Thurber: Electron mobility data
In NISTnls: Nonlinear least squares examples from NIST
Description
Format
Details
Source
Examples
Description
The Thurber data frame has 37 rows and 2 columns.
Format
This data frame contains the following columns:
- y
-
A numeric vector of electron mobility values.
- x
-
A numeric vector of logs of electron density values.
Details
These data are the result of a NIST study involving
semiconductor electron mobility. The response
variable is a measure of electron mobility, and the
predictor variable is the natural log of the density.
Source
Thurber, R., NIST (197?).
Semiconductor electron mobility modeling.
Examples
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24
Try <- function(expr) if (!inherits(val <- try(expr), "try-error")) val
plot(y ~ x, data = Thurber)
Try(fm1 <- nls(y ~ (b1+x*(b2+x*(b3+b4*x))) / (1+x*(b5+x*(b6+x*b7))),
data = Thurber, trace = TRUE,
start = c(b1 = 1000, b2 = 1000, b3 = 400, b4 = 40,
b5 = 0.7, b6 = 0.3, b7 = 0.03)))
Try(fm1a <- nls(y ~ (b1+x*(b2+x*(b3+b4*x))) / (1+x*(b5+x*(b6+x*b7))),
data = Thurber, trace = TRUE, alg = "port",
start = c(b1 = 1000, b2 = 1000, b3 = 400, b4 = 40,
b5 = 0.7, b6 = 0.3, b7 = 0.03)))
Try(fm2 <- nls(y ~ (b1+x*(b2+x*(b3+b4*x))) / (1+x*(b5+x*(b6+x*b7))),
data = Thurber, trace = TRUE,
start = c(b1 = 1300, b2 = 1500, b3 = 500, b4 = 75,
b5 = 1, b6 = 0.4, b7 = 0.05)))
Try(fm2a <- nls(y ~ (b1+x*(b2+x*(b3+b4*x))) / (1+x*(b5+x*(b6+x*b7))),
data = Thurber, trace = TRUE, alg = "port",
start = c(b1 = 1300, b2 = 1500, b3 = 500, b4 = 75,
b5 = 1, b6 = 0.4, b7 = 0.05)))
Try(fm3 <- nls(y ~ outer(x, 0:3, "^")/(1+x*(b5+x*(b6+x*b7))),
data = Thurber, trace = TRUE,
start = c(b5 = 0.7, b6 = 0.3, b7 = 0.03), alg = "plinear"))
Try(fm4 <- nls(y ~ outer(x, 0:3, "^")/(1+x*(b5+x*(b6+x*b7))),
data = Thurber, trace = TRUE,
start = c(b5 = 1, b6 = 0.4, b7 = 0.05), alg = "plinear"))
Example output
4528125 : 1e+03 1e+03 4e+02 4e+01 7e-01 3e-01 3e-02
2917906 : 1.017774e+03 1.154287e+03 5.125921e+02 7.798057e+01 8.450532e-01 3.683700e-01 6.079624e-02
2211529 : 1.051789e+03 1.190913e+03 5.099164e+02 7.455358e+01 8.587354e-01 3.623121e-01 5.733568e-02
1224789 : 1.111307e+03 1.269700e+03 5.209949e+02 7.197847e+01 8.947460e-01 3.641980e-01 5.364407e-02
382267.2 : 1.200294e+03 1.401285e+03 5.607404e+02 7.378506e+01 9.539195e-01 3.860523e-01 5.196946e-02
44571.9 : 1.288335e+03 1.490593e+03 5.806581e+02 7.350717e+01 9.668230e-01 3.970005e-01 4.801429e-02
7238.18 : 1.288056e+03 1.501821e+03 5.920959e+02 7.746722e+01 9.742647e-01 4.027496e-01 5.168974e-02
5672.839 : 1288.1119921 1489.2203965 582.2916995 75.2869241 0.9653677 0.3978018 0.0492034
5644.678 : 1.288113e+03 1.493502e+03 5.849139e+02 7.573836e+01 9.679718e-01 3.987011e-01 5.018908e-02
5643.374 : 1.288145e+03 1.489664e+03 5.822539e+02 7.522376e+01 9.653564e-01 3.975439e-01 4.943428e-02
5643.051 : 1.288133e+03 1.492129e+03 5.839723e+02 7.556005e+01 9.670083e-01 3.982979e-01 4.993479e-02
5642.85 : 1.288143e+03 1.490417e+03 5.827772e+02 7.532646e+01 9.658516e-01 3.977707e-01 4.959271e-02
5642.776 : 1.288137e+03 1.491545e+03 5.835635e+02 7.548018e+01 9.666099e-01 3.981164e-01 4.982011e-02
5642.738 : 1.288141e+03 1.490775e+03 5.830261e+02 7.537514e+01 9.660904e-01 3.978796e-01 4.966582e-02
5642.722 : 1.288138e+03 1.491288e+03 5.833844e+02 7.544518e+01 9.664362e-01 3.980372e-01 4.976916e-02
5642.714 : 1.288140e+03 1.490940e+03 5.831414e+02 7.539769e+01 9.662015e-01 3.979302e-01 4.969932e-02
5642.711 : 1.288139e+03 1.491174e+03 5.833043e+02 7.542953e+01 9.663587e-01 3.980019e-01 4.974624e-02
5642.71 : 1.288140e+03 1.491016e+03 5.831943e+02 7.540802e+01 9.662524e-01 3.979534e-01 4.971458e-02
5642.709 : 1.288139e+03 1.491122e+03 5.832682e+02 7.542247e+01 9.663238e-01 3.979860e-01 4.973587e-02
5642.709 : 1.288140e+03 1.491051e+03 5.832183e+02 7.541272e+01 9.662757e-01 3.979640e-01 4.972152e-02
5642.708 : 1.288140e+03 1.491099e+03 5.832518e+02 7.541927e+01 9.663080e-01 3.979788e-01 4.973117e-02
5642.708 : 1.288140e+03 1.491066e+03 5.832293e+02 7.541487e+01 9.662863e-01 3.979689e-01 4.972469e-02
5642.708 : 1.288140e+03 1.491088e+03 5.832445e+02 7.541784e+01 9.663009e-01 3.979755e-01 4.972906e-02
