If you are far away from the solution point, several things can go wrong.
Besides calculating the direction to step the parameters, the program
also has to decide how far to step. As the parameters near the solution
point, the discrepancy function graph is usually rather flat and smooth,
and the program can gauge very accurately how far to step. However, when
the parameters are far from the correct solution, both the step direction
and step size may be inaccurate.

The way line search algorithms work is they multiply the step increment vector by a constant (usually less than 1), use this altered vector to recompute new parameter values, and recompute the discrepancy function. If the discrepancy function has not improved, they try again, etc. Hence, when the initial step does not work well, you will see a slowdown in iteration and values of Lambda in the Iteration Results dialog that are less than 1. In some cases, iteration may seem to "hang up" briefly. Ultimately, iteration will cease, with a very small value of Lambda and Steplen.

If the program cannot find a multiple of the step increment vector that
reduces the discrepancy function, it means the program has chosen a very
bad step direction, or possibly that the program has iterated to a "saddle
point."

There are other telltale signs that indicate that you have iterated
into a "bad" region of parameter space.

An indication that this has happened is that the

When the program ends up in such an unfortunate situation, there is
little you can do but to try again.

For the maximum likelihood discrepancy function to be computable, both
the sample covariance and the covariance matrix reproduced by your model
and parameter estimates must be nonsingular. Sometimes during iteration,
the program steps to values that yield a singular estimated covariance
matrix. If this happens, iteration will terminate immediately.

If iteration hangs due to any of the above conditions, there are several things to try:

If iteration failed using arbitrary initial values (the default), try the Automatic option for Initial Values in the Analysis Parameters dialog box. These values may get closer to a solution than arbitrary starting values, especially when the covariance matrix is ill-scaled, i.e., has variables that vary widely in variance.

Often, a large step is taken on the first few iterations. Sometimes, this step will carry the parameters into a region from which the iterative process cannot recover. Consequently, one thing to try is to reduce the step size the program is allowed to take. Try reducing the step size to a small value (like .1) and see what happens. Keep in mind that iteration to a solution will take longer under these conditions. During the early phases of iteration, the program will indicate that the largest allowable step size has been taken by placing an asterisk next to the

StepLen value printed in the Iteration dialog window.Sometimes iteration will fail with one line search algorithm but succeed with another. Try an exact (Golden Search) line search by selecting this option in the Line Search Method group in the Analysis Parameters dialog.

When iteration encounters problems early, it is often because the approximate Hessian is too inaccurate far from the solution to be of use in calculating a proper step direction. In such cases, inserting steepest descent iterations at the beginning of iteration will eliminate the problem. Steepest descent iterations use only first derivative information in selecting a step direction, and do not employ the approximate Hessian calculated by the Gauss-Newton procedure.

If you are testing your model on the covariance matrix, try testing it on the correlation matrix instead. In many situations, models that fail to iterate properly with an ill-scaled covariance matrix will work fine when tested on the correlation matrix.

Keep in mind that you may need to try several of the above options in combination to produce successful iteration. Feel free to experiment.

Remember that a badly miss-specified model may fail to fit properly. One of the common mistakes beginners make is to forget to add disturbance terms to endogenous latent variables. The Structural Modeling Wizard will add these for you automatically, but if you are copying a model from a path diagram, remember that some authors consider disturbance terms to be "implicitly obvious," and don't bother to put them in the diagram itself.