我从包中使用nls.lmminpack.lm来适应很多非线性模型.
由于初始参数估计处的奇异梯度矩阵,它经常在20次迭代后失败.
问题是当我在failling(trace = T)之前看一下迭代时我可以看到结果没问题.
可重复的例子:
数据:
df <- structure(list(x1 = c(7L, 5L, 10L, 6L, 9L, 10L, 2L, 4L, 9L, 3L,
11L, 6L, 4L, 0L, 7L, 12L, 9L, 11L, 11L, 0L, 2L, 3L, 5L, 6L, 6L,
9L, 1L, 7L, 7L, 4L, 3L, 13L, 12L, 13L, 5L, 0L, 5L, 6L, 6L, 7L,
5L, 10L, 6L, 10L, 0L, 7L, 9L, 12L, 4L, 5L, 6L, 3L, 4L, 5L, 5L,
0L, 9L, 9L, 1L, 2L, 2L, 13L, 8L, 2L, 5L, 10L, 6L, 11L, 5L, 0L,
4L, 4L, 8L, 9L, 4L, 2L, 12L, 4L, 10L, 7L, 0L, 4L, 4L, 5L, 8L,
8L, 12L, 4L, 6L, 13L, 5L, 12L, 1L, 6L, 4L, 9L, 11L, 11L, 6L,
10L, 10L, 0L, 3L, 1L, 11L, 4L, 3L, 13L, 5L, 4L, 2L, 3L, 11L,
7L, 0L, 9L, 6L, 11L, 6L, 13L, 1L, 5L, 0L, 6L, 4L, 8L, 2L, 3L,
7L, 9L, 12L, 11L, 7L, 4L, 10L, 0L, 6L, 1L, 7L, 2L, 6L, 3L, 1L,
6L, 10L, 12L, 7L, 7L, 6L, 6L, 1L, 7L, 8L, 7L, 7L, 5L, 7L, 10L,
10L, 11L, 7L, 1L, 8L, 3L, 12L, 0L, 11L, 8L, 5L, 0L, 6L, 3L, 2L,
2L, 8L, 9L, 2L, 8L, 2L, 13L, 10L, 2L, 12L, 6L, 13L, 2L, 11L,
1L, 12L, 6L, 7L, 9L, 8L, 10L, 2L, 6L, 0L, 2L, 11L, 2L, 3L, 9L,
12L, 1L, 11L, 11L, 12L, 4L, 6L, 9L, 1L, 4L, 1L, 8L, 8L, 6L, 1L,
9L, 8L, 2L, 10L, 10L, 1L, 2L, 0L, 11L, 6L, 6L, 0L, 4L, 13L, 4L,
8L, 4L, 10L, 9L, 6L, 11L, 8L, 1L, 6L, 5L, 10L, 8L, 10L, 8L, 0L,
3L, 0L, 6L, 7L, 4L, 3L, 7L, 7L, 8L, 6L, 2L, 9L, 5L, 7L, 7L, 0L,
7L, 2L, 5L, 5L, 7L, 5L, 7L, 8L, 6L, 1L, 2L, 6L, 0L, 8L, 10L,
0L, 10L), x2 = c(4L, 6L, 1L, 5L, 4L, 1L, 8L, 9L, 4L, 7L, 2L,
6L, 9L, 11L, 5L, 1L, 3L, 2L, 2L, 12L, 8L, 9L, 6L, 4L, 4L, 2L,
9L, 6L, 6L, 6L, 8L, 0L, 0L, 0L, 8L, 10L, 7L, 7L, 4L, 5L, 5L,
3L, 6L, 3L, 12L, 6L, 1L, 0L, 8L, 6L, 6L, 7L, 8L, 5L, 8L, 11L,
3L, 2L, 12L, 11L, 10L, 0L, 2L, 8L, 8L, 3L, 7L, 2L, 7L, 10L, 7L,
8L, 2L, 4L, 7L, 11L, 1L, 8L, 2L, 5L, 11L, 9L, 7L, 5L, 5L, 3L,
1L, 8L, 4L, 0L, 5L, 0L, 12L, 5L, 9L, 1L, 2L, 0L, 5L, 0L, 2L,
10L, 9L, 10L, 0L, 8L, 10L, 0L, 6L, 8L, 8L, 7L, 1L, 6L, 10L, 1L,
5L, 1L, 6L, 0L, 12L, 7L, 13L, 6L, 9L, 2L, 11L, 10L, 5L, 2L, 0L,
2L, 5L, 6L, 2L, 10L, 4L, 10L, 4L, 9L, 5L, 9L, 11L, 4L, 3L, 1L,
6L, 3L, 7L, 7L, 10L, 3L, 3L, 6L, 3L, 7L, 4L, 1L, 0L, 1L, 4L,
11L, 4L, 10L, 0L, 11L, 0L, 3L, 5L, 11L, 5L, 8L, 10L, 9L, 4L,
3L, 10L, 4L, 10L, 0L, 3L, 9L, 1L, 7L, 0L, 8L, 1L, 11L, 0L, 5L,
4L, 2L, 2L, 0L, 11L, 6L, 13L, 9L, 1L, 9L, 7L, 3L, 1L, 12L, 2L,
2L, 1L, 6L, 4L, 2L, 10L, 6L, 10L, 2L, 3L, 4L, 9L, 2L, 5L, 10L,
0L, 0L, 10L, 9L, 12L, 0L, 7L, 5L, 10L, 6L, 0L, 9L, 4L, 8L, 1L,