5642.708 : 1288.1397125 1491.0733031 583.2342149 75.4158323 0.9662910 0.3979710 0.0497261
5642.708 : 1288.1396586 1491.0832617 583.2411657 75.4171911 0.9662977 0.3979741 0.0497281
5642.708 : 1.288140e+03 1.491076e+03 5.832364e+02 7.541626e+01 9.662931e-01 3.979720e-01 4.972674e-02
5642.708 : 1.288140e+03 1.491081e+03 5.832397e+02 7.541690e+01 9.662963e-01 3.979734e-01 4.972768e-02
5642.708 : 1.288140e+03 1.491078e+03 5.832375e+02 7.541647e+01 9.662942e-01 3.979725e-01 4.972704e-02
5642.708 : 1.288140e+03 1.491080e+03 5.832390e+02 7.541676e+01 9.662956e-01 3.979731e-01 4.972747e-02
Nonlinear regression model
model: y ~ (b1 + x * (b2 + x * (b3 + b4 * x)))/(1 + x * (b5 + x * (b6 + x * b7)))
data: Thurber
b1 b2 b3 b4 b5 b6 b7
1.288e+03 1.491e+03 5.832e+02 7.542e+01 9.663e-01 3.980e-01 4.973e-02
residual sum-of-squares: 5643
Number of iterations to convergence: 28
Achieved convergence tolerance: 8.254e-06
0: 2264062.3: 1000.00 1000.00 400.000 40.0000 0.700000 0.300000 0.0300000
1: 1070416.5: 1016.08 1017.06 394.472 41.8397 0.674785 0.307236 0.0273987
2: 281470.82: 1134.48 1047.98 384.370 45.5397 0.649669 0.312279 0.0241178
3: 121459.90: 1161.88 1045.52 386.124 52.6589 0.660895 0.300277 0.0157121
4: 15026.020: 1277.04 1081.70 379.608 48.9682 0.648625 0.333534 0.000213095
5: 4302.8786: 1292.80 1211.14 368.109 32.2489 0.749560 0.286840 0.00894884
6: 3483.6574: 1290.65 1328.37 463.489 52.1365 0.837971 0.337050 0.0279983
7: 3283.2846: 1289.73 1375.49 499.691 59.3684 0.875183 0.356005 0.0343985
8: 2873.4794: 1288.49 1476.35 571.236 73.0620 0.952494 0.390783 0.0490109
9: 2821.6840: 1288.26 1489.62 582.125 75.2100 0.964819 0.397402 0.0496889
10: 2821.3604: 1288.15 1491.04 583.197 75.4098 0.966211 0.397942 0.0497479
11: 2821.3551: 1288.14 1490.98 583.171 75.4036 0.966225 0.397942 0.0497116
12: 2821.3548: 1288.14 1490.99 583.171 75.4037 0.966219 0.397936 0.0497171
13: 2821.3547: 1288.14 1490.99 583.172 75.4039 0.966221 0.397938 0.0497171
14: 2821.3547: 1288.14 1490.99 583.175 75.4044 0.966224 0.397939 0.0497176
15: 2821.3542: 1288.14 1491.04 583.212 75.4116 0.966264 0.397958 0.0497247
16: 2821.3541: 1288.14 1491.08 583.240 75.4170 0.966296 0.397974 0.0497284
17: 2821.3541: 1288.14 1491.08 583.235 75.4161 0.966292 0.397972 0.0497265
18: 2821.3541: 1288.14 1491.08 583.240 75.4170 0.966297 0.397974 0.0497278
19: 2821.3541: 1288.14 1491.08 583.237 75.4164 0.966294 0.397972 0.0497269
20: 2821.3541: 1288.14 1491.08 583.239 75.4168 0.966296 0.397973 0.0497275
21: 2821.3541: 1288.14 1491.08 583.238 75.4165 0.966295 0.397973 0.0497272
22: 2821.3541: 1288.14 1491.08 583.239 75.4167 0.966295 0.397973 0.0497274
Nonlinear regression model
model: y ~ (b1 + x * (b2 + x * (b3 + b4 * x)))/(1 + x * (b5 + x * (b6 + x * b7)))
data: Thurber
b1 b2 b3 b4 b5 b6 b7
1.288e+03 1.491e+03 5.832e+02 7.542e+01 9.663e-01 3.980e-01 4.973e-02
residual sum-of-squares: 5643
Algorithm "port", convergence message: relative convergence (4)
85873750 : 1300.00 1500.00 500.00 75.00 1.00 0.40 0.05
733524.4 : 1.287773e+03 1.492396e+03 5.702054e+02 7.381027e+01 9.696534e-01 3.865921e-01 4.799485e-02
37931.65 : 1.288146e+03 1.477902e+03 5.721138e+02 7.390068e+01 9.568290e-01 3.915220e-01 4.815011e-02
5751.827 : 1.288190e+03 1.492522e+03 5.840796e+02 7.552001e+01 9.670473e-01 3.982726e-01 5.007822e-02
5643.339 : 1.288150e+03 1.489790e+03 5.823223e+02 7.523432e+01 9.654079e-01 3.975591e-01 4.947534e-02
5642.946 : 1.288135e+03 1.491946e+03 5.838447e+02 7.553530e+01 9.668808e-01 3.982410e-01 4.990069e-02
5642.808 : 1.288142e+03 1.490521e+03 5.828493e+02 7.534058e+01 9.659204e-01 3.978021e-01 4.961423e-02
5642.756 : 1.288137e+03 1.491468e+03 5.835100e+02 7.546973e+01 9.665580e-01 3.980927e-01 4.980497e-02
5642.729 : 1.288141e+03 1.490824e+03 5.830601e+02 7.538179e+01 9.661231e-01 3.978945e-01 4.967572e-02
5642.718 : 1.288139e+03 1.491254e+03 5.833605e+02 7.544052e+01 9.664131e-01 3.980267e-01 4.976235e-02
5642.713 : 1.288140e+03 1.490963e+03 5.831571e+02 7.540075e+01 9.662166e-01 3.979371e-01 4.970384e-02
5642.71 : 1.288139e+03 1.491158e+03 5.832935e+02 7.542742e+01 9.663483e-01 3.979971e-01 4.974315e-02
