Non-Linear Regression (NLR) Models
- a type of continuous regression model whose function/estimator is non-linear with respect to the regression coefficients {𝜃1, …, 𝜃𝑝}
- provides greater flexibility to fit curves than linear regression models
- like OLS, nonlinear regression estimates the parameters {𝜃1, …, 𝜃𝑝} by minimizing the SSE. However, nonlinear models use an iterative algorithm rather than the linear approach of solving them directly with matrix equations. What this means for you is that you need to worry about which algorithm to use, specifying good starting values, and the possibility of either not converging on a solution or converging on a local minimum rather than a global minimum SSE
NLR - Model Types
Non-Linear Regression Models - takes an input vector 𝑥∊ℝ𝑛 as input and predicts the value of a scalar 𝑦∊ℝ as output (whose function/estimator is linear wrt the coefficients {𝜃0, …, 𝜃𝑝})
|
Non-Linear Regression Type |
Function Form Example |
|---|---|
|
power |
𝑦̂ = 𝜃1𝑥𝜃2 |
|
weibull growth |
𝑦̂ = 𝜃1 + (𝜃2- 𝜃1)·𝑒𝑥𝑝(-𝜃3𝑥𝜃4) |
|
𝑦̂ = 𝜃0 + 𝜃1𝑐𝑜𝑠(𝑥 + 𝜃4) + 𝜃2𝑐𝑜𝑠(2𝑥 + 𝜃4) |