3L, 5L, 2L, 4L, 12L, 4L, 5L, 2L, 5L, 0L, 2L, 10L, 8L, 10L, 7L,
3L, 8L, 8L, 6L, 3L, 5L, 6L, 11L, 4L, 5L, 4L, 3L, 10L, 6L, 8L,
6L, 7L, 4L, 8L, 5L, 3L, 7L, 12L, 8L, 4L, 11L, 2L, 3L, 12L, 1L
), x3 = c(1, 1, 1, 1, 3, 1, 0, 3, 3, 0, 3, 2, 3, 1, 2, 3, 2,
3, 3, 2, 0, 2, 1, 0, 0, 1, 0, 3, 3, 0, 1, 3, 2, 3, 3, 0, 2, 3,
0, 2, 0, 3, 2, 3, 2, 3, 0, 2, 2, 1, 2, 0, 2, 0, 3, 1, 2, 1, 3,
3, 2, 3, 0, 0, 3, 3, 3, 3, 2, 0, 1, 2, 0, 3, 1, 3, 3, 2, 2, 2,
1, 3, 1, 0, 3, 1, 3, 2, 0, 3, 0, 2, 3, 1, 3, 0, 3, 1, 1, 0, 2,
0, 2, 1, 1, 2, 3, 3, 1, 2, 0, 0, 2, 3, 0, 0, 1, 2, 2, 3, 3, 2,
3, 2, 3, 0, 3, 3, 2, 1, 2, 3, 2, 0, 2, 0, 0, 1, 1, 1, 1, 2, 2,
0, 3, 3, 3, 0, 3, 3, 1, 0, 1, 3, 0, 2, 1, 1, 0, 2, 1, 2, 2, 3,
2, 1, 1, 1, 0, 1, 1, 1, 2, 1, 2, 2, 2, 2, 2, 3, 3, 1, 3, 3, 3,
0, 2, 2, 2, 1, 1, 1, 0, 0, 3, 2, 3, 1, 2, 1, 0, 2, 3, 3, 3, 3,
3, 0, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 3, 2, 0, 0, 1, 1, 2, 1, 3,
1, 0, 0, 3, 3, 2, 2, 1, 2, 1, 3, 2, 3, 0, 0, 2, 3, 0, 0, 0, 1,
0, 3, 0, 2, 1, 3, 0, 3, 2, 3, 3, 0, 1, 0, 0, 3, 0, 1, 2, 1, 3,
2, 1, 3, 3, 0, 0, 1, 0, 3, 2, 1), y = c(0.03688, 0.09105, 0.16246,
0, 0.11024, 0.16246, 0.13467, 0, 0.11024, 0.0807, 0.12726, 0.03934,
0, 0.0826, 0.03688, 0.06931, 0.1378, 0.12726, 0.12726, 0.08815,
0.13467, 0.01314, 0.09105, 0.12077, 0.12077, 0.02821, 0.15134,
0.03604, 0.03604, 0.08729, 0.04035, 0.46088, 0.20987, 0.46088,
0.06672, 0.24121, 0.08948, 0.07867, 0.12077, 0.03688, 0.02276,
0.04535, 0.03934, 0.04535, 0.08815, 0.03604, 0.50771, 0.20987,
0.08569, 0.09105, 0.03934, 0.0807, 0.08569, 0.02276, 0.06672,
0.0826, 0.1378, 0.02821, 0.03943, 0.03589, 0.04813, 0.46088,
0.22346, 0.13467, 0.06672, 0.04535, 0.07867, 0.12726, 0.08948,
0.24121, 0.06983, 0.08569, 0.22346, 0.11024, 0.06983, 0.03589,
0.06931, 0.08569, 0.04589, 0.03688, 0.0826, 0, 0.06983, 0.02276,
0.06238, 0.03192, 0.06931, 0.08569, 0.12077, 0.46088, 0.02276,
0.20987, 0.03943, 0, 0, 0.50771, 0.12726, 0.1628, 0, 0.41776,
0.04589, 0.24121, 0.01314, 0.03027, 0.1628, 0.08569, 0, 0.46088,
0.09105, 0.08569, 0.13467, 0.0807, 0.12912, 0.03604, 0.24121,
0.50771, 0, 0.12912, 0.03934, 0.46088, 0.03943, 0.08948, 0.07103,
0.03934, 0, 0.22346, 0.03589, 0, 0.03688, 0.02821, 0.20987, 0.12726,
0.03688, 0.08729, 0.04589, 0.24121, 0.12077, 0.03027, 0.03688,
0.03673, 0, 0.01314, 0.02957, 0.12077, 0.04535, 0.06931, 0.03604,
