dear members,
I have the following nls call:
> HF53nl <- nls(HF1 ~ ((m/HF6) + 1),data = data.frame(HF6,HF1),start =
list(m = 0.1))
> overview(HF53nl)
------
Formula: HF1 ~ ((m/HF6) + 1)
Parameters:
Estimate Std. Error t value Pr(>|t|)
m 2.147e-07 1.852e-06 0.116 0.908
Residual standard error: 0.03596 on 799 degrees of freedom
Number of iterations to convergence: 1
Achieved convergence tolerance: 1.246e-06
------
Residual sum of squares: 1.03
------
t-based confidence interval:
2.5% 97.5%
1 -3.420983e-06 3.850292e-06
------
Correlation matrix:
m
m 1
The scatter plot of HF6 and HF1 and the corresponding fitted line according to
the above output of nls is attached(HF53nl). The fitted line is almost a
straight line. But it should be a curve something of: y ~ 1/x. I think the very
small value of m is making the curve a straight line.
But the fitted curve of the following call makes sense(attached: HF43nl):
> HF43nl <- nls(HF1 ~ ((k/HF5) + 1),data = data.frame(HF5,HF1),start =
list(k = 0.1))
> overview(HF43nl)
------
Formula: HF1 ~ ((k/HF5) + 1)
Parameters:
Estimate Std. Error t value Pr(>|t|)
k -5.367e-04 5.076e-05 -10.57 <2e-16 ***
---
Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
Residual standard error: 0.03368 on 799 degrees of freedom
Number of iterations to convergence: 1
Achieved convergence tolerance: 3.076e-07
------
Residual sum of squares: 0.906
------
t-based confidence interval:
2.5% 97.5%
1 -0.0006363717 -0.0004370954
------
Correlation matrix:
k
k 1
The queer thing is that the RSS for HF53nl and HF43nl is almost the same, which
points to the purported validity of HF53nl. How is this possible? Can I go with
the above estimates for the coefficient m of HF6 being equal to 2.147 * 10^(-7)?
How do I make an nls call so that there is a better fit to HF1 and HF6.
NB: If you can't access the attached graphs, how do I send it to you
otherwise? I can also give you HF1,HF6,HF5 if needed....
very many thanks for your time and effort....
yours sincerely,
AKSHAY M KULKARNI
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dear members,
On a closer inspection, I can see that the
scatterplot of HF1 and HF5 is of the form y ~ -(1/x), while that of HF1 and HF6
is of the form y ~ (1/x). Is it possible that HF43nl is converging almost due to
chance? I mean, for HF53nl, a straight line minimizes the RSS rather than for a
curve like y ~ (1/x). Is it possible? If that is the case, should I model it
linearly rather than nonlinearly? It is unsettling(this would always gives the
wrong prediction given a predictor!). Or rather picewise nonlinear
regression(for HF6 < 0 and HF6 > 0)?
very many thanks for your time and effort....
yours sincerely,
AKSHAY M KULKARNI
________________________________________
From: R-help <r-help-bounces at r-project.org> on behalf of akshay
kulkarni <akshay_e4 at hotmail.com>
Sent: Thursday, March 21, 2019 5:26 PM
To: R help Mailing list
Subject: [R] problem with nls....
dear members,
I have the following nls call:
> HF53nl <- nls(HF1 ~ ((m/HF6) + 1),data = data.frame(HF6,HF1),start =
list(m = 0.1))
> overview(HF53nl)
------
Formula: HF1 ~ ((m/HF6) + 1)
Parameters:
Estimate Std. Error t value Pr(>|t|)
m 2.147e-07 1.852e-06 0.116 0.908
Residual standard error: 0.03596 on 799 degrees of freedom
Number of iterations to convergence: 1
Achieved convergence tolerance: 1.246e-06
------
Residual sum of squares: 1.03
------
t-based confidence interval:
2.5% 97.5%
1 -3.420983e-06 3.850292e-06
------
Correlation matrix:
m
m 1
The scatter plot of HF6 and HF1 and the corresponding fitted line according to
the above output of nls is attached(HF53nl). The fitted line is almost a
straight line. But it should be a curve something of: y ~ 1/x. I think the very
small value of m is making the curve a straight line.
But the fitted curve of the following call makes sense(attached: HF43nl):
> HF43nl <- nls(HF1 ~ ((k/HF5) + 1),data = data.frame(HF5,HF1),start =
list(k = 0.1))
> overview(HF43nl)
------
Formula: HF1 ~ ((k/HF5) + 1)
Parameters:
Estimate Std. Error t value Pr(>|t|)
k -5.367e-04 5.076e-05 -10.57 <2e-16 ***
---
Signif. codes: 0 ?***? 0.001 ?**? 0.01 ?*? 0.05 ?.? 0.1 ? ? 1
Residual standard error: 0.03368 on 799 degrees of freedom
Number of iterations to convergence: 1
Achieved convergence tolerance: 3.076e-07
------
Residual sum of squares: 0.906
------
t-based confidence interval:
2.5% 97.5%
1 -0.0006363717 -0.0004370954
------
Correlation matrix:
k
k 1
The queer thing is that the RSS for HF53nl and HF43nl is almost the same, which
points to the purported validity of HF53nl. How is this possible? Can I go with
the above estimates for the coefficient m of HF6 being equal to 2.147 * 10^(-7)?
How do I make an nls call so that there is a better fit to HF1 and HF6.
