Background
Nonlinear regression is a form of regression analysis in which the data is modeled by a function that is a nonlinear combination of the model parameters. This regression is inherently nonlinear in its parameters and cannot be transformed into a linear form.
Historical Context
Nonlinear regression techniques have evolved over time with advances in computational methods and mathematical modelling. Earlier limitations in computation constrained the extent to which nonlinear models could be practically utilized; however, modern computing allows for robust nonlinear regression analyses.
Definitions and Concepts
Nonlinear regression is fundamentally characterized by the inability to directly transform the nonlinearity in variable parameters into a simpler, linear relationship:
- Nonlinear Regression: A statistical technique in which the outcome variable is modeled as a nonlinear function of one or more explanatory variables.
- Nonlinear Least Squares: A method used to estimate the parameter values of a nonlinear model by minimizing the sum of the squared deviations between the observed and predicted values, assuming the function is continuously differentiable.
Major Analytical Frameworks
Classical Economics
Classical economics generally relies on linear models for simplicity; however, the emergence of more nuanced economic phenomena has brought more attention to nonlinear modeling.
Neoclassical Economics
Neoclassical economists may employ nonlinear regression in studying supply and demand, consumer behavior, and optimisation under constraints where nonlinear relationships exist.
Keynesian Economics
Nonlinear regression can be used in Keynesian economics for macroeconomic models, where certain variables such as government spending or investment display nonlinear effects on output.
Marxian Economics
Nonlinear models can be used to examine the complex relationships between variables like capital accumulation and labor dynamics within Marxian frameworks.
Institutional Economics
Nonlinear regression helps in capturing the nuanced and often complex dependencies between economic variables in different institutional settings.
Behavioral Economics
Behavioral economists use nonlinear regression to model bounded rationality, accounting for nonlinear behaviors and decisions under risk and uncertainty.
Post-Keynesian Economics
Post-Keynesian approaches leverage nonlinear regression to depict non-equilibrium dynamics in economic models.
Austrian Economics
Nonlinear approaches can be applied within Austrian economics to understand the spontaneous orders and emergent patterns within markets.
Development Economics
Research in development economics often involves nonlinear modeling to understand growth trajectories and disparities among developing countries.
Monetarism
Monetarist analyses sometimes apply nonlinear regression to forecast the impacts of monetary policy where linear relationships may not hold.
Comparative Analysis
Nonlinear regression offers greater flexibility than linear models in capturing the complexity of real-world phenomena. However, they require more sophisticated estimation techniques and greater computational power.
Case Studies
Studies in real-world applications of nonlinear regression include:
- Econometric analyses of market demand.
- Policy impact evaluations in macroeconomic studies.
- Behavioral data modeling to capture complex decision-making processes.
Suggested Books for Further Studies
- Nonlinear Econometric Modeling in Time Series by William A. Brock
- Nonlinear Regression Analysis and Its Applications by Douglas M. Bates and Donald G. Watts
- Nonlinear Time Series Models in Empirical Finance by Philip Hans Franses and Dick van Dijk
Related Terms with Definitions
- Linear Regression: A statistical method that models the relationship between a dependent variable and one or more independent variables using a linear function.
- Generalised Nonlinear Regression: A broader framework including models beyond the classical assumptions of regression.
- Spline Regression: A form of regression analysis involving piecewise polynomials joined together to form a flexible fit to given data.
This entry provides a comprehensive overview of nonlinear regression, highlighting its importance and distinctiveness in econometrics and statistical modeling.
