Linear vs. Nonlinear Models
Most people have difficulties in determining whether a model is linear
or nonlinear. Before discussing the issues of linear vs. nonlinear systems,
let's have a short look at some examples, displaying several types of discrimination
lines between two classes:
Have you already guessed the difference between linear and nonlinear models
? Here's the answer: linear models are linear in the parameters which
have to be estimated, but not necessarily in the independent variables.
This explains why the middle of the three figures above shows a linear
discrimination line between the two classes, although the line is not linear
in the sense of a straight line.
Another example of a linear model is shown in the figure below. It displays
a parabolic regression line, which of course has a curvature, but is a
linear model:
It's not the independent variable, x, which counts for linearity, but
the parameters of the model (in our parabolic example a, b, and c). From
this simple insight it follows that multiple
linear regression can be used to estimate the parameters of "curved"
models.
