NonLinear Regression n n 2212021 What is it

Non-Linear Regression n n 2/21/2021 What is it? Why and when to use? Model assumptions Typical non-linear models Obtaining parameter estimates AGR 206 1

Non-linear regression n What is it? u Model u Types is non-linear in the parameters. of models: F Linear. F Intrinsically u Non-linear. non-linear. regression minimizes SSE numerically, by trying many values of the parameter estimates. u Properties of parameters and predictions cannot be derived with equations. 2/21/2021 AGR 206 2

When and why to use? n Function relating Y to X's is known on the basis of a mechanistic understanding of the process. u n Parameters of the model have a direct biological meaning. The model may offer the only way to empirically estimate the value of the parameter. u n 2/21/2021 For example, the logistic growth model is based on the fact that for some populations, individuals compete for resources and reduce each other's growth rate linearly as density increases. In the previous example, the parameters of the logistic equations are the intrinsic relative growth rate (r) and carrying capacity (K). Nonlinear models may characterize responses better with fewer parameters than linear ones, even when no apriori functional form is available. AGR 206 3

Exponential growth 2/21/2021 AGR 206 4

Two-term exponential 2/21/2021 AGR 206 5

Mitscherlich’s response 2/21/2021 AGR 206 6

Mitscherlich graph 2/21/2021 AGR 206 7

Michaelis-Menten 2/21/2021 AGR 206 8

Segmented Model 2/21/2021 AGR 206 9