0.36883, 0.07867, 0.07867, 0.03027, 0.36883, 0.03192, 0.03604,
0.36883, 0.08948, 0.03688, 0.16246, 0.41776, 0.12912, 0.03688,
0.02957, 0.1255, 0, 0.20987, 0.0826, 0.1628, 0.03192, 0.02276,
0.0826, 0, 0.04035, 0.04813, 0.03673, 0.1255, 0.1378, 0.04813,
0.1255, 0.04813, 0.46088, 0.04535, 0.03673, 0.06931, 0.07867,
0.46088, 0.13467, 0.12912, 0.02957, 0.20987, 0, 0.03688, 0.02821,
0.22346, 0.41776, 0.03589, 0.03934, 0.07103, 0.03673, 0.12912,
0.03673, 0.0807, 0.1378, 0.06931, 0.03943, 0.12726, 0.12726,
0.06931, 0.08729, 0.12077, 0.02821, 0.03027, 0.08729, 0.03027,
0.22346, 0.03192, 0.12077, 0.15134, 0.02821, 0.06238, 0.04813,
0.41776, 0.41776, 0.03027, 0.03673, 0.08815, 0.1628, 0.07867,
0, 0.24121, 0.08729, 0.46088, 0, 0.1255, 0.08569, 0.16246, 0.1378,
0, 0.12726, 0.1255, 0.03943, 0.12077, 0.02276, 0.04589, 0.06238,
0.41776, 0.22346, 0.24121, 0.04035, 0.24121, 0.07867, 0.36883,
0.08569, 0.04035, 0.03604, 0.36883, 0.06238, 0.03934, 0.03589,
0.11024, 0.02276, 0.03688, 0.36883, 0.24121, 0.03604, 0.13467,
0.09105, 0.08948, 0.03688, 0.06672, 0.03688, 0.03192, 0.07867,
0.03943, 0.13467, 0.12077, 0.0826, 0.22346, 0.04535, 0.08815,
0.16246)), .Names = c("x1", "x2", "x3", "y"), row.names = c(995L,
1416L, 281L, 1192L, 1075L, 294L, 1812L, 2235L, 1097L, 1583L,
670L, 1485L, 2199L, 2495L, 1259L, 436L, 803L, 631L, 617L, 2654L,
1813L, 2180L, 1403L, 911L, 927L, 533L, 2024L, 1517L, 1522L, 1356L,
1850L, 222L, 115L, 204L, 1974L, 2292L, 1695L, 1746L, 915L, 1283L,
1128L, 880L, 1467L, 887L, 2665L, 1532L, 267L, 155L, 1933L, 1447L,
1488L, 1609L, 1922L, 1168L, 1965L, 2479L, 813L, 550L, 2707L,
2590L, 2373L, 190L, 504L, 1810L, 2007L, 843L, 1770L, 659L, 1730L,
2246L, 1668L, 1923L, 465L, 1108L, 1663L, 2616L, 409L, 1946L,
589L, 1277L, 2493L, 2210L, 1662L, 1142L, 1331L, 735L, 430L, 1916L,
922L, 208L, 1134L, 127L, 2693L, 1213L, 2236L, 240L, 623L, 108L,
1190L, 9L, 575L, 2268L, 2171L, 2308L, 103L, 1953L, 2409L, 184L,
1437L, 1947L, 1847L, 1570L, 365L, 1550L, 2278L, 270L, 1204L,
384L, 1472L, 205L, 2694L, 1727L, 2800L, 1476L, 2229L, 453L, 2630L,
2426L, 1275L, 523L, 163L, 635L, 1287L, 1349L, 561L, 2261L, 931L,
2339L, 973L, 2113L, 1229L, 2155L, 2554L, 936L, 892L, 433L, 1560L,
697L, 1791L, 1755L, 2351L, 720L, 740L, 1558L, 674L, 1736L, 988L,
321L, 18L, 375L, 959L, 2560L, 1047L, 2429L, 119L, 2468L, 98L,
773L, 1158L, 2520L, 1216L, 1872L, 2364L, 2094L, 1035L, 826L,
