The MODEL Procedure

The options ITPRINT, ITDETAILS, XPX, I, and ITALL specify a detailed listing of each iteration of the minimization process.

### ITPRINT Option

The ITPRINT information is selected whenever any iteration information is requested.

The following information is displayed for each iteration:

N

is the number of usable observations.

Objective

is the corrected objective function value.

Trace(S)

is the trace of the S matrix.

subit

is the number of subiterations required to find a or a damping factor that reduces the objective function.

R

is the R convergence measure.

The estimates for the parameters at each iteration are also printed.

### ITDETAILS Option

The additional values printed for the ITDETAILS option are:

Theta

is the angle in degrees between , the parameter change vector, and the negative gradient of the objective function.

Phi

is the directional derivative of the objective function in the direction scaled by the objective function.

Stepsize

is the value of the damping factor used to reduce if the Gauss-Newton method is used.

Lambda

is the value of if the Marquardt method is used.

Rank(XPX)

is the rank of the matrix (output if the projected Jacobian crossproducts matrix is singular).

The definitions of PPC and R are explained in the section Convergence Criteria. When the values of PPC are large, the parameter associated with the criteria is displayed in parentheses after the value.

### XPX and I Options

The XPX and the I options select the printing of the augmented matrix and the augmented matrix after a sweep operation (Goodnight 1979) has been performed on it. An example of the output from the following statements is shown in Figure 18.34.

```   proc model data=test2;
y1 = a1 * x2 * x2 - exp( d1*x1);
y2 = a2 * x1 * x1 + b2 * exp( d2*x2);
fit y1 y2 / itall XPX I ;
run;
```

Figure 18.34 XPX and I Options Output
The MODEL Procedure
OLS Estimation

Cross Products for System At OLS Iteration 0
a1 d1 a2 b2 d2 Residual
a1 1839468 -33818.35 0.0 0.00 0.000000 3879959
d1 -33818 1276.45 0.0 0.00 0.000000 -76928
a2 0 0.00 42925.0 1275.15 0.154739 470686
b2 0 0.00 1275.2 50.01 0.003867 16055
d2 0 0.00 0.2 0.00 0.000064 2
Residual 3879959 -76928.14 470686.3 16055.07 2.329718 24576144

XPX Inverse for System At OLS Iteration 0
a1 d1 a2 b2 d2 Residual
a1 0.000001 0.000028 0.000000 0.0000 0.00 2
d1 0.000028 0.001527 0.000000 0.0000 0.00 -9
a2 0.000000 0.000000 0.000097 -0.0025 -0.08 6
b2 0.000000 0.000000 -0.002455 0.0825 0.95 172
d2 0.000000 0.000000 -0.084915 0.9476 15746.71 11931
Residual 1.952150 -8.546875 5.823969 171.6234 11930.89 10819902

The first matrix, labeled "Cross Products," for OLS estimation is

The column labeled Residual in the output is the vector , which is the gradient of the objective function. The diagonal scalar value is the objective function uncorrected for degrees of freedom. The second matrix, labeled "XPX Inverse," is created through a sweep operation on the augmented matrix to get:

Note that the residual column is the change vector used to update the parameter estimates at each iteration. The corner scalar element is used to compute the R convergence criteria.

### ITALL Option

The ITALL option, in addition to causing the output of all of the preceding options, outputs the S matrix, the inverse of the S matrix, the CROSS matrix, and the swept CROSS matrix. An example of a portion of the CROSS matrix for the preceding example is shown in Figure 18.35.

Figure 18.35 ITALL Option Crossproducts Matrix Output
The MODEL Procedure
OLS Estimation

Crossproducts Matrix At OLS Iteration 0
1 @PRED.y1/@a1 @PRED.y1/@d1 @PRED.y2/@a2 @PRED.y2/@b2 @PRED.y2/@d2 RESID.y1 RESID.y2
1 50.00 6409 -239.16 1275.0 50.00 0.003803 14700 16053
@PRED.y1/@a1 6409.08 1839468 -33818.35 187766.1 6409.88 0.813934 3879959 4065028
@PRED.y1/@d1 -239.16 -33818 1276.45 -7253.0 -239.19 -0.026177 -76928 -85084
@PRED.y2/@a2 1275.00 187766 -7253.00 42925.0 1275.15 0.154739 420583 470686
@PRED.y2/@b2 50.00 6410 -239.19 1275.2 50.01 0.003867 14702 16055
@PRED.y2/@d2 0.00 1 -0.03 0.2 0.00 0.000064 2 2
RESID.y1 14699.97 3879959 -76928.14 420582.9 14701.77 1.820356 11827102 12234106
RESID.y2 16052.76 4065028 -85083.68 470686.3 16055.07 2.329718 12234106 12749042

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