Nonlinear ModelsIt is a mathematical expression that is used to express the nonlinear relationship between the independent variable and the dependent variable. Compared with the linear model, its dependent variable and independent variable cannot express a linear relationship in the coordinate space.

Nonlinear function definition

If the explanatory variable X changes with the dependent variable $latex {\beta}$latexβ is a constant, then the regression model is a variable linear model if $latex {\beta}$latexβ is not a constant, then the regression model is a variable nonlinear model.

The general form of the nonlinear model is:$latex {\mathop{{Y}}\nolimits\_{{i}}=f \left( \mathop{{X}}\nolimits\_{{i1}},\mathop{{X}}\nolimits\_{{i2}},…,\mathop{{X}}\nolimits\_{{ik}}, \beta \mathop{{}}\nolimits\_{{1}},…, \beta \mathop{{}}\nolimits\_{{j}} \left) + \mu \mathop{{}}\nolimits\_{{i}}\right. \right. }$latexY_i=f(X_i1,X_i2,…,X_ik,β_1,…,β_j)+μ_i

where $latex {\mathop{{Y}}\nolimits\_{{i}}}$latexY_i is the explained variable; $latex {\mathop{{X}}\nolimits\_{{i1}},\mathop{{X}}\nolimits\_{{i2}},…,\mathop{{X}}\nolimits\_{{ik}}}$latexX_i1,X_i2,…,X_ik is the explanatory variable; $latex {\beta \mathop{{}}\nolimits\_{{1}},…, \beta \mathop{{}}\nolimits\_{{j}}}$latexβ_1,…,β_j is the model parameter; $latex {\mu \mathop{{}}\nolimits\_{{i}}}$latexμ_i is the disturbance term; $latex f( \beta \mathop{{}}\nolimits\_{{1}},…, \beta \mathop{{}}\nolimits\_{{j}} )$latexf(β_1,…,β_j) is a nonlinear function, and the number of explanatory variables k is not necessarily equal to the number of parameters j.

Difference between linear and nonlinear models

Linear models can use curves to fit samples, but the decision boundary of the classification must be a straight line, such as the Logistics model; in addition, whether it is a linear model can be determined by the coefficient w before the independent variable x. If w only affects one x, then this model is a linear model, otherwise it is a nonlinear model.