Solving Iteration Problems - How Iteration Procedures Work

When iteration begins, each parameter in your model has an initial value, or start value. These values are "plugged in" to your model equations and used to generate an estimated covariance matrix. This estimated covariance matrix is compared to the actual sample covariance matrix, and the value of the discrepancy function is calculated.

The program then has to decide how to alter the parameter values to improve the discrepancy function value, i.e., make it smaller. The program calculates a step direction, using an approximation procedure called the Gauss-Newton method. A step increment vector is calculated, and added to the original parameter estimates to produce a new set of values.

The program takes this new set of values and computes a new value of the discrepancy function. If the discrepancy function has improved sufficiently, the program goes on to the next iteration. If you are anywhere near the correct solution, this is generally what will happen. The process will then continue smoothly until you reach the minimum, usually in 20 iterations or less.