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 19.34.

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;

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 19.35.