Non Linear estimation is used to compute the relationship that exists between a set of independent variables and one dependent variable. For instance, the researcher may want to compute the relationship that exists between the dose of drugs and its effectiveness, the relationship that exists between training and subsequent performance of a task and the relationship. For instance the relationship between a house and the amount of time it takes to sell it.
We often research issues getting addressed by the use of simple techniques such as multiple regression or ANOVA. Non-linear estimation may be a generalisation of those methods. When we talk of multiple regressions we assume that the relationship that exists between the variables is on linear nature. When we talk of non-linear estimation, it leaves on the researcher to specify the nature of the relationship. For example, the researcher may specify the dependent variable to be a logarithm function of the independent variable an exponential function.
When trying to establish the relationship between the independent and dependent variable, there are two concerns of importance. The first thing is what type of relationship is meaningful and correct interpretations can be made. Simple linear relationship is very convenient when making interpretations. The second issue that is needed to be addresses is to know the method in which the relationship is to be computed. That is how to arrive at results that allow saying whether to predict or not a non-linear relationship.
Non-linear estimation techniques give way for the specification of any type of continuous or discontinuous regression model. The common non-linear models are probit, logit, exponential growth and breakpoint regression. It is also possible to define any type of regression equation to be able to fit into your data. It is also possible to specify standard least squares estimation, maximum likelihood estimation by the process of equation definition.
Whenever in research , the simple regression model does not prove to represent the relationship between the variables adequately then it may be advisable to choose the non-linear estimation method.