5642.709 : 1.288140e+03 1.491026e+03 5.832015e+02 7.540943e+01 9.662594e-01 3.979566e-01 4.971666e-02
5642.709 : 1.288139e+03 1.491115e+03 5.832633e+02 7.542152e+01 9.663191e-01 3.979838e-01 4.973447e-02
5642.708 : 1.288140e+03 1.491055e+03 5.832216e+02 7.541337e+01 9.662788e-01 3.979655e-01 4.972247e-02
5642.708 : 1.288140e+03 1.491096e+03 5.832497e+02 7.541886e+01 9.663060e-01 3.979779e-01 4.973056e-02
5642.708 : 1288.1397397 1491.0683289 583.2307453 75.4151540 0.9662877 0.3979695 0.0497251
5642.708 : 1.288140e+03 1.491087e+03 5.832435e+02 7.541764e+01 9.663000e-01 3.979751e-01 4.972877e-02
5642.708 : 1.288140e+03 1.491074e+03 5.832349e+02 7.541597e+01 9.662917e-01 3.979713e-01 4.972631e-02
5642.708 : 1.288140e+03 1.491083e+03 5.832407e+02 7.541710e+01 9.662973e-01 3.979739e-01 4.972796e-02
5642.708 : 1.288140e+03 1.491077e+03 5.832369e+02 7.541635e+01 9.662936e-01 3.979722e-01 4.972686e-02
5642.708 : 1288.1396715 1491.0807585 583.2394198 75.4168497 0.9662960 0.3979733 0.0497276
5642.708 : 1.288140e+03 1.491078e+03 5.832376e+02 7.541650e+01 9.662943e-01 3.979725e-01 4.972709e-02
Nonlinear regression model
model: y ~ (b1 + x * (b2 + x * (b3 + b4 * x)))/(1 + x * (b5 + x * (b6 + x * b7)))
data: Thurber
b1 b2 b3 b4 b5 b6 b7
1.288e+03 1.491e+03 5.832e+02 7.542e+01 9.663e-01 3.980e-01 4.973e-02
residual sum-of-squares: 5643
Number of iterations to convergence: 22
Achieved convergence tolerance: 9.86e-06
0: 42936875.: 1300.00 1500.00 500.000 75.0000 1.00000 0.400000 0.0500000
1: 9836930.4: 1364.41 1471.54 508.400 72.5239 0.991765 0.402424 0.0492796
2: 357554.05: 1297.01 1453.00 542.850 70.1898 0.967070 0.401874 0.0491312
3: 13180.584: 1288.08 1498.42 587.584 75.4691 0.971399 0.399992 0.0503704
4: 2868.2679: 1288.12 1488.84 581.454 74.9858 0.964869 0.397085 0.0491808
5: 2821.9563: 1288.13 1492.92 584.549 75.6775 0.967565 0.398575 0.0500809
6: 2821.5368: 1288.14 1490.03 582.511 75.2745 0.965599 0.397656 0.0495112
7: 2821.4449: 1288.13 1491.84 583.772 75.5209 0.966813 0.398209 0.0498787
8: 2821.3926: 1288.14 1490.59 582.897 75.3499 0.965967 0.397823 0.0496281
9: 2821.3724: 1288.14 1491.42 583.476 75.4631 0.966525 0.398078 0.0497953
10: 2821.3621: 1288.14 1490.85 583.082 75.3861 0.966144 0.397904 0.0496821
11: 2821.3578: 1288.14 1491.23 583.345 75.4376 0.966398 0.398020 0.0497580
12: 2821.3558: 1288.14 1490.98 583.167 75.4027 0.966226 0.397941 0.0497067
13: 2821.3549: 1288.14 1491.15 583.287 75.4261 0.966342 0.397994 0.0497412
14: 2821.3545: 1288.14 1491.03 583.206 75.4103 0.966264 0.397959 0.0497180
15: 2821.3543: 1288.14 1491.11 583.260 75.4209 0.966316 0.397983 0.0497336
16: 2821.3542: 1288.14 1491.06 583.224 75.4138 0.966281 0.397966 0.0497231
17: 2821.3542: 1288.14 1491.09 583.248 75.4186 0.966305 0.397977 0.0497302
18: 2821.3541: 1288.14 1491.07 583.232 75.4153 0.966289 0.397970 0.0497254
19: 2821.3541: 1288.14 1491.09 583.243 75.4175 0.966299 0.397975 0.0497286
20: 2821.3541: 1288.14 1491.07 583.235 75.4161 0.966292 0.397972 0.0497264
21: 2821.3541: 1288.14 1491.08 583.240 75.4170 0.966297 0.397974 0.0497279
22: 2821.3541: 1288.14 1491.08 583.237 75.4164 0.966294 0.397972 0.0497269
23: 2821.3541: 1288.14 1491.08 583.239 75.4168 0.966296 0.397973 0.0497276
24: 2821.3541: 1288.14 1491.08 583.238 75.4165 0.966294 0.397973 0.0497271
25: 2821.3541: 1288.14 1491.08 583.239 75.4167 0.966295 0.397973 0.0497274
Nonlinear regression model
model: y ~ (b1 + x * (b2 + x * (b3 + b4 * x)))/(1 + x * (b5 + x * (b6 + x * b7)))
data: Thurber
b1 b2 b3 b4 b5 b6 b7
1.288e+03 1.491e+03 5.832e+02 7.542e+01 9.663e-01 3.980e-01 4.973e-02
residual sum-of-squares: 5643
Algorithm "port", convergence message: relative convergence (4)
15342.21 : 0.7000 0.3000 0.0300 1302.6450 1202.1374 380.3813 39.0765
9418.713 : 9.957833e-01 4.056820e-01 5.789391e-02 1.284409e+03 1.532009e+03 6.107927e+02 8.064974e+01
6130.941 : 9.837839e-01 4.062383e-01 5.564791e-02 1.288437e+03 1.518224e+03 6.017817e+02 7.903103e+01
5647.933 : 9.706971e-01 4.000814e-01 5.002773e-02 1.288043e+03 1.495842e+03 5.868597e+02 7.610432e+01
5642.843 : 9.664310e-01 3.980114e-01 4.963913e-02 1.288110e+03 1.491050e+03 5.832480e+02 7.541495e+01