2374L, 1028L, 2368L, 176L, 895L, 2090L, 399L, 1789L, 179L, 1800L,
369L, 2568L, 140L, 1207L, 1001L, 518L, 481L, 12L, 2597L, 1474L,
2749L, 2097L, 379L, 2110L, 1615L, 800L, 423L, 2733L, 626L, 662L,
421L, 1363L, 898L, 530L, 2315L, 1365L, 2331L, 468L, 768L, 900L,
2027L, 544L, 1337L, 2376L, 53L, 44L, 2338L, 2075L, 2655L, 78L,
1782L, 1231L, 2291L, 1379L, 212L, 2212L, 1032L, 1929L, 331L,
790L, 1226L, 664L, 1018L, 2735L, 916L, 1157L, 590L, 1343L, 7L,
490L, 2257L, 1853L, 2251L, 1748L, 719L, 1941L, 1885L, 1544L,
725L, 1294L, 1494L, 2601L, 1077L, 1169L, 979L, 709L, 2282L, 1526L,
1797L, 1424L, 1690L, 993L, 1979L, 1268L, 730L, 1739L, 2697L,
1842L, 952L, 2483L, 479L, 864L, 2677L, 283L), class = "data.frame")
起始价值
starting_value <- structure(c(0.177698291502873, 0.6, 0.0761564106440883, 0.05,
1.9, 1.1, 0.877181493020499, 1.9), .Names = c("F_initial_x2",
"F_decay_x2", "S_initial_x2", "S_decay_x2", "initial_x1", "decay_x1",
"initial_x3", "decay_x3"))
NLSLM失败
coef(nlsLM(
formula = y ~ (F_initial_x2 * exp(- F_decay_x2 * x2) + S_initial_x2 * exp(- S_decay_x2 * x2)) *
(1 + initial_x1 * exp(- decay_x1 * x1)) *
(1 + initial_x3 * exp(- decay_x3 * x3 )),
data = df,
start = coef(brute_force),
lower = c(0, 0, 0, 0, 0, 0, 0, 0),
control = nls.lm.control(maxiter = 200),
trace = T))
It. 0, RSS = 1.36145, Par. = 0.177698 0.6 0.0761564 0.05 1.9 1.1 0.877181 1.9
It. 1, RSS = 1.25401, Par. = 0.207931 0.581039 0.0769047 0.0577244 2.01947 1.22911 0.772957 5.67978
It. 2, RSS = 1.19703, Par. = 0.188978 0.604515 0.0722749 0.0792141 2.44179 1.1258 0.96305 8.67253
It. 3, RSS = 1.1969, Par. = 0.160885 0.640958 0.0990201 0.145187 3.5853 0.847158 0.961844 13.2183
It. 4, RSS = 1.19057, Par. = 0.142138 0.685678 0.11792 0.167417 4.27977 0.936981 0.959606 13.2644
It. 5, RSS = 1.19008, Par. = 0.124264 0.757088 0.136277 0.188896 4.76578 0.91274 0.955142 21.0167
It. 6, RSS = 1.18989, Par. = 0.118904 0.798296 0.141951 0.194167 4.93099 0.91529 0.952972 38.563
It. 7, RSS = 1.18987, Par. = 0.115771 0.821874 0.145398 0.197773 5.02251 0.914204 0.949906 38.563
It. 8, RSS = 1.18986, Par. = 0.113793 0.837804 0.147573 0.199943 5.07456 0.914192 0.948289 38.563
It. 9, RSS = 1.18986, Par. = 0.112458 0.848666 0.149033 0.201406 5.11024 0.914099 0.947232 38.563
It. 10, RSS = 1.18986, Par. = 0.111538 0.856282 0.150035 0.202411 5.13491 0.914051 0.946546 38.563