NB: If you can't access the attached graphs, how do I send it to you
otherwise? I can also give you HF1,HF6,HF5 if needed....
very many thanks for your time and effort....
yours sincerely,
AKSHAY M KULKARNI
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One of the assumptions made by least squares method is that the residuals are independent and normally distributed with same parameters (or, in case of weighted regression, the standard deviation of the residual is known for every point). If this is the case, the parameters that minimize the sum of squared residuals are the maximum likelihood estimation of the true parameter values. The problem is, your data doesn't seem to adhere well to your formula. Have you tried plotting your HF1 - ((m/HF6) + 1) against HF6 (i.e. the residuals themselves)? With large residual values (outliers?), the loss function (i.e. sum of squared residuals) is disturbed and doesn't reflect the values you would expect to get otherwise. Try computing sum((HF1 - ((m/HF6) + 1))^2) for different values of m and see if changing m makes any difference. Try looking up "robust regression" (e.g. minimize sum of absolute residuals instead of squared residuals; a unique solution is not guaranteed, but it's be less disturbed by outliers). -- Best regards, Ivan
dear Ivan,
I've not gone into residual analysis; but my observation
is simple: I've checked the hist of both HF5 and HF6. There is not much
difference. Also I've replaced all outliers.
HF1 ~ (m/HF5 )+ 1 is getting fitted properly, but not HF1 ~ (m/HF6) + 1.
The following are the actual values:
> HF1
Time Series:
Start = 1
End = 800
Frequency = 1
[1] 1.0319256 0.9842066 1.0098243 1.0446384 0.9177308 1.0060822 0.9609599
1.0374124 1.0139675 0.9973329 0.9559346 0.9848896
[13] 0.9749513 1.0511627 0.9789968 1.0964832 0.9879833 0.9549759 0.9787043
1.0203225 0.9947078 0.9813439 1.0138056 0.9670097
[25] 0.9711946 0.9873085 1.0858024 1.0394149 0.9766102 0.9689002 1.0097453
1.0235376 0.9873976 0.9705998 1.0356838 1.0165155
[37] 0.9855907 1.0757638 1.0072182 1.0280799 0.9281543 0.9587241 1.1086856
1.0446199 1.0158398 0.9529567 1.0610853 0.9976204
[49] 0.9575143 0.9803208 1.1238821 1.0118991 1.0112989 0.9415333 1.0424331
0.9912462 1.0106361 0.9802978 1.0108935 1.0159902
[61] 0.9892313 0.9438749 1.0118004 0.9953912 0.9175923 0.9479009 1.0235502
1.0060517 0.9890903 0.9885812 0.9900430 1.0350717
[73] 1.0108698 1.0468498 1.0656555 1.0436655 0.9908752 0.9751098 1.0163194
0.9851445 0.9710072 0.9885114 1.0109649 1.0490736
[85] 0.9795251 1.0108749 1.0029784 1.0149087 0.9965277 0.9893746 0.9917926
1.0115123 1.0472170 1.0437206 1.0139089 1.0372349
[97] 1.0038352 0.9586151 1.0085806 1.0119048 1.0118624 0.9896469 1.0272961
1.0172400 1.0134005 0.9757968 0.9717420 1.0269058
[109] 1.0114416 0.9512890 1.0181753 1.0565599 1.0376291 0.9865798 1.0212159
1.0701965 1.0324734 0.9899814 0.9973403 1.0172419
[121] 1.0020050 0.9889063 1.0129236 1.0277797 0.9826509 0.9922282 1.0988522
1.0275115 1.0183555 0.9774303 1.0172997 1.0150803
[133] 0.9685015 0.9924186 0.9937192 1.0072210 0.9673327 1.0473338 1.0562761
0.9707440 0.9771936 0.9883559 1.0208805 0.9894798
[145] 1.0694593 0.9754638 1.0383527 1.0013232 0.9863309 0.8778824 1.0157532
1.0438316 1.0000022 0.9740199 1.0305441 1.0275372
[157] 0.9723386 0.9954525 1.0046082 0.9531964 0.9768512 0.9899314 1.0496263
1.0546074 0.9616430 1.0210772 0.9901334 1.0689765
[169] 1.0154938 0.8765444 0.9919604 1.0082690 0.9860675 0.9823378 0.9897682
1.0363582 0.9805102 0.9723787 1.0741545 1.0290322
[181] 0.9760903 0.9850951 1.0500385 0.9774908 0.9861186 0.9898369 0.9941887
1.0097938 1.0187774 1.0591694 1.0270933 1.0466363
[193] 1.0000043 0.9815685 1.0238718 0.9740055 0.9717232 1.0251001 0.9946316
1.0075567 0.9751129 0.9871612 1.0643235 1.0075491
[205] 0.9888058 0.9396797 1.0068366 0.9962325 1.0455487 1.0442334 1.0103938
1.0236919 0.9852552 0.9767037 1.0063593 1.0518584
[217] 0.9705860 0.9718808 1.0178662 1.0414515 0.9883699 0.9860597 1.0394941
1.0103630 0.9082023 0.9889798 0.9646139 1.0052705
[229] 0.9688456 1.0559528 1.0401153 0.9785603 1.0169463 0.9929363 0.9812825
0.9302532 1.0272447 1.0644704 1.0201468 1.0248872
[241] 0.9587034 0.9884793 1.0065787 1.0568458 1.0167972 0.9702934 1.0233577
1.0052691 0.9690838 0.9900543 1.0171212 1.0093782
[253] 0.9518359 0.8953816 1.1180924 1.0126421 0.9847542 0.9731075 0.9906067
1.0191311 0.9757062 0.9819144 1.0392988 1.0358210
[265] 0.9842700 1.0057314 1.0206313 1.0088607 0.9779384 0.9860996 0.9894232
1.0180867 1.0060215 0.9419578 1.0604701 1.0186874
[277] 0.9824626 0.9303484 1.0491317 1.0204767 0.9892820 0.9971268 1.0322837
1.0435960 1.0123649 0.9791956 0.9880841 1.0203823
[289] 0.9696436 0.9769832 1.0704628 1.0230000 0.9665417 0.8624573 1.0152342
1.0538081 0.9885551 0.9605257 1.0196322 1.0135050
