Model Estimation - Advanced Tab

Select the Advanced tab of the Model Estimation dialog box to access the options described here.

Estimation method. The Estimation method box contains six options from which you select an estimation procedure. There are four different estimation procedures available in Nonlinear Estimation, which can also be combined. These methods and their strengths and weaknesses are described in Nonlinear estimation procedures. For more information on the options in the Estimation method box, see Model Estimation - Quick tab.

Asymptotic standard errors. Select the Asymptotic standard errors check box if you want to compute the standard errors for the parameter estimates (and the variance/covariance matrix of parameter estimates). These standard errors are computed via finite difference approximation of the second-order partial derivatives (i.e., the Hessian matrix; refer to Nonlinear Estimation Procedures for details). Note that the Summary: Parameters & standard errors button in the Results dialog is only available if this check box is selected.

Eta for finite diff. approx., 1.E-. The standard errors for the parameter estimates are computed via finite differencing. Specifically, the matrix of second-order partial derivatives is approximated. In order to obtain accurate estimates for the derivatives, some a priori knowledge is necessary of the reliability of the loss value. This reliability can be expressed as parameter h (Eta ) so that h = 10-Digits; where Digits is the number of reliable base-10 digits computed from the loss function. By default (i.e., when this check box is selected) STATISTICA automatically estimates h (by checking the "responsiveness" of the loss function to small changes in the parameter values). However, in some cases, when the magnitudes of the first order partial derivatives for two or more parameters are very different, the default estimation of h may not be optimal. In that case, you can enter a user-defined constant; specifically, the integer value entered into the box to the right of the  Eta for finite diff. approx., 1.E- check box will be interpreted as the Digits in h.

In practice, experiment with this parameter (start with the default value of 10-8) in cases when the parameter estimation converges with reasonable values, but when requesting the spreadsheet with parameter values and their standard errors (from the Results dialog box) the message appears: Matrix ill-conditioned; cannot compute standard errors.

Note that the Eta for finite diff. approx., 1.E- check box is only available if the Asymptotic standard errors check box is selected (see above).

Maximum number of iterations. Use the Maximum number of iterations box to specify the maximum number of iterations to be performed. The estimation of parameters in nonlinear regression is an iterative procedure (see Nonlinear Estimation Procedures). At each iteration, STATISTICA evaluates whether the fit of the model (to the data) has improved from the previous iteration.

Convergence criterion. Use the Convergence criterion box to change the convergence criterion value (by default, 0.0001). The exact meaning of this parameter depends, among other things, on the estimation method that is selected. Refer to Fletcher (1972) for details about the quasi-Newton method; refer to O'Neill (1971) or Nelder and Mead (1965) for a discussion of the Simplex procedure; refer to Fletcher and Reeves (1964), and Hooke and Jeeves (1961) for details concerning the Hooke-Jeeves method and the Rosenbrock pattern method.

Start values. Click the Start values button to display the Specify start values dialog box, in which you enter the individual start values for each parameter or one common value for all parameters. When you return to the Model Estimation - Advanced tab, the field adjacent to the Start values button will display "Various" if there are different values in the list of start/step values, or "xxx for all parameters" if the parameters are all the same, and valued xxx.

Initial step sizes. Click the Initial step sizes button to display the Specify initial step sizes dialog box, in which you enter the individual step size values for each parameter or one common step size for all parameters. Use this dialog to change the default step size (0.5 for quasi-Newton, 1.0 for Simplex and Rosenbrock, 2.0 for Hooke-Jeeves). The step size values are used during the initial iterations to "scale" the problem, that is, to determine by how much to move each parameter. The exact impact of these values on the estimation depends, among other things, on the estimation method that is selected.