It. 11, RSS = 1.18986, Par. = 0.110889 0.861702 0.15074 0.203118 5.15244 0.914013 0.946076 38.563
It. 12, RSS = 1.18986, Par. = 0.110426 0.865606 0.151243 0.203623 5.16501 0.913986 0.945747 38.563
It. 13, RSS = 1.18986, Par. = 0.110092 0.868441 0.151605 0.203986 5.17412 0.913966 0.945512 38.563
It. 14, RSS = 1.18986, Par. = 0.109849 0.87051 0.151868 0.20425 5.18075 0.913952 0.945343 38.563
It. 15, RSS = 1.18985, Par. = 0.109672 0.872029 0.15206 0.204443 5.18561 0.913941 0.94522 38.563
It. 16, RSS = 1.18985, Par. = 0.109542 0.873147 0.152201 0.204585 5.18918 0.913933 0.945131 38.563
It. 17, RSS = 1.18985, Par. = 0.109446 0.873971 0.152305 0.204689 5.19181 0.913927 0.945065 38.563
Error in nlsModel(formula, mf, start, wts) :
singular gradient matrix at initial parameter estimates
问题:
使用在奇异梯度矩阵问题之前找到的最佳参数是否有意义,即在迭代= 17时找到的参数？
如果有,是否有办法获取它们？发生错误时,我没有成功保存结果.
我注意到如果我将maxiter的数量减少到17以下的数字,我仍然会出现在新的最后一次迭代中出现的相同错误,这对我来说没有意义
例如,maxiter = 10
It. 0, RSS = 1.36145, Par. = 0.177698 0.6 0.0761564 0.05 1.9 1.1 0.877181 1.9
It. 1, RSS = 1.25401, Par. = 0.207931 0.581039 0.0769047 0.0577244 2.01947 1.22911 0.772957 5.67978
It. 2, RSS = 1.19703, Par. = 0.188978 0.604515 0.0722749 0.0792141 2.44179 1.1258 0.96305 8.67253
It. 3, RSS = 1.1969, Par. = 0.160885 0.640958 0.0990201 0.145187 3.5853 0.847158 0.961844 13.2183
It. 4, RSS = 1.19057, Par. = 0.142138 0.685678 0.11792 0.167417 4.27977 0.936981 0.959606 13.2644
It. 5, RSS = 1.19008, Par. = 0.124264 0.757088 0.136277 0.188896 4.76578 0.91274 0.955142 21.0167
It. 6, RSS = 1.18989, Par. = 0.118904 0.798296 0.141951 0.194167 4.93099 0.91529 0.952972 38.563
It. 7, RSS = 1.18987, Par. = 0.115771 0.821874 0.145398 0.197773 5.02251 0.914204 0.949906 38.563
It. 8, RSS = 1.18986, Par. = 0.113793 0.837804 0.147573 0.199943 5.07456 0.914192 0.948289 38.563
It. 9, RSS = 1.18986, Par. = 0.112458 0.848666 0.149033 0.201406 5.11024 0.914099 0.947232 38.563
It. 10, RSS = 0.12289, Par. = 0.112458 0.848666 0.149033 0.201406 5.11024 0.914099 0.947232 38.563
Error in nlsModel(formula, mf, start, wts) :
singular gradient matrix at initial parameter estimates
In addition: Warning message:
In nls.lm(par = start, fn = FCT, jac = jac, control = control, lower = lower, :
lmdif: info = -1. Number of iterations has reached `maxiter' == 10.