5642.741 : 9.665614e-01 3.980917e-01 4.979156e-02 1.288134e+03 1.491447e+03 5.834987e+02 7.546713e+01
5642.722 : 9.661598e-01 3.979109e-01 4.968504e-02 1.288140e+03 1.490875e+03 5.830964e+02 7.538883e+01
5642.715 : 9.663926e-01 3.980173e-01 4.975607e-02 1.288139e+03 1.491223e+03 5.833391e+02 7.543632e+01
5642.711 : 9.662306e-01 3.979435e-01 4.970803e-02 1.288140e+03 1.490984e+03 5.831716e+02 7.540359e+01
5642.71 : 9.663389e-01 3.979929e-01 4.974034e-02 1.288139e+03 1.491144e+03 5.832838e+02 7.542552e+01
5642.709 : 9.662657e-01 3.979595e-01 4.971854e-02 1.288140e+03 1.491036e+03 5.832080e+02 7.541070e+01
5642.709 : 9.663149e-01 3.979819e-01 4.973322e-02 1.288140e+03 1.491109e+03 5.832590e+02 7.542067e+01
5642.708 : 9.662817e-01 3.979668e-01 4.972331e-02 1.288140e+03 1.491059e+03 5.832245e+02 7.541394e+01
5642.708 : 9.663040e-01 3.979770e-01 4.972998e-02 1.288140e+03 1.491093e+03 5.832477e+02 7.541847e+01
5642.708 : 9.662890e-01 3.979701e-01 4.972549e-02 1.288140e+03 1.491070e+03 5.832321e+02 7.541542e+01
5642.708 : 9.662991e-01 3.979747e-01 4.972851e-02 1.288140e+03 1.491085e+03 5.832426e+02 7.541747e+01
5642.708 : 9.662922e-01 3.979716e-01 4.972646e-02 1.288140e+03 1.491075e+03 5.832355e+02 7.541608e+01
5642.708 : 9.662969e-01 3.979737e-01 4.972786e-02 1.288140e+03 1.491082e+03 5.832403e+02 7.541703e+01
5642.708 : 0.9662936 0.3979722 0.0497269 1288.1396901 1491.0772210 583.2369470 75.4163665
5642.708 : 9.662959e-01 3.979732e-01 4.972755e-02 1.288140e+03 1.491080e+03 5.832392e+02 7.541681e+01
5642.708 : 9.662944e-01 3.979726e-01 4.972712e-02 1.288140e+03 1.491078e+03 5.832377e+02 7.541652e+01
5642.708 : 9.662954e-01 3.979730e-01 4.972741e-02 1.288140e+03 1.491080e+03 5.832388e+02 7.541672e+01
5642.708 : 9.662948e-01 3.979728e-01 4.972724e-02 1.288140e+03 1.491079e+03 5.832382e+02 7.541661e+01
Nonlinear regression model
model: y ~ outer(x, 0:3, "^")/(1 + x * (b5 + x * (b6 + x * b7)))
data: Thurber
b5 b6 b7 .lin1 .lin2 .lin3 .lin4
9.663e-01 3.980e-01 4.973e-02 1.288e+03 1.491e+03 5.832e+02 7.542e+01
residual sum-of-squares: 5643
Number of iterations to convergence: 22
Achieved convergence tolerance: 6.743e-06
7762.272 : 1.00000 0.40000 0.05000 1277.99118 1521.58858 605.60816 79.36523
5658.355 : 9.704452e-01 3.987413e-01 4.942063e-02 1.287280e+03 1.494322e+03 5.856819e+02 7.582895e+01
5642.843 : 9.670238e-01 3.982925e-01 4.976933e-02 1.288106e+03 1.491849e+03 5.838208e+02 7.552616e+01
5642.713 : 9.663067e-01 3.979744e-01 4.970995e-02 1.288135e+03 1.491059e+03 5.832292e+02 7.541428e+01
5642.709 : 9.663447e-01 3.979951e-01 4.973969e-02 1.288139e+03 1.491149e+03 5.832874e+02 7.542616e+01
5642.709 : 9.662683e-01 3.979606e-01 4.971905e-02 1.288140e+03 1.491039e+03 5.832104e+02 7.541118e+01
5642.708 : 0.9663140 0.3979815 0.0497329 1288.1395217 1491.1072959 583.2579492 75.4204709
5642.708 : 9.662825e-01 3.979671e-01 4.972354e-02 1.288140e+03 1.491061e+03 5.832253e+02 7.541410e+01
5642.708 : 9.663035e-01 3.979767e-01 4.972983e-02 1.288140e+03 1.491092e+03 5.832472e+02 7.541837e+01
5642.708 : 9.662894e-01 3.979703e-01 4.972562e-02 1.288140e+03 1.491071e+03 5.832326e+02 7.541551e+01
5642.708 : 9.662988e-01 3.979746e-01 4.972843e-02 1.288140e+03 1.491085e+03 5.832423e+02 7.541741e+01
5642.708 : 9.662925e-01 3.979717e-01 4.972654e-02 1.288140e+03 1.491075e+03 5.832357e+02 7.541613e+01
5642.708 : 0.9662967 0.3979736 0.0497278 1288.1396653 1491.0817809 583.2401327 75.4169890
5642.708 : 9.662937e-01 3.979723e-01 4.972692e-02 1.288140e+03 1.491077e+03 5.832370e+02 7.541639e+01
5642.708 : 9.662959e-01 3.979732e-01 4.972754e-02 1.288140e+03 1.491080e+03 5.832392e+02 7.541681e+01
5642.708 : 9.662945e-01 3.979726e-01 4.972715e-02 1.288140e+03 1.491079e+03 5.832379e+02 7.541655e+01
5642.708 : 9.662953e-01 3.979730e-01 4.972738e-02 1.288140e+03 1.491080e+03 5.832386e+02 7.541670e+01
Nonlinear regression model
model: y ~ outer(x, 0:3, "^")/(1 + x * (b5 + x * (b6 + x * b7)))
data: Thurber
b5 b6 b7 .lin1 .lin2 .lin3 .lin4
9.663e-01 3.980e-01 4.973e-02 1.288e+03 1.491e+03 5.832e+02 7.542e+01
residual sum-of-squares: 5643
Number of iterations to convergence: 16
Achieved convergence tolerance: 8.582e-06
NISTnls documentation built on May 2, 2019, 2:37 a.m.