[301] 1.0420189 0.9875982 1.0228686 1.0224319 0.9778704 0.9912653 1.0116106
1.0226598 0.9387455 0.9717815 1.0122788 0.9889690
[313] 1.0232488 1.0276606 1.0173681 1.0159885 0.9877074 0.9838069 1.0374707
1.0152624 0.9789677 0.9612178 1.0192874 1.0644549
[325] 0.9715407 0.9787567 0.9925342 0.9790322 0.9777879 0.9680505 1.0224064
1.0348370 0.9875051 0.9457753 0.9914921 0.9591109
[337] 0.9629202 0.9995519 1.0136481 1.0221348 1.0148608 0.9912785 1.0439862
1.0330749 0.9762325 0.9983923 0.9348918 1.0227065
[349] 0.9794121 0.9733227 1.0082373 1.0421889 0.9767361 0.9726911 1.0100370
0.9921361 0.9861159 0.9749961 1.0594331 1.0806732
[361] 1.0276992 1.0329190 1.0686383 1.0466639 0.9740776 0.9672371 1.0128714
0.9934691 0.9582222 0.9332858 1.0029784 1.0250300
[373] 1.0059249 0.9999445 1.0082015 1.0252359 0.9760324 0.9493543 0.9996351
1.0116540 0.9675301 0.9470141 1.0127507 1.0112527
[385] 0.9766712 0.9703953 1.0592567 1.0360448 0.9790881 0.9680051 0.9711350
1.0049626 0.9738689 0.9819661 1.0835125 0.9765333
[397] 0.9138484 1.0220322 1.0465788 1.0065803 1.0273082 0.9838126 1.0151329
1.0146824 0.9452442 0.9489901 0.9921946 1.0101152
[409] 0.9730738 0.9354592 0.9542558 0.9681532 0.9792620 1.0352246 1.0426173
1.0180344 0.9576323 0.9533448 0.9846387 1.0261479
[421] 0.9453757 0.9455791 1.0691109 1.0084141 0.9844405 0.9537970 1.0118840
1.0094733 1.1493009 0.9922558 0.9941628 1.0290179
[433] 1.0020050 0.9971342 1.0436267 1.0726863 1.0925811 1.1072580 1.0390200
1.0376942 1.0302470 0.9838505 1.0420336 0.9793092
[445] 0.9850191 1.0196805 1.0065491 1.0158645 1.0117730 0.9406381 1.0097070
0.9870108 0.9818856 1.0040046 0.9712323 0.9951345
[457] 1.0199816 1.0551752 1.0112867 1.0763534 1.0253155 1.0029784 1.0251464
1.0814414 0.9987183 0.9771628 0.9726044 1.0482059
[469] 1.0020050 0.8931139 1.0367775 1.0260033 0.9728766 1.0225689 0.9908196
1.0068729 0.9912127 0.9931128 1.0158280 1.0433496
[481] 1.0203120 1.0085496 0.9812741 1.0615742 1.0119223 0.9849236 0.9992032
0.9879929 0.9000571 0.9891419 1.0345521 1.0381184
[493] 0.9886766 0.9574869 1.0149106 1.0294410 0.9882982 1.0244778 0.9812230
1.0082813 0.9664091 1.0283733 1.0124268 0.9992115
[505] 0.9872004 0.9884649 1.0386713 0.9763343 0.9597727 0.9567414 1.0086152
1.0165768 0.9848861 0.9620526 1.0123326 1.0447678
[517] 0.9934084 0.9669690 1.0360421 0.9829837 0.9761610 0.9708850 1.0014170
1.0195497 0.9806560 0.9757284 1.0251931 1.0116233
[529] 0.9868054 0.9756085 1.0303624 1.0077517 1.0505017 0.9414114 1.0124536
1.0131595 0.9638660 0.9887363 1.0132553 1.0052792
[541] 0.9820370 0.9460134 1.0125483 1.0426700 0.9818528 0.9762532 0.9582658
0.9814603 0.9618717 0.9615659 0.9496436 0.9877108
[553] 0.9999971 1.0284677 1.0106125 1.0031898 0.9793703 0.9486161 1.0226473
1.0236002 0.9538295 0.9689285 1.0313897 1.0212912
[565] 0.9505638 0.9921170 1.0130086 1.0419494 1.0000323 0.9607922 1.0211809
1.0424671 0.9795343 0.9497697 1.0231071 1.0142700
[577] 0.9765539 0.9492815 1.0267628 1.0135138 0.9885966 0.9529603 1.0264062
1.0249176 0.9872525 0.9849608 0.9986306 1.0437033
[589] 1.0041780 0.9931204 1.0329029 0.9939742 0.9459785 0.9629758 0.9456565
0.9836949 0.9754926 0.9976241 1.0232742 1.0050830
[601] 0.9481952 0.9854969 1.0352188 1.0337062 0.9892019 0.9554122 1.0189333
0.9793607 0.9899167 0.9503345 1.0117583 1.0371750
[613] 1.0070349 0.9804208 1.0500940 1.0107281 1.0698735 0.9881469 1.0565684
1.0179031 0.9856278 1.0314952 1.0720689 1.0011222
[625] 0.9743944 1.0034468 0.9824861 1.0192735 0.9991494 0.9842630 1.0060971
1.0294506 0.9695057 0.9725408 1.0227924 1.0088150
[637] 0.9765886 0.9889828 1.0108903 1.0068109 0.9905286 0.9517037 1.0527706
1.0257783 0.9932039 1.0121870 1.0506565 0.9816386
[649] 0.9843450 0.9552800 1.0124886 1.0332463 1.0021401 0.9885442 1.0136001
1.0381933 0.9594773 1.0679251 0.9653448 0.9997715
[661] 0.9890589 0.9658054 1.0079124 1.1292276 0.9873225 0.9730770 1.0699042
1.0174021 1.0041981 1.0232245 1.0389181 0.9720513
[673] 0.8686271 0.9915428 0.9606290 1.0482094 0.9898013 0.9510998 0.9602020
0.9976802 1.1427011 0.9917742 0.9770992 0.8638270
[685] 0.9991782 1.0455336 1.1043633 1.0489159 1.0029784 0.9906192 1.0307161
1.0182152 0.9677313 1.0090984 0.9851279 0.9596324
[697] 0.9743092 0.9748568 1.0206321 1.0517142 0.9876535 0.9732838 1.0656093
1.0603864 0.9980164 0.9795437 0.9746766 0.9784871
[709] 0.9746066 1.0484975 1.0228157 1.0165735 0.9785301 1.0322862 1.0303562
1.0203352 0.9606113 1.0674109 1.0051598 1.0095761
[721] 1.0138837 0.9862772 1.0173451 0.9879873 0.9761662 0.9828150 0.9839169
0.9887962 0.9474475 0.9786754 1.0405266 1.0246702
[733] 0.9764242 0.9782060 1.0004626 1.0653315 1.1480925 0.9567859 1.0410088
1.0246378 1.0025964 0.9894414 1.0146759 1.0449204
[745] 0.9917509 0.9706269 1.0199806 1.0044524 0.9942750 1.0145927 0.9917488
