Some Nonlinear Modeling - shaking off some rusty knowledge.

[iiibbb]

Hello--

I have a data set that shows a nonlinear response.  I was trying to model it to the generic Y=AB**X algebraic curve.  Since I need to reflect and translate it I think the form is

Y = [AB**(-X+H)] + K

/* where: Y is the response */
/* -X reflects Y=AB**X */
/* A and B affect the shape the curve */
/* H translates the curve on the X axis */
/* K translates the curve on the Y axis */

However, when I run PROC NLIN, the procedure doesn't try to optimize a value for H.  It just accepts the value I set in the PARM statement.  The model it creates fits okay, but I am forced to wonder if I am doing this right since I haven't done my own non-linear model in quite some time.

I am not opposed to using another function either, but I am rusty on my algebra.  Comments on my choice of function would also be welcome.

I am aware of the observation at line 106  

7.044 28.2205

----------code------------

data a;
input X csfc;

cards;
19.894 2.1695
14.357 3.1134
14.634 2.8468
16.849 2.8502
20.73 2.0644
21.313 1.885
21.078 2.0202
22.711 1.828
18.571 2.2236
17.324 5.1571
16.833 2.3027
7.787 5.2283
13.571 3.2182
16.709 2.4278
103.36 1.9032
14.626 2.7794
11.961 4.0494
16.649 2.4224
11.9 3.1598
12.037 3.4
15.27 2.7087
15.71 3.1774
16.64 2.4366
22.985 1.8892
13.589 3.0338
13.231 3.5303
9.916 2.3978
16.875 2.6956
15.502 2.6239
62.418 1.8696
67.368 1.9096
12.707 4.5418
13.646 3.5238
12.347 3.7747
10.492 5.9589
12.92 5.6311
15.703 4.804
15.945 3.7153
17.812 2.906
19.456 2.3938
16.081 2.8086
15.193 2.8184
12.06 3.7871
11.997 3.464
13.977 3.0224
17.165 2.3578
9.955 4.2154
10.078 3.8764
11.896 3.5085
10.837 3.8571
8.536 4.7339
8.312 4.9184
9.301 4.9311
10.705 3.8221
9.366 5.0422
22.31 2.5539
21.365 2.1591
21.251 2.1821
19.524 2.2874
19.934 2.1676
13.886 3.8416
15.718 2.8793
14.531 3.3531
14.332 3.3009
17.202 2.7417
16.869 2.4636
14.337 3.108
16.054 2.7407
10.45 6.3506
34.281 1.8753
40.231 1.6295
34.453 1.8897
38.428 1.7759
40.005 1.6519
90.734 0.9022
36.63 1.726
35.402 1.7388
76.791 0.8395
35.249 1.6582
48.56 1.2963
39.266 1.6639
44.37 1.452
41.683 1.4932
45.59 1.5308
74.01 0.8218
45.272 1.376
44.352 1.5411
37.685 1.8526
42.117 1.7654
38.659 1.7523
45.305 1.537
46.625 1.4801
45.971 1.435
42.783 1.4562
39.755 1.6883
47.272 1.4124
43.601 1.5922
49.839 1.8895
49.527 1.5169
46.418 1.5731
55.454 1.3089
7.044 28.2205
48.519 1.5486
48.658 1.4955
54.508 1.5457
46.313 1.7545
9.346 5.3788
9.147 5.1461
10.428 5.0431
18.505 2.7788
16.651 3.2919
22.862 2.5291
25.334 2.0102
12.182 4.1494
10.23 5.3308
9.134 5.0723
8.594 5.6128
10.669 4.3122
9.316 5.1614
16.287 3.1224
12.83 3.883
63.214 1.586
58.959 1.3681
55.911 1.6491
65.894 1.8837
56.965 1.3704
56.958 1.3552
62.972 1.3213
78.47 1.2049
64.248 1.348
72.855 1.1896
63.487 1.41
57.215 1.3024
56.201 1.4495
60.765 1.3704
65.9 1.3719
62.118 1.3137
26.976 1.7391
26.521 1.5494
29.442 1.6611
26.807 1.5139
26.365 1.5992
30.367 1.5658
21.368 2.3015
14.443 3.1963
19.454 3.3426
21.448 2.1596
14.986 5.916
20.085 2.3998
27.787 1.7884
26.624 1.809
32.641 1.5445
23.44 2.1039
65.804 1.8539
21.747 1.873
28.834 1.4601
25.411 1.6552
21.637 1.9228
37.783 1.3651
32.867 1.9354
34.038 1.0684
29.043 1.5156
38.605 1.7499
42.605 1.4879
38.399 0.8986
37.153 1.3436
18.009 1.5775
19.849 1.7135
19.305 1.9004
20.067 1.6874
20.61 1.6846
23.473 1.5383
16.409 2.246
32.881 1.0103
20.855 1.6756
22.072 1.5011
22.399 1.5077
22.422 1.6045
28.705 1.5148
21.491 2.0123
24.138 1.6838
23.237 1.5113
18.886 1.7919
23.216 1.4259
23.471 1.4605
23.227 1.5253
25.337 1.3194
19.049 1.7622
19.681 1.8024
20.113 1.6858
19.748 1.8308
26.875 1.2624
31.016 1.1567
16.783 2.9245
21.099 1.6738
20.545 1.6725
18.909 2.8377
32.773 1.1761
26.978 1.2892
36.644 1.7227
23.856 1.4219
22.931 1.4248
22.589 1.6277
13.077 2.6969
19.172 1.9055
12.508 2.0986
24.206 1.4886
;;
run;

/* CSFC by X appears to follow a modified version of AB**X */
/* */
/* Y = AB**(-X + H) + K */
/* */
/* where: Y is the response */
/* -X reflects Y=AB**X */
/* A and B affect the shape the curve */
/* H translates the curve on the X axis */
/* K translates the curve on the Y axis */

proc nlin data=a;
parameters A = 1
B = 1.0125
H = 17
K = 2;

model CSFC = A * B**(-X + H) + K;

* output out=pred p=Yhat l95m=low_conf u95m=up_conf sse=sse;
run;

[PGStats · Accepted solution]

Try this instead:

proc nlin data=a plots=fitplot;
parameters 
A = 1
B = 0
H = -1
K = 2;
model CSFC = A * (X-B)**H + K;
run;

[iiibbb]

Wonderful.

So my algebra is the weak link.  Thank you.

The last time I had to fit a curve this way was 2004.  Thanks.