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Description Format Details Source Examples
Description
The Thurber data frame has 37 rows and 2 columns.
Format
This data frame contains the following columns:
- y
-
A numeric vector of electron mobility values.
- x
-
A numeric vector of logs of electron density values.
Details
These data are the result of a NIST study involving semiconductor electron mobility. The response variable is a measure of electron mobility, and the predictor variable is the natural log of the density.
Source
Thurber, R., NIST (197?). Semiconductor electron mobility modeling.
Examples
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | Try <- function(expr) if (!inherits(val <- try(expr), "try-error")) val
plot(y ~ x, data = Thurber)
Try(fm1 <- nls(y ~ (b1+x*(b2+x*(b3+b4*x))) / (1+x*(b5+x*(b6+x*b7))),
data = Thurber, trace = TRUE,
start = c(b1 = 1000, b2 = 1000, b3 = 400, b4 = 40,
b5 = 0.7, b6 = 0.3, b7 = 0.03)))
Try(fm1a <- nls(y ~ (b1+x*(b2+x*(b3+b4*x))) / (1+x*(b5+x*(b6+x*b7))),
data = Thurber, trace = TRUE, alg = "port",
start = c(b1 = 1000, b2 = 1000, b3 = 400, b4 = 40,
b5 = 0.7, b6 = 0.3, b7 = 0.03)))
Try(fm2 <- nls(y ~ (b1+x*(b2+x*(b3+b4*x))) / (1+x*(b5+x*(b6+x*b7))),
data = Thurber, trace = TRUE,
start = c(b1 = 1300, b2 = 1500, b3 = 500, b4 = 75,
b5 = 1, b6 = 0.4, b7 = 0.05)))
Try(fm2a <- nls(y ~ (b1+x*(b2+x*(b3+b4*x))) / (1+x*(b5+x*(b6+x*b7))),
data = Thurber, trace = TRUE, alg = "port",
start = c(b1 = 1300, b2 = 1500, b3 = 500, b4 = 75,
b5 = 1, b6 = 0.4, b7 = 0.05)))
Try(fm3 <- nls(y ~ outer(x, 0:3, "^")/(1+x*(b5+x*(b6+x*b7))),
data = Thurber, trace = TRUE,
start = c(b5 = 0.7, b6 = 0.3, b7 = 0.03), alg = "plinear"))
Try(fm4 <- nls(y ~ outer(x, 0:3, "^")/(1+x*(b5+x*(b6+x*b7))),
data = Thurber, trace = TRUE,
start = c(b5 = 1, b6 = 0.4, b7 = 0.05), alg = "plinear"))
|
Example output
4528125 : 1e+03 1e+03 4e+02 4e+01 7e-01 3e-01 3e-02
2917906 : 1.017774e+03 1.154287e+03 5.125921e+02 7.798057e+01 8.450532e-01 3.683700e-01 6.079624e-02
2211529 : 1.051789e+03 1.190913e+03 5.099164e+02 7.455358e+01 8.587354e-01 3.623121e-01 5.733568e-02
1224789 : 1.111307e+03 1.269700e+03 5.209949e+02 7.197847e+01 8.947460e-01 3.641980e-01 5.364407e-02
382267.2 : 1.200294e+03 1.401285e+03 5.607404e+02 7.378506e+01 9.539195e-01 3.860523e-01 5.196946e-02
44571.9 : 1.288335e+03 1.490593e+03 5.806581e+02 7.350717e+01 9.668230e-01 3.970005e-01 4.801429e-02
7238.18 : 1.288056e+03 1.501821e+03 5.920959e+02 7.746722e+01 9.742647e-01 4.027496e-01 5.168974e-02
5672.839 : 1288.1119921 1489.2203965 582.2916995 75.2869241 0.9653677 0.3978018 0.0492034
5644.678 : 1.288113e+03 1.493502e+03 5.849139e+02 7.573836e+01 9.679718e-01 3.987011e-01 5.018908e-02
5643.374 : 1.288145e+03 1.489664e+03 5.822539e+02 7.522376e+01 9.653564e-01 3.975439e-01 4.943428e-02
5643.051 : 1.288133e+03 1.492129e+03 5.839723e+02 7.556005e+01 9.670083e-01 3.982979e-01 4.993479e-02
5642.85 : 1.288143e+03 1.490417e+03 5.827772e+02 7.532646e+01 9.658516e-01 3.977707e-01 4.959271e-02
5642.776 : 1.288137e+03 1.491545e+03 5.835635e+02 7.548018e+01 9.666099e-01 3.981164e-01 4.982011e-02
5642.738 : 1.288141e+03 1.490775e+03 5.830261e+02 7.537514e+01 9.660904e-01 3.978796e-01 4.966582e-02
5642.722 : 1.288138e+03 1.491288e+03 5.833844e+02 7.544518e+01 9.664362e-01 3.980372e-01 4.976916e-02
5642.714 : 1.288140e+03 1.490940e+03 5.831414e+02 7.539769e+01 9.662015e-01 3.979302e-01 4.969932e-02
5642.711 : 1.288139e+03 1.491174e+03 5.833043e+02 7.542953e+01 9.663587e-01 3.980019e-01 4.974624e-02
5642.71 : 1.288140e+03 1.491016e+03 5.831943e+02 7.540802e+01 9.662524e-01 3.979534e-01 4.971458e-02
5642.709 : 1.288139e+03 1.491122e+03 5.832682e+02 7.542247e+01 9.663238e-01 3.979860e-01 4.973587e-02
5642.709 : 1.288140e+03 1.491051e+03 5.832183e+02 7.541272e+01 9.662757e-01 3.979640e-01 4.972152e-02
5642.708 : 1.288140e+03 1.491099e+03 5.832518e+02 7.541927e+01 9.663080e-01 3.979788e-01 4.973117e-02
5642.708 : 1.288140e+03 1.491066e+03 5.832293e+02 7.541487e+01 9.662863e-01 3.979689e-01 4.972469e-02
5642.708 : 1.288140e+03 1.491088e+03 5.832445e+02 7.541784e+01 9.663009e-01 3.979755e-01 4.972906e-02
