NLR problem

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I really need a help...

I am trying to learn how to use properly non-linear regression.

I got some data (I pasted some below) and theory about modelling this type
of data. I attached few scans.

My DATA is vary similar to what others researchers used on theirs examples.
I want to reproduce step by step all process.

The equation for modelling this type of data is known, I need to find
parameters, I tried to do this with NLR, but I failed...;(  




DATASET CLOSE all.
new file.


data list list
/age(f8.0) age_s(a3) var(f8.5).
begin data.
0 0 ,01491
1 1 ,03406
2 2 ,03537
3 3 ,04037
4 4 ,03079
5 5 ,02825
6 6 ,03621
7 7 ,02539
8 8 ,01810
9 9 ,01694
10 10 ,01718
11 11 ,01457
12 12 ,01602
13 13 ,01887
14 14 ,01079
15 15 ,01001
16 16 ,01013
17 17 ,00805
18 18 ,01308
19 19 ,00751
20 20 ,00653
21 21 ,00691
22 22 ,00930
23 23 ,01236
24 24 ,01734
25 25 ,02035
26 26 ,02734
27 27 ,03293
28 28 ,03696
29 29 ,03391
30 30 ,03638
31 31 ,03580
32 32 ,03183
33 33 ,03198
34 34 ,03009
35 35 ,02749
36 36 ,02683
37 37 ,02367
38 38 ,02265
39 39 ,02017
40 40 ,01838
41 41 ,01531
42 42 ,01493
43 43 ,01367
44 44 ,01318
45 45 ,01108
46 46 ,01015
47 47 ,00850
48 48 ,01000
49 49 ,00708
50 50 ,00901
51 51 ,00791
52 52 ,00680
53 53 ,00732
54 54 ,00706
55 55 ,00711
56 56 ,00702
57 57 ,00823
58 58 ,00689
59 59 ,00718
60 60 ,00737
61 61 ,00806
62 62 ,00667
63 63 ,00763
64 64 ,00811
65 65 ,00661
66 66 ,00654
67 67 ,00708
68 68 ,00602
69 69 ,00607
70 70+ ,00529
end data.
execute.
dataset name b1.
DATASET ACTIVATE b1.


*to make interval variable for aggregation

recode age
(lo thru 5=5)
(lo thru 10=10)
(lo thru 15=15)
(lo thru 20=20)
(lo thru 25=25)
(lo thru 30=30)
(lo thru 35=35)
(lo thru 40=40)
(lo thru 45=45)
(lo thru 50=50)
(lo thru 55=55)
(lo thru 60=60)
(lo thru 65=65)
(lo thru 70=70)
into age_c.
EXECUTE.

*Aggregation with mean

AGGREGATE
/OUTFILE=* MODE=ADDVARIABLES
/BREAK=age_c
/var5years=mean(var).
 

*Interpolation -  cubic splines with knots

do repeat a = 1 to 14/ b=knot1 to knot14.
compute b=a*5.
end repeat.
execute.

do repeat a=knot1 to knot14 / b=k1 to k14.
do if a le age.
compute b=1.
else.
compute b=0.
end if.
end repeat.
execute.

DATASET ACTIVATE b1.
DATASET DECLARE res_int.
MODEL PROGRAM  c0=0 c1=0 c2=0 c3=0  b3=0 b4=0 b5=0 b6=0 b7=0 b9=0 b10=0
b12=0 b13=0
b14=0 .
COMPUTE pred_int = c0 + c1*age + c2*(age**2) + c3*(age**3)
+ b3*((age-knot3)**3)*k3
+ b4*((age-knot4)**3)*k4
+ b5*((age-knot5)**3)*k5
+ b6*((age-knot6)**3)*k6
+ b7*((age-knot7)**3)*k7
+ b9*((age-knot9)**3)*k9
+ b10*((age-knot10)**3)*k10
+ b12*((age-knot12)**3)*k12
+ b13*((age-knot13)**3)*k13
+ b14*((age-knot14)**3)*k14
.
NLR var5years
   /OUTFILE='res_int'
  /PRED pred_int
  /SAVE PRED
  /CRITERIA SSCONVERGENCE 1E-8 PCON 1E-8.


*to see fitted values

DATASET ACTIVATE b1.
GRAPH
/line(MULTIPLE)=value(var var5years pred_int).


*I read that sum of all observation need to equal 1.

FREQUENCIES VARIABLES pred_int
/STATISTICS=sum
/FORMAT=NOTABLE.


compute pred_int = pred_int/1.17.
execute.

FREQUENCIES VARIABLES pred_int
/STATISTICS=sum
/FORMAT=NOTABLE.




*Using NLR to find parameter's value, equations (exponential) are known.
*Below equation with 11 parameters


dataset declare res.
MODEL PROGRAM  a1=0 alfa1=0 a2=0 alfa2=0 mi2=0 lambda2=0 a3=0 alfa3=0 mi3=0
lambda3=0
 c=0.
COMPUTE  pred=a1*exp(-alfa1*age) +
a2*exp(-alfa2*(age-mi2)-exp(-lambda2*(age-mi2)))
+ a3*exp(-alfa3*(age-mi3)-exp(-lambda3*(age-mi3)))
+ c.
NLR pred_int
  /OUTFILE='res'
  /PRED pred
  /SAVE PRED RESID
  /CRITERIA SSCONVERGENCE 1E-8 PCON 1E-8.


*to see predicted values

GRAPH
/LINE(MULTIPLE)=value(pred pred_int var).
*it is quite good fit on this graph, but I don't understand two things right
now:
*1) Why when I use estimated parameters and put them into original equation
values
*are far away from what was saved in dataset earlier as "pred" with NLR
command?

*Why predicted values (NLR command) and predicted got after filling original
equation with estimated values are not the same??????


*estimates values as variables

dataset activate b1.
compute a1=8.215.
compute alfa1=-0.004.
compute a2=-11.932.
compute alfa2=-0.014.
compute mi2=17.708.
compute lambda2=-0.005.
compute a3=-0.063.
compute alfa3=-0.052.
compute mi3=22.799.
compute lambda3=-0.192.
compute c=-4.408.
EXECUTE.

*using estimated values in original equation

COMPUTE  pred4=a1*exp(-alfa1*age) +
a2*exp(-alfa2*(age-mi2)-exp(-lambda2*(age-mi2)))
+ a3*exp(-alfa3*(age-mi3)-exp(-lambda3*(age-mi3)))
+ c.
EXECUTE.

* This is not the same....why?

GRAPH
/line(MULTIPLE)=value(pred pred4).


*2) Second problem might (or might not) be consequence of first problem, but
i will ask anyway.
* Parameters, which I got are far away from typical range, (why I am not
surprised;) )
e.g. a2 need to be within 0.5 - 0.10 . When my estimated values are out of
range i lose ability to interpret phenomenon what
* i try to analyse.

*But my first question is fundamental, I don't even know whether I found (or
not) right parameters....  










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