![]() ![]() If you are not familiar with multiple linear regression, you may want to read the introductory section to Multiple Regression at this point (however, it is not necessary to understand all of the nuances of multiple linear regression techniques in order to understand the methods discussed here). For this model, we assume the dependent variable to be a linear function of the independent variables, that is: In most general terms, we are interested in whether and how a dependent variable is related to a list of independent variables the term F(x…) in the expression above means that y, the dependent or response variable, is a function of the x‘s, that is, the independent variables.Īn example of this type of model would be the linear multiple regression model as described in Multiple Regression. In general, all regression models may be stated as: ![]() Technically speaking, Nonlinear Estimation is a general fitting procedure that will estimate any kind of relationship between a dependent (or response variable), and a list of independent variables. Let us now discuss the nonlinear regression problem in a somewhat more formal manner, that is, introduce the common terminology that will allow us to examine the nature of these techniques more closely, and how they are used to address important questions in various research domains (medicine, social sciences, physics, chemistry, pharmacology, engineering, etc.). The second issue that needs to be addressed is how to exactly compute the relationship, that is, how to arrive at results that allow us to say whether or not there is a nonlinear relationship as predicted. First, what types of relationships “make sense”, that is, are interpretable in a meaningful manner? Note that 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. When allowing for any type of relationship between the independent variables and the dependent variable, two issues raise their heads. (However, if all variables of interest are categorical in nature, or can be converted into categorical variables, you may also consider Correspondence Analysis.) Nonlinear Estimation leaves it up to you to specify the nature of the relationship for example, you may 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. Specifically, multiple regression (and ANOVA) assumes that the relationship between the independent variable(s) and the dependent variable is linear in nature. In fact, you may think of Nonlinear Estimation as a generalization of those methods. You may recognize research issues in these examples that are commonly addressed by such techniques as multiple regression (see Multiple Regression) or analysis of variance (see ANOVA/MANOVA). 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. In the most general terms, Nonlinear Estimation will compute the relationship between a set of independent variables and a dependent variable.
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