How to proceed non-linear regression by the mitscherlich model?

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Hello, good afternoon!

need to perform a nonlinear regression analysis nls(), and suggested me the mitscherlich model:

inserir a descrição da imagem aqui

I don’t know how to accomplish, I’d like your help!

follows the example of the data:

dados<-structure(list(TEMPO = c(4, 4, 4, 7, 7, 7, 10, 10, 10, 15, 15, 
15, 20, 20, 20, 25, 25, 25, 30, 30, 30, 35, 35, 35, 40, 40, 40
), COM = c(102.7408349, 46.42860925, 46.42860925, 193.9867874, 
77.78158526, 77.78158526, 259.2226911, 142.9585464, 142.9585464, 
338.2513753, 201.6268249, 201.6268249, 540.8096753, 230.0649675, 
230.0649675, 621.6945295, 243.5781577, 356.2446836, 678.4896365, 
303.6745224, 532.1778946, 731.7253377, 317.1877126, 621.6366503, 
794.4532011, 353.1853056, 688.7228286)), class = "data.frame", row.names = 82:108)
r regression
  • 2

    A first step is to rotate ?nls inside the R console. See examples of using the function and, if you don’t understand something, edit your question with your question.

  • can’t run nls(), usually always asks for initial kicks, and I don’t know how to put this formula inside the function nls(), apparently alpha means the expected maximum value, as it doesn’t exist, I’m using the found maximum, gamma would be "b" I do not know for sure, and theta for the little that I could understand has to do with the slope of the line (I do not know if it is a straight), I saw several works that use the model but do not explain how they use :/ I would like help! variable x is "TIME", and the response variable is "COM". Reference values to the total mineralized organic carbon.

1 answer

3


The setting is not good but follows:

fm <- nls(COM ~ Alfa*(1-10^(-Gama*(TEMPO+Tetha))),
                 data = dados,
                 start = list(Alfa = 900, Gama = .1, Tetha = 1))
summary(fm)

# Parameters:
#   Estimate Std. Error t value Pr(>|t|)
# Alfa   1.785e+03  3.844e+03   0.464    0.647
# Gama   4.703e-03  1.265e-02   0.372    0.713
# Tetha -6.293e-01  4.629e+00  -0.136    0.893

plot(COM~TEMPO,dados)
lines(dados$TEMPO,predict(fm),col=3)

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  • 1

    The setting’s not as bad as that, hist(resid(fm)) gives Gaussian.

  • In this case, as I must do, unfortunately, I have no statistical knowledge of non-linear analyses :/

  • Is this data real, is it multiple measurements per period? Model analysis is similar to other linear models

  • these data are only a dismemberment of a factorial 3, the ai time represents inoculation days, when it rotates, the Anova to factorial 3, the adjustment tends to a quadratic regression, with plateau, so according to her advisor, who is not in the area of statistics requested an adjustment for an asymptotic distribution model, indicating that of mitscherlich, who saw that Pimentel-Gomes presents in the book: Statistics Applied to Agricultural and Forestry Experiments.

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