LOSS Subcommand (NLR command)

LOSS specifies a loss function for CNLR to minimize. By default, CNLR minimizes the sum of squared residuals. LOSS can be used only with CNLR; it cannot be used with NLR.

  • The loss function must first be computed in the model program. LOSS is then used to specify the name of the computed variable.
  • The minimizing algorithm may fail if it is given a loss function that is not smooth, such as the absolute value of residuals.
  • If derivatives are supplied, the derivative of each parameter must be computed with respect to the loss function, rather than the predicted value. The easiest way to do this is in two steps: First compute derivatives of the model, and then compute derivatives of the loss function with respect to the model and multiply by the model derivatives.
  • When LOSS is used, the usual summary statistics are not computed. Standard errors, confidence intervals, and correlations of the parameters are available only if the BOOTSTRAP subcommand is specified.

Example

MODEL PROGRAM  A=1 B=1.
COMPUTE PRED=EXP(A+B*T)/(1+EXP(A+B*T)).
COMPUTE LOSS=-W*(Y*LN(PRED)+(1-Y)*LN(1-PRED)).
 
DERIVATIVES.
COMPUTE D.A=PRED/(1+EXP(A+B*T)).
COMPUTE D.B=T*PRED/(1+EXP(A+B*T)).
COMPUTE D.A=(-W*(Y/PRED - (1-Y)/(1-PRED)) * D.A).
COMPUTE D.B=(-W*(Y/PRED - (1-Y)/(1-PRED)) * D.B).
 
CNLR Y /LOSS=LOSS.
  • The second COMPUTE command in the model program computes the loss function and stores its values in the variable LOSS, which is then specified on the LOSS subcommand.
  • Because derivatives are supplied in the derivatives program, the derivatives of all parameters are computed with respect to the loss function, rather than the predicted value.