5642.708 : 1288.1397125 1491.0733031 583.2342149 75.4158323 0.9662910 0.3979710 0.0497261
5642.708 : 1288.1396586 1491.0832617 583.2411657 75.4171911 0.9662977 0.3979741 0.0497281
5642.708 : 1.288140e+03 1.491076e+03 5.832364e+02 7.541626e+01 9.662931e-01 3.979720e-01 4.972674e-02
5642.708 : 1.288140e+03 1.491081e+03 5.832397e+02 7.541690e+01 9.662963e-01 3.979734e-01 4.972768e-02
5642.708 : 1.288140e+03 1.491078e+03 5.832375e+02 7.541647e+01 9.662942e-01 3.979725e-01 4.972704e-02
5642.708 : 1.288140e+03 1.491080e+03 5.832390e+02 7.541676e+01 9.662956e-01 3.979731e-01 4.972747e-02
Nonlinear regression model
model: y ~ (b1 + x * (b2 + x * (b3 + b4 * x)))/(1 + x * (b5 + x * (b6 + x * b7)))
data: Thurber
b1 b2 b3 b4 b5 b6 b7
1.288e+03 1.491e+03 5.832e+02 7.542e+01 9.663e-01 3.980e-01 4.973e-02
residual sum-of-squares: 5643
Number of iterations to convergence: 28
Achieved convergence tolerance: 8.254e-06
0: 2264062.3: 1000.00 1000.00 400.000 40.0000 0.700000 0.300000 0.0300000
1: 1070416.5: 1016.08 1017.06 394.472 41.8397 0.674785 0.307236 0.0273987
2: 281470.82: 1134.48 1047.98 384.370 45.5397 0.649669 0.312279 0.0241178
3: 121459.90: 1161.88 1045.52 386.124 52.6589 0.660895 0.300277 0.0157121
4: 15026.020: 1277.04 1081.70 379.608 48.9682 0.648625 0.333534 0.000213095
5: 4302.8786: 1292.80 1211.14 368.109 32.2489 0.749560 0.286840 0.00894884
6: 3483.6574: 1290.65 1328.37 463.489 52.1365 0.837971 0.337050 0.0279983
7: 3283.2846: 1289.73 1375.49 499.691 59.3684 0.875183 0.356005 0.0343985
8: 2873.4794: 1288.49 1476.35 571.236 73.0620 0.952494 0.390783 0.0490109
9: 2821.6840: 1288.26 1489.62 582.125 75.2100 0.964819 0.397402 0.0496889
10: 2821.3604: 1288.15 1491.04 583.197 75.4098 0.966211 0.397942 0.0497479
11: 2821.3551: 1288.14 1490.98 583.171 75.4036 0.966225 0.397942 0.0497116
12: 2821.3548: 1288.14 1490.99 583.171 75.4037 0.966219 0.397936 0.0497171
13: 2821.3547: 1288.14 1490.99 583.172 75.4039 0.966221 0.397938 0.0497171
14: 2821.3547: 1288.14 1490.99 583.175 75.4044 0.966224 0.397939 0.0497176
15: 2821.3542: 1288.14 1491.04 583.212 75.4116 0.966264 0.397958 0.0497247
16: 2821.3541: 1288.14 1491.08 583.240 75.4170 0.966296 0.397974 0.0497284
17: 2821.3541: 1288.14 1491.08 583.235 75.4161 0.966292 0.397972 0.0497265
18: 2821.3541: 1288.14 1491.08 583.240 75.4170 0.966297 0.397974 0.0497278
19: 2821.3541: 1288.14 1491.08 583.237 75.4164 0.966294 0.397972 0.0497269
20: 2821.3541: 1288.14 1491.08 583.239 75.4168 0.966296 0.397973 0.0497275
21: 2821.3541: 1288.14 1491.08 583.238 75.4165 0.966295 0.397973 0.0497272
22: 2821.3541: 1288.14 1491.08 583.239 75.4167 0.966295 0.397973 0.0497274
Nonlinear regression model
model: y ~ (b1 + x * (b2 + x * (b3 + b4 * x)))/(1 + x * (b5 + x * (b6 + x * b7)))
data: Thurber
b1 b2 b3 b4 b5 b6 b7
1.288e+03 1.491e+03 5.832e+02 7.542e+01 9.663e-01 3.980e-01 4.973e-02
residual sum-of-squares: 5643
Algorithm "port", convergence message: relative convergence (4)
85873750 : 1300.00 1500.00 500.00 75.00 1.00 0.40 0.05
733524.4 : 1.287773e+03 1.492396e+03 5.702054e+02 7.381027e+01 9.696534e-01 3.865921e-01 4.799485e-02
37931.65 : 1.288146e+03 1.477902e+03 5.721138e+02 7.390068e+01 9.568290e-01 3.915220e-01 4.815011e-02
5751.827 : 1.288190e+03 1.492522e+03 5.840796e+02 7.552001e+01 9.670473e-01 3.982726e-01 5.007822e-02
5643.339 : 1.288150e+03 1.489790e+03 5.823223e+02 7.523432e+01 9.654079e-01 3.975591e-01 4.947534e-02
5642.946 : 1.288135e+03 1.491946e+03 5.838447e+02 7.553530e+01 9.668808e-01 3.982410e-01 4.990069e-02
5642.808 : 1.288142e+03 1.490521e+03 5.828493e+02 7.534058e+01 9.659204e-01 3.978021e-01 4.961423e-02
5642.756 : 1.288137e+03 1.491468e+03 5.835100e+02 7.546973e+01 9.665580e-01 3.980927e-01 4.980497e-02
5642.729 : 1.288141e+03 1.490824e+03 5.830601e+02 7.538179e+01 9.661231e-01 3.978945e-01 4.967572e-02
5642.718 : 1.288139e+03 1.491254e+03 5.833605e+02 7.544052e+01 9.664131e-01 3.980267e-01 4.976235e-02
5642.713 : 1.288140e+03 1.490963e+03 5.831571e+02 7.540075e+01 9.662166e-01 3.979371e-01 4.970384e-02
5642.71 : 1.288139e+03 1.491158e+03 5.832935e+02 7.542742e+01 9.663483e-01 3.979971e-01 4.974315e-02
5642.709 : 1.288140e+03 1.491026e+03 5.832015e+02 7.540943e+01 9.662594e-01 3.979566e-01 4.971666e-02