1.0314604 0.9495737 1.0005564 0.9972033 0.9849848
[757] 0.9741118 0.9693319 1.0061280 0.9892915 0.9944768 1.0101943 1.0545997
1.0044063 1.0020050 1.0127975 1.0164313 1.0285558
[769] 1.0043574 0.9854983 1.0122655 1.0123857 0.9879603 0.9734764 0.9995228
1.0315182 0.9564373 1.0543879 1.0099970 0.9987432
[781] 0.9580883 0.9724853 1.0167722 1.0102822 0.9629902 0.9908875 0.9838395
0.9733901 1.0207349 0.9848377 1.0633785 1.0312998
[793] 1.0316422 1.0335433 0.9890110 1.0334082 0.9915590 0.9909167 1.0208474
0.9899497
> HF6
Time Series:
Start = 1
End = 800
Frequency = 1
[1] 9.703261e-02 -3.302060e-01 5.100922e+00 1.932550e+00 -1.386912e-01
1.482268e-02 -1.137384e+00 3.732522e-01 2.506729e-01
[10] -2.919045e-01 -6.675508e-02 -1.267444e+00 -4.271286e-01 1.539651e-01
-1.424168e-01 2.632788e-01 -6.013491e-02 -5.743224e-02
[19] -1.955379e-01 7.423308e-01 -3.041726e-03 -2.667225e-02 2.409421e-01
-4.339732e-02 -2.372542e-01 -2.194143e-01 2.712374e-01
[28] 1.764577e+00 -1.583502e-01 -1.558412e-01 4.859185e+00 6.595212e-02
-6.227563e-02 -3.663468e-02 9.338089e-01 1.165410e+00
[37] -3.776054e-02 1.015936e+01 4.269841e+00 8.659153e-01 -1.045996e+00
-8.061952e-01 2.627137e-01 1.023131e-01 2.757644e-01
[46] -6.199723e-02 1.466399e-01 -3.353696e-01 -2.881873e-01 -1.560865e-01
2.946743e-01 1.825263e-01 6.075510e-01 -7.659018e-02
[55] 9.332004e-02 -7.924914e-01 -2.995696e+00 -2.625424e-01 6.959834e+00
2.882190e-01 -5.555718e-02 -3.191530e+00 -2.894247e+00
[64] -7.495410e-01 -5.698178e-01 -2.920025e-01 7.262345e-02 6.955618e-01
-7.509777e-01 -3.111461e-02 -1.757717e+00 9.583333e-02
[73] 2.022944e-01 1.481875e-01 3.709509e-01 3.297667e+00 -1.679928e-02
-6.633111e-01 3.081464e-01 -1.522342e-01 -2.697393e-01
[82] -2.474069e-01 1.267182e+00 2.990766e-01 -1.483910e-01 1.851073e-02
-3.320246e+00 5.365467e-01 3.685251e-02 -5.869044e-02
[91] -5.304953e-01 8.510204e-02 -1.943394e+00 6.796528e-01 8.707915e+00
5.339946e-01 3.334323e-01 -5.567989e-01 1.741750e-01
[100] 3.974109e-01 -1.180250e-01 -3.248193e-01 2.839601e-01 8.396776e-01
1.587400e+00 -1.052848e-01 -5.427561e-02 1.308345e+00
[109] -4.321102e+00 -2.114642e+00 2.545551e-01 2.608206e-01 2.468002e-01
-3.503397e-01 8.657229e-02 4.993098e-01 2.432785e+00
[118] -1.896142e-02 -2.014234e+00 2.029458e+00 6.079714e+00 -2.764164e-01
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[127] 2.728479e+00 2.063365e+00 3.873700e-01 -9.717373e-01 2.802471e-01
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[136] 1.453974e-01 -9.212878e-01 6.660146e-01 2.698844e-01 -2.378487e-01
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[199] 7.658868e+00 1.125989e+00 -1.923856e-01 -2.441550e+00 5.024290e-01
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[217] -2.189162e-01 -1.161234e+00 6.972145e-01 2.780796e-01 -6.312992e-02
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[226] -8.490826e-01 -1.288512e-01 4.011994e-02 -2.048321e-01 3.272460e+00
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[280] 7.426660e-01 -6.825884e-02 -3.435546e-02 1.707858e+00 2.714363e-01
2.583534e-01 -1.856543e-01 -2.983154e-02 1.084806e+00
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[298] -6.363805e-01 8.216420e-01 2.398677e+00 2.481079e-01 -1.493501e+00
1.788803e+00 4.053156e-01 -1.932145e-01 -1.698920e-01
[307] 3.829476e+00 1.608798e+00 -1.129716e-01 -1.141733e+00 1.621158e+00
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[316] 2.501457e+00 -7.836369e-02 -1.908722e-01 1.028320e+01 5.647405e-02
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[325] -3.025440e-01 -9.047322e-02 -6.460067e-01 -6.844164e-01 -1.881830e-01
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[334] -2.220902e-01 -3.856785e+00 -1.094635e+00 -7.540428e-02 3.058904e-02
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[343] 1.553016e-01 2.089815e+00 -1.232086e+00 -6.334727e-03 -7.148192e-01
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[352] 2.434295e-01 -1.831071e-01 -9.457498e-01 2.459490e+00 -4.414135e-02
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[361] 4.049245e+00 2.017318e+00 2.488363e-01 2.780003e-01 -1.550511e+00
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[370] -1.594693e-01 -6.449885e+00 8.850238e-01 2.298414e-01 2.548747e-02
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[379] -9.192395e-03 1.659781e+00 -3.100714e-01 -2.432555e+00 2.493722e+00
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[388] 1.873401e+00 -3.159656e-01 -1.063461e+00 -2.275333e-01 2.545551e-01
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[397] -1.404096e+00 5.942892e-01 1.850712e-01 2.305337e+00 1.519311e+00
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[406] -1.422570e-01 -1.017652e-01 6.907890e-01 -2.043544e-01 -1.268577e-01
