and if you kindly could answer, that would be appreciated.
The firs part of my research was to find the best fitted models between 8 proposed models (the attached file). Now that reviewers requested to run additive models, is it correct to run NSUR based on the selected models and write down the coefficients or I should do something else before best fit selection? And, should I write the total formula too in the initial system, because different models with different predictors has been selected as the best models, so I can not just simply sum up the coefficient for total.
Lots of thanks in advance,
First question:
You can run NSUR (nlsystemfit) with the best independent models, as they are spected to be the best in a previous step
Second question:
You have to specify:
Wtot ~ a0*D + b0*D*H,
being (for example)
a0*D=Wbranches
b0*D*H=Wstem
if you don't specify this, or you make another equation for Wtot then the system won't be an additive system.
In advance, I recommend you to use SAS for this kind of equations instead of R, although R is my working software.
Dear García-Villabrille
Thank you again. I guess I don't need to put the total model in the equations system through the analysis. Deriving the regression coefficient for tree components using NSUR guarantees that the total (#predicted) biomass will be equal to the sum of the predicted components biomass (being exactly equal will occur just in the case that we use the same predictors for different components). Am I right? What should I report for total? Parresol only wrote the components models. Maybe I should just report the result of standard regression procedure for total biomass!
Also, in some cases, the coefficients of the regression equations for the components change more than my expectation. By expectations, I mean the changes in the results of different Parresol studies. I don't know is there something wrong with the procedure I used or it depends on dataset.
Best wishes,
Hormoz
In R you need to specify the total model as the sum of the RHS of the other equations (other fractions)
Had you been get solution? Can you share to me how to do this? In the my Fitting Linear Simultaneous Equation, I got WARNING: "The covariance across equations (the S matrix) is singular" so Some estimates are marked 'Biased'
- Badges
- Science topic
- Similar topics
- Methodology
- Research Methodology
- Research Papers