5642.709 : 1.288139e+03 1.491115e+03 5.832633e+02 7.542152e+01 9.663191e-01 3.979838e-01 4.973447e-02
5642.708 : 1.288140e+03 1.491055e+03 5.832216e+02 7.541337e+01 9.662788e-01 3.979655e-01 4.972247e-02
5642.708 : 1.288140e+03 1.491096e+03 5.832497e+02 7.541886e+01 9.663060e-01 3.979779e-01 4.973056e-02
5642.708 : 1288.1397397 1491.0683289 583.2307453 75.4151540 0.9662877 0.3979695 0.0497251
5642.708 : 1.288140e+03 1.491087e+03 5.832435e+02 7.541764e+01 9.663000e-01 3.979751e-01 4.972877e-02
5642.708 : 1.288140e+03 1.491074e+03 5.832349e+02 7.541597e+01 9.662917e-01 3.979713e-01 4.972631e-02
5642.708 : 1.288140e+03 1.491083e+03 5.832407e+02 7.541710e+01 9.662973e-01 3.979739e-01 4.972796e-02
5642.708 : 1.288140e+03 1.491077e+03 5.832369e+02 7.541635e+01 9.662936e-01 3.979722e-01 4.972686e-02
5642.708 : 1288.1396715 1491.0807585 583.2394198 75.4168497 0.9662960 0.3979733 0.0497276
5642.708 : 1.288140e+03 1.491078e+03 5.832376e+02 7.541650e+01 9.662943e-01 3.979725e-01 4.972709e-02
Nonlinear regression model
model: y ~ (b1 + x * (b2 + x * (b3 + b4 * x)))/(1 + x * (b5 + x * (b6 + x * b7)))
data: Thurber
b1 b2 b3 b4 b5 b6 b7
1.288e+03 1.491e+03 5.832e+02 7.542e+01 9.663e-01 3.980e-01 4.973e-02
residual sum-of-squares: 5643
Number of iterations to convergence: 22
Achieved convergence tolerance: 9.86e-06
0: 42936875.: 1300.00 1500.00 500.000 75.0000 1.00000 0.400000 0.0500000
1: 9836930.4: 1364.41 1471.54 508.400 72.5239 0.991765 0.402424 0.0492796
2: 357554.05: 1297.01 1453.00 542.850 70.1898 0.967070 0.401874 0.0491312
3: 13180.584: 1288.08 1498.42 587.584 75.4691 0.971399 0.399992 0.0503704
4: 2868.2679: 1288.12 1488.84 581.454 74.9858 0.964869 0.397085 0.0491808
5: 2821.9563: 1288.13 1492.92 584.549 75.6775 0.967565 0.398575 0.0500809
6: 2821.5368: 1288.14 1490.03 582.511 75.2745 0.965599 0.397656 0.0495112
7: 2821.4449: 1288.13 1491.84 583.772 75.5209 0.966813 0.398209 0.0498787
8: 2821.3926: 1288.14 1490.59 582.897 75.3499 0.965967 0.397823 0.0496281
9: 2821.3724: 1288.14 1491.42 583.476 75.4631 0.966525 0.398078 0.0497953
10: 2821.3621: 1288.14 1490.85 583.082 75.3861 0.966144 0.397904 0.0496821
11: 2821.3578: 1288.14 1491.23 583.345 75.4376 0.966398 0.398020 0.0497580
12: 2821.3558: 1288.14 1490.98 583.167 75.4027 0.966226 0.397941 0.0497067
13: 2821.3549: 1288.14 1491.15 583.287 75.4261 0.966342 0.397994 0.0497412
14: 2821.3545: 1288.14 1491.03 583.206 75.4103 0.966264 0.397959 0.0497180
15: 2821.3543: 1288.14 1491.11 583.260 75.4209 0.966316 0.397983 0.0497336
16: 2821.3542: 1288.14 1491.06 583.224 75.4138 0.966281 0.397966 0.0497231
17: 2821.3542: 1288.14 1491.09 583.248 75.4186 0.966305 0.397977 0.0497302
18: 2821.3541: 1288.14 1491.07 583.232 75.4153 0.966289 0.397970 0.0497254
19: 2821.3541: 1288.14 1491.09 583.243 75.4175 0.966299 0.397975 0.0497286
20: 2821.3541: 1288.14 1491.07 583.235 75.4161 0.966292 0.397972 0.0497264
21: 2821.3541: 1288.14 1491.08 583.240 75.4170 0.966297 0.397974 0.0497279
22: 2821.3541: 1288.14 1491.08 583.237 75.4164 0.966294 0.397972 0.0497269
23: 2821.3541: 1288.14 1491.08 583.239 75.4168 0.966296 0.397973 0.0497276
24: 2821.3541: 1288.14 1491.08 583.238 75.4165 0.966294 0.397973 0.0497271
25: 2821.3541: 1288.14 1491.08 583.239 75.4167 0.966295 0.397973 0.0497274
Nonlinear regression model
model: y ~ (b1 + x * (b2 + x * (b3 + b4 * x)))/(1 + x * (b5 + x * (b6 + x * b7)))
data: Thurber
b1 b2 b3 b4 b5 b6 b7
1.288e+03 1.491e+03 5.832e+02 7.542e+01 9.663e-01 3.980e-01 4.973e-02
residual sum-of-squares: 5643
Algorithm "port", convergence message: relative convergence (4)
15342.21 : 0.7000 0.3000 0.0300 1302.6450 1202.1374 380.3813 39.0765
9418.713 : 9.957833e-01 4.056820e-01 5.789391e-02 1.284409e+03 1.532009e+03 6.107927e+02 8.064974e+01
6130.941 : 9.837839e-01 4.062383e-01 5.564791e-02 1.288437e+03 1.518224e+03 6.017817e+02 7.903103e+01
5647.933 : 9.706971e-01 4.000814e-01 5.002773e-02 1.288043e+03 1.495842e+03 5.868597e+02 7.610432e+01
5642.843 : 9.664310e-01 3.980114e-01 4.963913e-02 1.288110e+03 1.491050e+03 5.832480e+02 7.541495e+01
5642.741 : 9.665614e-01 3.980917e-01 4.979156e-02 1.288134e+03 1.491447e+03 5.834987e+02 7.546713e+01
