Non-linear regression (NLR) with variance of residuals as the loss function

 

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* (Q) In a Non linear interpolation, how can I use the variance of the residuals as the loss function.

*(A) This is using example from page 98 of SPSS regression models 9.0.
* However the loss function is the variance of the residuals.
* This is NOT TRIVIAL because only transformations may be used to calculate the 
	loss functions. In addition, LAG cannot be used after the MODEL command.
* Raynald Levesque rlevesque@videotron.ca 2002/02/03.
* Visit my SPSS pages http://pages.infinit.net/rlevesqu/index.htm.

DATA LIST LIST /pop.
BEGIN DATA
3.895
5.267
7.182
9.566
12.834
16.985
23.069
31.278
38.416
49.924
62.692
75.734
91.812
109.806
122.775
131.669
150.697
178.464
END DATA.

COMPUTE decade=$CASENUM-1.
COMPUTE yr=1790+decade*10.
FORMATS decade yr(F8.0).
LIST.

SET MPRINT=no.
*//////////////////////.
DEFINE !leave (!POS=!TOKENS(1) /!POS=!TOKENS(1))
!DO !cnt=1 !TO 17
DO IF idx=!cnt.
LEAVE !CONCAT(v,!cnt).
END IF.
!DOEND
!ENDDEFINE.
*//////////////////////.
SET MPRINT=yes.
COMPUTE idx=$CASENUM.

* NonLinear Regression.
MODEL PROGRAM A=3.9 B=-0.29 C=200 .
COMPUTE pred_ = C/(1+EXP(A+ B * decade)).
COMPUTE resid_ = pop - PRED_.

* The next 3 lines copy all the resid_ values into the LAST case.
VECTOR v(18F8.0).
COMPUTE v(idx)=resid_.
!leave.

* Calculate variance of resid_. 
COMPUTE sigma2=SD(v1 TO v18)**2.
* Keep only the value calculated in the LAST case.
IF idx<18 sigma2=0.
* sigma2 is the LOSS function.

CNLR pop
  /OUTFILE='C:\\temp\\SPSSFNLR.TMP'
  /PRED pred_ 
  /LOSS sigma2
  /BOUNDS C >= 150
  /CRITERIA ITER 20 STEPLIMIT 2 ISTEP 1E+20 .
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