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[415] 2.758053e-01 5.519530e-01 -4.779812e+00 -8.598340e-01 -2.733269e-01
1.746146e+00 -1.152102e-01 -1.696746e-01 8.731155e+00
[424] 4.202525e-01 -8.863015e-02 -1.811685e+00 1.030848e+00 6.446866e+00
4.923567e+00 -2.394358e-02 -1.384412e-01 1.970634e-01
[433] 5.853398e+00 -5.313277e-01 2.451911e-01 5.068814e-01 1.001283e+01
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[442] -6.436663e-01 2.865144e-01 -2.985307e+00 -7.993755e-02 6.913159e+00
1.263291e-01 4.946523e-01 2.384704e-01 -2.053579e-01
[451] 1.041425e+00 -3.840293e-02 -2.728177e-01 1.088364e-01 -2.959904e+00
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[460] 5.289729e-01 9.353198e-02 -5.891475e+00 2.352159e-01 1.773673e+00
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[469] 5.832009e+00 -1.372102e+00 3.681388e-01 2.022951e-01 -1.088937e+00
1.301919e+00 -1.351298e-01 1.666197e+00 -4.925816e-01
[478] -2.756112e-01 4.107335e-01 2.707616e-01 2.778384e-01 2.869210e-01
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[487] -6.508053e-02 -5.386767e-02 -1.319746e+00 -5.511262e-01 2.439812e-01
3.581400e-01 -1.816593e-02 -2.177485e+00 1.568457e+00
[496] 2.416807e+00 -6.700124e-01 1.588973e-01 -8.862605e-02 2.121985e-01
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[505] -9.119583e-02 -1.900989e-01 3.154147e-01 -5.464995e-01 -2.187182e-01
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[514] -6.472309e-01 3.239172e-01 2.761212e-01 -1.826730e-01 -1.782663e-01
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[523] 2.251821e-01 5.553531e-01 -2.023192e-01 -9.014496e-01 6.563737e-01
4.016597e-01 -9.749756e-02 -6.402956e-02 2.750496e-01
[532] 2.754876e-01 3.293551e-01 -5.005642e+00 3.231129e-01 2.545811e-01
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[550] -1.742599e-01 -1.984759e+00 -8.682619e-02 2.071753e-02 1.087379e+00
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[559] 8.950929e-02 2.394501e+00 -2.165059e+00 -1.233829e-01 2.701741e+00
2.282062e+00 -1.924431e+00 -2.082254e-01 3.412529e-01
[568] 2.607147e-01 1.124918e-03 -1.203852e-01 2.657898e+00 1.957524e-01
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[577] -2.326451e-01 -8.473731e-01 6.189609e-01 5.287915e-01 -7.740822e-01
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[586] -2.170038e-01 -2.635905e-02 2.472973e-01 3.868325e-02 -1.159021e-01
2.500380e-01 -6.085198e-01 -1.899817e-01 -1.431927e-01
[595] -3.052454e+00 -3.469223e-01 -2.444967e-01 1.652156e-02 2.119758e-01
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[604] 2.756286e+00 -3.906295e-01 -1.484883e-01 6.719161e-01 -3.866083e-01
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[613] 9.538629e-02 -2.011244e-01 2.984296e-01 2.771165e+00 8.282686e+00
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[622] 2.470832e-01 5.270764e-01 3.958194e-01 -6.165985e-02 5.335154e-01
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[631] 9.252352e-01 6.461865e-01 -4.461937e-01 -7.364934e-01 2.285105e+00
7.138954e-01 -2.720298e-01 -8.693912e-01 2.993691e+00
[640] 8.028559e-01 -6.743009e-02 -5.307888e-01 3.119620e-01 3.434619e+00
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[649] -3.553324e-01 -1.896185e+00 3.446842e+00 7.830310e-01 -1.711669e+00
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[658] 8.163954e-01 -7.261633e-01 -1.299687e-02 -8.016282e-02 -1.140658e-01
1.323860e+00 2.545551e-01 -2.675428e-01 -8.433672e-01
[667] 5.228999e-01 1.632592e-01 -2.957998e-01 -5.553013e-01 3.011379e-01
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[685] 2.999499e-01 3.040171e-01 7.464381e+00 6.972166e+00 -8.403415e+00
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[694] 5.528044e-01 -3.616451e-01 -1.591170e-01 -5.733156e-01 -3.732071e-01
1.612954e+00 4.521562e-01 -2.379350e-01 -7.817489e-01
[703] 5.615589e-01 7.984968e+00 -1.419967e-03 -3.413697e-01 -5.719286e-01
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[712] 1.435803e-01 -2.474860e-01 1.093524e+00 2.347177e-01 1.730654e-01
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[721] 4.993324e-01 -3.569028e-01 1.399057e+00 -1.404911e+00 -2.982227e-01
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[730] -6.386024e-02 5.534418e+00 1.260242e+00 -8.166069e-01 -2.222623e-01
7.545084e-02 5.541968e-01 5.556761e+00 -8.453119e-01
[739] 3.526444e-01 2.922084e+00 2.172985e-01 -1.469902e+00 1.632111e-01
3.493874e-01 -1.966893e-01 -2.924236e-01 1.102409e-01
[748] 6.462530e-02 -1.704171e-02 4.125223e-01 -2.080039e-01 2.607025e-01
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[757] -3.093319e-01 -1.073459e-01 1.363464e+00 -1.401023e+00 -2.107503e-02
5.597599e-01 5.385795e-01 1.863389e+00 6.397418e+00
[766] 1.861240e+00 1.194237e+00 2.997435e-01 1.611484e-01 -5.484613e-01
