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 The MODEL Procedure

## Iteration History

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
the number of usable observations

Objective
the corrected objective function value

Trace(S)
the trace of the S matrix

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

R
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)
If the projected Jacobian crossproducts matrix is singular, the rank of the X'X matrix is output.

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 X'X matrix and the augmented X'X matrix after a sweep operation (Goodnight 1979) has been performed on it. An example of the output from:
   proc model data=test2 ;
y1 = a1 * x2 * x2 - exp( d1*x1);
y2 = a2 * x1 * x1 + b2 * exp( d2*x2);
fit y1 y2 / XPX I ;
run;

is shown in Figure 14.27.

 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

Figure 14.27: XPX and I Options Output

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

The column labeled "Residual" in the output is the vector X'r, which is the gradient of the objective function. The diagonal scalar value r'r is the objective function uncorrected for degrees of freedom. The second matrix, labeled "XPX Inverse," is created through a sweep operation on the augmented X'X 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 14.28.

 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

Figure 14.28: ITALL Option Cross-Products Matrix Output

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