The Nonlinear Estimation module computes the relationship between a set of independent variables and a dependent variable. For example, we may want to compute the relationship between the dose of a drug and its effectiveness, the relationship between training and subsequent performance on a task, the relationship between the price of a house and the time it takes to sell it, etc.

You may recognize these examples are commonly addressed by such techniques as multiple regression or analysis of variance. In fact, you may think of nonlinear estimation as a generalization of those methods. Whenever the simple linear regression model does not appear to adequately represent the relationships between variables, then the nonlinear regression model approach is appropriate.

Multiple regression and ANOVA assume that the relationship between the independent variable(s) and the dependent variable is linear in nature. Nonlinear estimation leaves it up to you to specify the nature of the relationship. For example, you can specify the dependent variable to be a logarithmic function of the independent variable(s), an exponential function, a function of some complex ratio of independent measures, etc.

This module supports user-specified regression least squares, user-specified regression with custom loss function, Quick Logit regression, Quick Probit regression, Exponential growth regression, and Piecewise linear regression.

If all variables of interest are categorical in nature or can be converted into categorical variables, you can also consider using Correspondence Analysis.

Note that nonlinear regression techniques can be considered hypothesis testing procedures. Therefore they should generally not be used for exploratory data analyses.

Second note... The simple linear relationship is very convenient in that it allows us to make such straightforward interpretations as "the more of x (e.g., the higher the price of a house), the more there is of y (the longer it takes to sell it); and given a particular increase in x, a proportional increase in y can be expected." Nonlinear relationships cannot usually be interpreted and verbalized in such a simple manner.

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