1.189842e+00 3.837644e+00 -2.338096e-01 -5.737762e-01
[775] 2.413753e-03 3.455508e+00 -6.577547e-01 3.693522e-01 1.219843e-01
-2.947803e-02 -2.569075e-01 -1.664628e-01 2.123460e+00
[784] 4.798212e+00 -1.675385e-01 -7.847523e-02 -3.216411e-01 -2.386470e-01
2.017492e+00 -2.721515e-01 2.467115e+00 5.415200e-01
[793] 1.157133e+00 4.056428e-01 -2.823108e-01 4.366070e-01 -9.937483e-01
-6.383019e-02 2.599436e-01 -2.154435e-01
> HF5
Time Series:
Start = 1
End = 800
Frequency = 1
[1] -0.053649858 0.473045129 -1.855791134 -0.218807875 0.014571536
0.159596481 0.081564240 0.155658287 -0.106533556
[10] 1.349296039 0.043722595 1.184981768 2.936701948 -0.020890782
0.287209659 -0.343506862 0.182125744 0.321655319
[19] 0.152265596 -0.130765767 0.301479728 0.237639510 -0.113640154
0.116768441 0.245115225 2.653399743 -0.014934997
[28] -0.376484031 0.098036596 0.078589972 -10.566796506 -0.033271764
0.007003626 0.336061740 -0.290931130 -1.003161849
[37] 2.126410832 -0.339519118 -1.984023750 -0.188090224 8.562631062
1.515090731 -0.089723677 -0.035854499 -0.156259607
[46] 0.087586561 -0.099550560 -0.386082232 1.231825926 0.665419202
-0.018845938 -0.273064427 -0.441205599 0.058367119
[55] -0.035881404 0.231425905 -1.731548372 0.511813720 -2.652292762
-0.163362295 0.112082704 2.127449901 -1.984516819
[64] -1.681618131 -0.291551146 1.301356201 -0.231139629 -1.761747111
2.198414002 0.031431206 4.817803230 -0.053835827
[73] -0.241400896 -0.132737682 -0.494221853 -3.427015165 0.158200929
6.618433733 -0.255699644 0.399170676 0.469394277
[82] 1.403215236 -0.539113590 -0.074840353 0.315268293 0.017757466
-0.069162940 -0.591611166 0.952482170 0.040122193
[91] -0.224477562 -0.035925567 -0.213900914 -2.517367299 -6.371690768
-0.379127361 1.742901426 0.115588677 -0.070774432
[100] -0.042019349 -0.203094162 6.187633937 -0.030255588 -14.135776862
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[109] -0.028013930 1.196397848 -3.136609657 -0.016623343 -0.047866621
0.235623521 -0.033250628 -0.029950585 -0.152733306
[118] 0.283585876 0.725438532 -5.321553815 -0.262818166 0.333358093
-0.127887678 -0.825616353 0.729752381 0.161256587
[127] -0.127870499 -3.504392573 -0.056818942 1.051455503 -0.610581967
-1.772628876 7.763088022 6.377255877 0.982331777
[136] -0.049720167 1.668057546 -0.081526679 -0.016646304 0.027828635
0.021019397 0.638606658 -2.639610493 0.252214128
[145] -0.021177179 0.309961739 -0.159709264 -0.791889902 0.221659320
0.071520603 -0.191792830 -0.095849781 0.147118019
[154] 0.423879172 -0.015966532 -0.814997357 0.182181232 0.740886403
-0.425878632 0.063399111 0.084086002 6.242629054
[163] -0.166059640 -0.164944798 0.047540050 0.077867048 0.210206725
-0.059959501 -0.134972375 0.724032252 1.208053371
[172] -1.450416248 0.767002941 0.567248602 0.203201419 -0.017947959
0.723492119 2.315582396 -0.003250712 -0.214061467
[181] 0.140103172 1.485875229 -0.063942314 0.504794752 1.203681332
2.916254637 -0.599141209 -0.504639390 -0.035917702
[190] -0.066508032 -0.774334925 -0.044962400 0.539379226 0.035552430
-0.852486162 0.582649427 0.511438446 -0.054846737
[199] -1.363899566 -0.925264908 0.378290631 8.418752812 -0.329694296
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[208] 0.035566960 -0.048042626 -0.230902834 -0.983361624 -0.524604472
0.142112334 3.178630141 -0.679181149 -0.021673949
[217] 0.455549743 2.884246546 0.995534936 -0.074915836 0.294327209
8.707540120 -0.891039780 -5.116943345 1.807300268
[226] 4.653522444 0.176254186 0.096643906 0.097676112 -0.442654494
-0.176779103 0.047338893 -0.206053506 24.897248697
[235] -0.558294814 0.015836695 -0.754272940 -0.071928292 -4.065491270
-1.044690836 0.376283222 0.588343352 -0.355257156
[244] -0.083364082 -0.007105364 0.529359954 -8.021221450 -0.546179595
0.646916952 0.178089665 -0.051864657 0.253082405
[253] 20.713299311 0.759143878 -0.539982015 -0.368425364 3.538669564
0.567510757 0.191253562 -0.053957999 0.047407002
[262] 1.072823567 -2.268748418 -0.033168432 0.252976417 4.010509758
-0.085581899 -1.500184616 2.623411867 0.129878721
[271] 0.196248634 -0.481771250 -0.056828978 0.031878859 -0.144508992
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[289] 5.803557957 0.898143581 -0.016638145 -2.870511105 12.535882950
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[298] 2.549915204 -1.388314210 -5.815539352 -0.210410307 -0.046665442
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0.530886207 -14.858856834 -10.332358918 3.337007186
[406] 0.029548722 -0.177707477 -0.465327158 0.126175184 0.079632842
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[478] 1.618053635 -0.568450760 -0.100185900 -0.218372487 -0.533170368
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[496] -2.321447242 7.091924992 -0.100624956 0.014795836 -0.127924982
