Nonlinear Estimation - Parameter Estimation

Click the OK button in the Model Estimation dialog box to display the Parameter Estimation dialog box. STATISTICA will begin the iterative estimation process and display the resulting iterations, loss values, and parameter estimates in the Parameter Estimation dialog box.  

Summary box. The Summary box at the top of the dialog box displays the headings of the Parameter Estimation dialog box.

Copy button. Click the Copy button to copy either the selected text (if text has been selected) in the Summary box or all of the text (if no text has been selected) to the Clipboard. Note that the copied text retains formatting information (such as font, color, etc.).

Contract/Expand button. Click the Contract/Expand button to contract or expand the Summary box. When contracted, you can see only one line of the Summary box text and can scroll through the text using a scroll bar. Note that when contracted the text is scrolled so that the first non-blank line is at the top. When expanded (the default setting), the entire Summary box will be displayed on the Parameter Estimation dialog box.

Cancel. Click the Cancel button to close this dialog box and return to the Model Estimation dialog box.

OK. Click the OK button to display the Results dialog box.

Note: When the Estimation Process Does Not Converge. In general, follow these steps to estimate the parameters for any nonlinear regression model:

  1. First, accept the default values for the starting parameters, step sizes, and convergence criterion.

  2. If the estimation procedure does not converge, set the convergence criterion to 0.1, and then experiment with the start values (try different sets of reasonable values).

  3. If the estimation process continues to "go astray," change the step sizes to smaller values (e.g., 0.05).

  4. The different estimation procedures in Nonlinear Estimation use very different minimization algorithms (see Nonlinear Estimation Procedures), each with its own strengths and weaknesses. If problems persist, switch to a different estimation procedure.  Try them in the order suggested by the respective dialog, that is, begin with the Simplex method. Start with the default settings for all parameters. However, you may want to increase the maximum number of iterations (Simplex usually requires more, but each iteration is faster). Next use the Hooke-Jeeves method, and finally, try the Rosenbrock method.

  5. Continue to experiment with the starting values and step sizes. For example, Simplex sometimes converges more easily when the convergence criterion is set to the minimum (0.0000001). If Simplex returns a very large loss value (e.g., 1E+37), it indicates that the estimation got "trapped" with illegal parameters; continue to change the start values and step sizes.

  6. Try combining the methods of estimation. Because the Simplex, Hooke-Jeeves, and Rosenbrock methods are generally less sensitive to local minima, you may use any one of these methods with the quasi-Newton method. This is particularly useful if you are not sure about the appropriate start values for the estimation. In that case, the first method may generate initial parameter estimates, that will then be used in subsequent quasi-Newton iterations.  

Nonlinear regression is not well suited for exploratory data analysis purposes. Rather, the researcher should bring to the analysis some understanding of the nature of and relationships between variables. Such understanding will suggest appropriate models that can be estimated, and start values that are fairly close to the actual parameters. Given such prior understanding of one's data, and some experience with the different estimation methods, it is usually not difficult to fit models that "make sense" and satisfactorily reproduce the data.