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 The NLIN Procedure

## Troubleshooting

This section describes a number of problems that can occur in your analysis with PROC NLIN.

### Excessive Time

If you specify a grid of starting values that contains many points, the analysis may take excessive time since the procedure must go through the entire data set for each point on the grid.

The analysis may also take excessive time if your problem takes many iterations to converge since each iteration requires as much time as a linear regression with predicted values and residuals calculated.

### Dependencies

The matrix of partial derivatives may be singular, possibly indicating an over-parameterized model. For example, if b0 starts at zero in the following model, the derivatives for b1 are all zero for the first iteration.

```   parms b0=0 b1=.022;
model pop=b0*exp(b1*(year-1790));
der.b0=exp(b1*(year-1790));
der.b1=(year-1790)*b0*exp(b1*(year-1790));
```

The first iteration changes a subset of the parameters; then the procedure can make progress in succeeding iterations. This singularity problem is local. The next example displays a global problem.

You may have a term b2 in the exponent that is nonidentifiable since it trades roles with b0.

```   parms b0=3.9 b1=.022 b2=0;
model pop=b0*exp(b1*(year-1790)+b2);
der.b0=exp(b1*(year-1790)+b2);
der.b1=(year-1790)*b0*exp(b1*(year-1790)+b2);
der.b2=b0*exp(b1*(year-1790)+b2);
```

### Unable to Improve

The method may lead to steps that do not improve the estimates even after a series of step halvings. If this happens, the procedure issues a message stating that it is unable to make further progress, but it then displays the warning message

```   PROC NLIN failed to converge
```

and displays the results. This often means that the procedure has not converged at all. If you provided the derivatives, check them very closely and then check the sum-of-squares error surface before proceeding. If PROC NLIN has not converged, try a different set of starting values, a different METHOD= specification, the G4 option, or a different model.

### Divergence

The iterative process may diverge, resulting in overflows in computations. It is also possible that parameters enter a space where arguments to such functions as LOG and SQRT become illegal. For example, consider the following model:

```   parms b=0;
model y=x / b;
```

Suppose that y happens to be all zero and x is nonzero. There is no least squares estimate for b since the SSE declines as b approaches infinity or minus infinity. The same model could be parameterized with no problem into y = a*x.

If you have divergence problems, try reparameterizing, selecting different starting values, increasing the maximum allowed number of iterations (the MAXITER= option), specifying an alternative METHOD= option, or including a BOUNDS statement.

### Local Minimum

The program may converge to a local rather than a global minimum. For example, consider the following model:

```   parms a=1 b=-1;
model y=(1-a*x)*(1-b*x);
```

Once a solution is found, an equivalent solution with the same SSE can be obtained by swapping the values of a and b.

### Discontinuities

The computational methods assume that the model is a continuous and smooth function of the parameters. If this is not true, the method does not work. For example, the following models do not work:

```   model y=a+int(b*x);

model y=a+b*x+4*(z>c);
```

### Responding to Trouble

PROC NLIN does not necessarily produce a good solution the first time. Much depends on specifying good initial values for the parameters. You can specify a grid of values in the PARMS statement to search for good starting values. While most practical models should give you no trouble, other models may require switching to a different iteration method or an inverse computation method. Specifying the option METHOD=MARQUARDT sometimes works when the default method (Gauss-Newton) does not work.

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