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[505] 0.133267731 1.334596328 -0.080741903 1.136959798 0.103590046
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[514] 0.203784749 -0.241718413 -0.418653153 7.263519760 0.175385478
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[532] -0.190871159 -0.016198856 1.582199545 -0.355298930 -0.119154942
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[541] 0.182400471 0.290090107 -0.544720386 -0.704947881 0.182413507
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[550] 0.579123775 0.276916517 0.336730820 0.166459998 -0.165019677
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[559] -0.180776170 -0.412514852 1.919485711 0.564221261 -1.814078186
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[568] -0.064963825 0.315600383 0.208368575 -1.362624306 -0.036163560
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[577] 0.792613097 0.461937482 -0.549182039 -0.201497868 0.559521219
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[586] 1.414073413 -0.568775940 -0.324689599 0.489813834 -0.149345898
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[604] -0.903460198 0.524895605 0.044527148 -0.461720956 -0.547639601
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[622] -0.184791050 -0.076097183 -1.798061452 0.080099125 2.062484105
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[631] -0.915838960 -0.220861746 0.077200047 0.610466280 -0.688401758
-0.207153770 0.049139553 22.362186197 -5.441551857
[640] -1.708605711 0.926299855 0.207035751 -0.106446657 -2.675294607
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[649] -0.085333035 0.977385829 -16.826537503 -0.200423157 -0.051340705
6.499090143 -0.304213082 -0.065082852 0.048070630
[658] 0.666539778 -0.064016381 -0.109602571 0.533325153 0.528565621
-0.248317213 -3.473373955 1.272400022 1.711836935
[667] -0.228344960 -0.252753461 -0.488373752 -0.401594723 -0.030427542
-0.455079097 3.252051577 0.960391227 -0.256075733
[676] -0.136915862 0.098237444 1.674612416 0.044609980 -0.248469202
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[685] 1.036270876 -0.152137097 -0.048105658 -1.277109207 0.059431246
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[694] 0.220699810 -0.312873635 0.014867680 -0.241851486 0.032156787
-1.816522484 -0.167733410 4.158794025 2.099466739
[703] -0.030488507 0.112566051 0.075675048 0.302820106 -0.469476310
0.210115120 0.056139143 -0.030484607 -0.072570524
[712] -0.033886465 0.091219120 -0.248023454 -0.081455556 -0.203068185
0.054095543 -0.015255905 -3.701371648 -0.623879061
[721] 0.853410776 6.103753013 -1.341198580 1.247921308 0.751060465
0.781642884 0.379135477 1.145320110 0.313305428
[730] 0.112618403 -1.412256823 -0.103142715 -0.007113346 0.659901598
-2.519498558 -0.365995410 -0.184937991 0.897416670
[739] -0.518805259 -3.353209940 1.867572217 9.205127781 -0.187969046
-0.778383177 -0.042669664 0.806807477 -0.090799820
[748] -0.021826161 0.448223805 -0.164371146 -0.618774302 -0.244839681
0.194235170 1.570125546 1.754972837 0.500679719
[757] 0.870366653 0.433784961 -1.002863246 2.101960944 0.697030522
7.950881827 -0.061270167 -2.371332122 -0.142291873
[766] -1.729969712 -1.941166110 -0.245036824 -0.106730528 5.057757700
-1.038846526 -0.858866602 3.386084663 1.395573786
[775] -0.291650577 -2.212035645 0.856991031 -1.532383568 -0.185747818
-0.711396025 1.062315644 0.241829929 -1.838103065
[784] -12.577074634 1.735801542 0.484405184 0.013854970 0.416285923
-1.975226723 0.938110382 -0.647308291 -0.706063547
[793] -0.082810695 -0.054601369 -0.014973073 0.127614348 18.906618087
0.502810107 -0.152371107 -0.036187828
very many thanks for your time and effort....
Yours sincerely,
AKSHAY M KULKARNI
________________________________
From: Ivan Krylov <krylov.r00t at gmail.com>
Sent: Thursday, March 21, 2019 9:06 PM
To: r-help at r-project.org
Cc: akshay kulkarni
Subject: Re: [R] problem with nls....
One of the assumptions made by least squares method is that the
residuals are independent and normally distributed with same parameters
(or, in case of weighted regression, the standard deviation of the
residual is known for every point). If this is the case, the parameters
that minimize the sum of squared residuals are the maximum likelihood
estimation of the true parameter values.
The problem is, your data doesn't seem to adhere well to your formula.
Have you tried plotting your HF1 - ((m/HF6) + 1) against HF6 (i.e. the
residuals themselves)? With large residual values (outliers?), the loss
function (i.e. sum of squared residuals) is disturbed and doesn't
reflect the values you would expect to get otherwise. Try computing
sum((HF1 - ((m/HF6) + 1))^2) for different values of m and see if
changing m makes any difference.
