Methods and starting values for Nonlinear Regression

Find definitions and interpretation guidance for every statistic in the Method table.

Algorithm

In nonlinear regression, there is no direct solution for minimizing the error sums of squares (SSE). Thus, an iterative algorithm estimates parameters by systematically adjusting the parameter estimates to reduce the SSE. For each iteration, the algorithm adjusts the parameter estimates in a manner that it predicts should reduce the SSE compared to the previous iteration. Different algorithms use different approaches to determine the adjustments at each iteration. The iterations continue until the algorithm converges on the minimum SSE, a problem prevents the subsequent iteration, or Minitab reaches the maximum number of iterations.

Interpretation

Use the algorithm information to verify that you performed the analysis as you intended. If the algorithm fails to converge, you can try the other algorithm or change the other starting conditions.

Max iterations

The maximum number of iterations is the point at which Minitab stops the iterative algorithm if it fails to converge on a solution. Nonlinear regression uses an iterative algorithm to reduce the error sums of squares (SSE). For each iteration, the algorithm adjusts the parameter estimates in a manner that it predicts should reduce the SSE compared to the previous iteration. The iterations continue until the algorithm converges on the minimum SSE, a problem prevents the subsequent iteration, or Minitab reaches the maximum number of iterations.

Interpretation

Use the maximum iterations information to verify that you performed the analysis as you intended. If the algorithm fails to converge, you can try increasing the number of iterations or change the other starting conditions.

Tolerance

The tolerance defines how small the change in the error from one step to the next must be to declare that the iterative algorithm has converged on a solution. By default, Minitab declares convergence when the relative offset is less than 1.0e-5. This assures that any inferences are not affected materially by the fact that the current parameter vector is less than 0.001% of the radius of the confidence region disk from the least squares point.

Smaller values can produce more precise parameter estimates but require additional iterations. Usually, the default value works well.

Starting values for parameters

The Starting Values for Parameters table displays the values that you specified for each parameter. Nonlinear regression uses an iterative algorithm to reduce the error sums of squares (SSE). The algorithm starts by setting the parameter values to equal the values in this table. For each iteration, the algorithm adjusts the parameter values in a manner that it predicts should reduce the SSE compared to the previous iteration.

Interpretation

Use the starting values to verify that you performed the analysis as you intended. If the algorithm fails to converge, you can try different starting values or change the other starting conditions.

Note

For some models and data sets, the starting values can significantly affect the results. Certain starting values may lead to failure to converge or convergence to a local, rather than global, SSE minimum. In some cases, you may need to expend considerable effort to develop good starting values.

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