5642.722 : 9.661598e-01 3.979109e-01 4.968504e-02 1.288140e+03 1.490875e+03 5.830964e+02 7.538883e+01
5642.715 : 9.663926e-01 3.980173e-01 4.975607e-02 1.288139e+03 1.491223e+03 5.833391e+02 7.543632e+01
5642.711 : 9.662306e-01 3.979435e-01 4.970803e-02 1.288140e+03 1.490984e+03 5.831716e+02 7.540359e+01
5642.71 : 9.663389e-01 3.979929e-01 4.974034e-02 1.288139e+03 1.491144e+03 5.832838e+02 7.542552e+01
5642.709 : 9.662657e-01 3.979595e-01 4.971854e-02 1.288140e+03 1.491036e+03 5.832080e+02 7.541070e+01
5642.709 : 9.663149e-01 3.979819e-01 4.973322e-02 1.288140e+03 1.491109e+03 5.832590e+02 7.542067e+01
5642.708 : 9.662817e-01 3.979668e-01 4.972331e-02 1.288140e+03 1.491059e+03 5.832245e+02 7.541394e+01
5642.708 : 9.663040e-01 3.979770e-01 4.972998e-02 1.288140e+03 1.491093e+03 5.832477e+02 7.541847e+01
5642.708 : 9.662890e-01 3.979701e-01 4.972549e-02 1.288140e+03 1.491070e+03 5.832321e+02 7.541542e+01
5642.708 : 9.662991e-01 3.979747e-01 4.972851e-02 1.288140e+03 1.491085e+03 5.832426e+02 7.541747e+01
5642.708 : 9.662922e-01 3.979716e-01 4.972646e-02 1.288140e+03 1.491075e+03 5.832355e+02 7.541608e+01
5642.708 : 9.662969e-01 3.979737e-01 4.972786e-02 1.288140e+03 1.491082e+03 5.832403e+02 7.541703e+01
5642.708 : 0.9662936 0.3979722 0.0497269 1288.1396901 1491.0772210 583.2369470 75.4163665
5642.708 : 9.662959e-01 3.979732e-01 4.972755e-02 1.288140e+03 1.491080e+03 5.832392e+02 7.541681e+01
5642.708 : 9.662944e-01 3.979726e-01 4.972712e-02 1.288140e+03 1.491078e+03 5.832377e+02 7.541652e+01
5642.708 : 9.662954e-01 3.979730e-01 4.972741e-02 1.288140e+03 1.491080e+03 5.832388e+02 7.541672e+01
5642.708 : 9.662948e-01 3.979728e-01 4.972724e-02 1.288140e+03 1.491079e+03 5.832382e+02 7.541661e+01
Nonlinear regression model
model: y ~ outer(x, 0:3, "^")/(1 + x * (b5 + x * (b6 + x * b7)))
data: Thurber
b5 b6 b7 .lin1 .lin2 .lin3 .lin4
9.663e-01 3.980e-01 4.973e-02 1.288e+03 1.491e+03 5.832e+02 7.542e+01
residual sum-of-squares: 5643
Number of iterations to convergence: 22
Achieved convergence tolerance: 6.743e-06
7762.272 : 1.00000 0.40000 0.05000 1277.99118 1521.58858 605.60816 79.36523
5658.355 : 9.704452e-01 3.987413e-01 4.942063e-02 1.287280e+03 1.494322e+03 5.856819e+02 7.582895e+01
5642.843 : 9.670238e-01 3.982925e-01 4.976933e-02 1.288106e+03 1.491849e+03 5.838208e+02 7.552616e+01
5642.713 : 9.663067e-01 3.979744e-01 4.970995e-02 1.288135e+03 1.491059e+03 5.832292e+02 7.541428e+01
5642.709 : 9.663447e-01 3.979951e-01 4.973969e-02 1.288139e+03 1.491149e+03 5.832874e+02 7.542616e+01
5642.709 : 9.662683e-01 3.979606e-01 4.971905e-02 1.288140e+03 1.491039e+03 5.832104e+02 7.541118e+01
5642.708 : 0.9663140 0.3979815 0.0497329 1288.1395217 1491.1072959 583.2579492 75.4204709
5642.708 : 9.662825e-01 3.979671e-01 4.972354e-02 1.288140e+03 1.491061e+03 5.832253e+02 7.541410e+01
5642.708 : 9.663035e-01 3.979767e-01 4.972983e-02 1.288140e+03 1.491092e+03 5.832472e+02 7.541837e+01
5642.708 : 9.662894e-01 3.979703e-01 4.972562e-02 1.288140e+03 1.491071e+03 5.832326e+02 7.541551e+01
5642.708 : 9.662988e-01 3.979746e-01 4.972843e-02 1.288140e+03 1.491085e+03 5.832423e+02 7.541741e+01
5642.708 : 9.662925e-01 3.979717e-01 4.972654e-02 1.288140e+03 1.491075e+03 5.832357e+02 7.541613e+01
5642.708 : 0.9662967 0.3979736 0.0497278 1288.1396653 1491.0817809 583.2401327 75.4169890
5642.708 : 9.662937e-01 3.979723e-01 4.972692e-02 1.288140e+03 1.491077e+03 5.832370e+02 7.541639e+01
5642.708 : 9.662959e-01 3.979732e-01 4.972754e-02 1.288140e+03 1.491080e+03 5.832392e+02 7.541681e+01
5642.708 : 9.662945e-01 3.979726e-01 4.972715e-02 1.288140e+03 1.491079e+03 5.832379e+02 7.541655e+01
5642.708 : 9.662953e-01 3.979730e-01 4.972738e-02 1.288140e+03 1.491080e+03 5.832386e+02 7.541670e+01
Nonlinear regression model
model: y ~ outer(x, 0:3, "^")/(1 + x * (b5 + x * (b6 + x * b7)))
data: Thurber
b5 b6 b7 .lin1 .lin2 .lin3 .lin4
9.663e-01 3.980e-01 4.973e-02 1.288e+03 1.491e+03 5.832e+02 7.542e+01
residual sum-of-squares: 5643
Number of iterations to convergence: 16
Achieved convergence tolerance: 8.582e-06
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