SPSS data Analysis-Nonlinear regression

The first satisfying condition of linear regression is the linear relationship between the dependent variable and the independent variable, and then the fitting method is based on it, but if the dependent variable and the independent variable are nonlinear, then the nonlinear regression is needed to analyze it.

There are two processes that can be called in the nonlinear regression of SPSS, one is analysis-regression-curve estimation, the other is analysis-regression-nonlinearity, the two methods are different, which is also two kinds of analysis method of nonlinear regression, the former is through variable transformation, the curve linearization, and then using linear regression to fit The latter is fitted directly to the non-linear model.

We propose a set of data for each contract in two ways, comparing the results.

Analysis-regression-curve estimation





The method of variable conversion is simple and is preferred in some cases, but it can only fit into a relatively simple (optional) nonlinear relationship, and the method has some drawbacks, such as

1. By using the results of the least squares fitting for variable conversion, it is not necessarily the optimal solution after the transformation back to the original value, and the variable conversion may change the distribution and independence of the residuals.
2. When the curve relationship is complex, it cannot be linear by variable transformation
3. After the curve is straight, it can only be fitted by the least squares method, and the other fitting methods cannot be achieved.

Based on the above problems, the nonlinear regression model can be solved very well, as well as the linear regression model, it also proposes a basic model framework, the difference is that the expected function in the model can be any form, or even no expression, on the parameter estimation, because it is a curve, can not directly use the least squares to estimate, A Gaussian-Newton method is needed to estimate the method, which is more dependent on the initial value setting.

Let's fit directly into the non-linear model to see how the results

Analysis-Regression-nonlinearity





The above two kinds of variance to fit, from the decision coefficient seems to be a better non-linear regression, but it should be noted that the curve regression calculation of the decision coefficient is a variable conversion, and does not necessarily represent the transformation before the interpretation of the degree of variation, which also shows that the decision coefficient is not necessarily comparable. We can judge the merits and demerits by comparing the predicted values calculated by the two methods with the residual plots, and first save the relevant results as variables, then make the diagram

SPSS data Analysis-Nonlinear regression