Try looking up "robust regression" (e.g. minimize sum of absolute
residuals instead of squared residuals; a unique solution is not
guaranteed, but it's be less disturbed by outliers).
--
Best regards,
Ivan
[[alternative HTML version deleted]]
>>>>> Ivan Krylov >>>>> on Thu, 21 Mar 2019 18:36:20 +0300 writes:> One of the assumptions made by least squares method is that the > residuals are independent and normally distributed with same parameters > (or, in case of weighted regression, the standard deviation of the > residual is known for every point). If this is the case, the parameters > that minimize the sum of squared residuals are the maximum likelihood > estimation of the true parameter values. > The problem is, your data doesn't seem to adhere well to your formula. > Have you tried plotting your HF1 - ((m/HF6) + 1) against HF6 (i.e. the > residuals themselves)? With large residual values (outliers?), the loss > function (i.e. sum of squared residuals) is disturbed and doesn't > reflect the values you would expect to get otherwise. Try computing > sum((HF1 - ((m/HF6) + 1))^2) for different values of m and see if > changing m makes any difference. > Try looking up "robust regression" (e.g. minimize sum of absolute > residuals instead of squared residuals; a unique solution is not > guaranteed, but it's be less disturbed by outliers). Very good point, Ivan (as your previous ones on this thread - thank you! it's great to have a couple of smart and patient R-helpers such as you !!). CRAN package robustbase https://cran.r-project.org/package=robustbase has function nlrob() to do non-linear regression *robustly*, even using several methods, the default one using robustly re-weighted nls(). I'm the maintainer of the package and have been the "moderator" of the current nlrob() function, but as you can read on it's help page, I'm not the author of that function and its submethods: https://www.rdocumentation.org/packages/robustbase/versions/0.93-4/topics/nlrob Martin Maechler ETH Zurich > -- > Best regards, > Ivan > ______________________________________________ > R-help at r-project.org mailing list -- To UNSUBSCRIBE and more, see > https://stat.ethz.ch/mailman/listinfo/r-help > PLEASE do read the posting guide http://www.R-project.org/posting-guide.html > and provide commented, minimal, self-contained, reproducible code.
dear Ivan,
I think my nls call is not converging to the proper value.
I've gone through the Gauss Newton algorithm implemented by nls. How do I
get the gradient, Hessian, and the jacobian of the objective function created by
call to the nls? Perhaps I can compare all of them between my succesful nls call
and the one that didn't. I've gone through debug(nls) but of no avail.
Also, I've checked the residuals...they are approximately normally
distributed....I am still wondering why the nls call is not getting
converged....!
Also, is it possible that if I give the vectors HF1,Hf5,HF6 it will help members
in the mailing list to get to the bottom of the problem( I am sorry to have
given the printed values of the vectors in my previous response to your
mail...The dput values were very large. However, I will give the dput values
this time around )?
very many thanks for your time and effort....
yours sincerely,
AKSHAY M KULKARNI
________________________________
From: Ivan Krylov <krylov.r00t at gmail.com>
Sent: Thursday, March 21, 2019 9:06 PM
To: r-help at r-project.org
Cc: akshay kulkarni
Subject: Re: [R] problem with nls....
One of the assumptions made by least squares method is that the
residuals are independent and normally distributed with same parameters
(or, in case of weighted regression, the standard deviation of the
residual is known for every point). If this is the case, the parameters
that minimize the sum of squared residuals are the maximum likelihood
estimation of the true parameter values.
The problem is, your data doesn't seem to adhere well to your formula.
Have you tried plotting your HF1 - ((m/HF6) + 1) against HF6 (i.e. the
residuals themselves)? With large residual values (outliers?), the loss
function (i.e. sum of squared residuals) is disturbed and doesn't
reflect the values you would expect to get otherwise. Try computing
sum((HF1 - ((m/HF6) + 1))^2) for different values of m and see if
changing m makes any difference.
Try looking up "robust regression" (e.g. minimize sum of absolute
residuals instead of squared residuals; a unique solution is not
guaranteed, but it's be less disturbed by outliers).
--
Best regards,
Ivan
[[alternative HTML version deleted]]
dear Ivan and members,
I was able to solve my problem.
After going through Gauss Newton method, I tried to extract the Hessian,Gradient
and the Jacobian from the nls call. But I could not succeed. However I observed
that my formula contained only one parameter. Then the objective function is
just a quadratic in that parameter. I applied directly Newton Raphson method and
got the value of the parameter. To my surprise, it was the same as the output of
the nls call!
I think I have to accept the value of the parameter, even though it is not a
good fit. The world is very harsh(sometimes only?)!
I should thank Ivan for initiating me in the right direction...
very many thanks for your time and effort...
Yours sincerely,
AKSHAY M KULKARNI
________________________________
From: Ivan Krylov <krylov.r00t at gmail.com>
Sent: Thursday, March 21, 2019 9:06 PM
To: r-help at r-project.org
Cc: akshay kulkarni
Subject: Re: [R] problem with nls....
One of the assumptions made by least squares method is that the
residuals are independent and normally distributed with same parameters
(or, in case of weighted regression, the standard deviation of the
residual is known for every point). If this is the case, the parameters
that minimize the sum of squared residuals are the maximum likelihood
estimation of the true parameter values.
The problem is, your data doesn't seem to adhere well to your formula.
Have you tried plotting your HF1 - ((m/HF6) + 1) against HF6 (i.e. the
residuals themselves)? With large residual values (outliers?), the loss
function (i.e. sum of squared residuals) is disturbed and doesn't
reflect the values you would expect to get otherwise. Try computing
sum((HF1 - ((m/HF6) + 1))^2) for different values of m and see if
changing m makes any difference.
Try looking up "robust regression" (e.g. minimize sum of absolute
residuals instead of squared residuals; a unique solution is not
guaranteed, but it's be less disturbed by outliers).
--
Best regards,
Ivan
[[alternative HTML version deleted]]