你看到有什么解释吗？
通常，当发生此错误时，问题不在于代码，而在于所使用的模型。Asingular gradient matrix at the initial parameter estimates可能表明模型没有唯一的解决方案，或者模型对于手头的数据过度指定。
回答您的问题：
是的，这是有道理的。该函数nlsLM首先调用nls.lm执行迭代的函数。当到达迭代结束时（由于最佳拟合或因为max.iter），结果将传递给函数nlsModel。该函数对梯度矩阵乘以权重平方进行 QR 分解。并且您的初始梯度矩阵包含一列仅为零的列。因此，虽然nls.lm可以进行迭代，但只有在下一步时才能nlsModel真正检查和发现梯度矩阵的问题。
有一种方法，但这需要您更改 R 本身内的选项，特别是选项error。通过将其设置为dump.frames，您可以转储发生错误时存在的所有环境。这些存储在名为的列表中last.dump，您可以使用这些环境来查找所需的值。
在这种情况下，参数由getPars()驻留在主力函数环境中的函数返回nlsModel：
old.opt <- options(error = dump.frames)
themod <- nlsLM(
formula = y ~ (F_initial_x2 * exp(- F_decay_x2 * x2) +
S_initial_x2 * exp(- S_decay_x2 * x2)) *
(1 + initial_x1 * exp(- decay_x1 * x1)) *
(1 + initial_x3 * exp(- decay_x3 * x3 )),
data = df,
start = starting_value,
lower = c(0, 0, 0, 0, 0, 0, 0, 0),
control = nls.lm.control(maxiter = 200),
trace = TRUE)
thecoefs <- llast.dump[["nlsModel(formula, mf, start, wts)"]]$getPars()
options(old.opt) # reset to the previous value.
请注意，这不是您想要在生产环境中使用或与同事共享的代码类型。而且它也不能解决您的问题，因为问题在于模型，而不是代码。
我做了一个非常简短的测试，看看它是否真的是模型，如果我用它的起始值替换最后一个参数（decay_x3），则模型拟合没有问题。我不知道我们在这里处理什么，所以删除另一个参数可能在现实世界中更有意义，但只是为了证明您的代码没问题：
themod <- nlsLM(
formula = y ~ (F_initial_x2 * exp(- F_decay_x2 * x2) +
S_initial_x2 * exp(- S_decay_x2 * x2)) *
(1 + initial_x1 * exp(- decay_x1 * x1)) *
(1 + initial_x3 * exp(- 1.9* x3 )),
data = df,
start = starting_value[-8],
lower = c(0, 0, 0, 0, 0, 0, 0, 0)[-8],
control = nls.lm.control(maxiter = 200),
trace = TRUE)
在迭代 10 时退出且没有错误。
编辑：我一直在更深入地研究它，根据数据，“额外”解决方案基本上是将 x3 从模型中剔除。其中只有 3 个唯一值，参数的初始估计约为 38。因此：
> exp(-38*c(1,2,3)) < .Machine$double.eps
[1] TRUE TRUE TRUE
如果将其与实际 Y 值进行比较，很明显这initial_x3 * exp(- decay_x3 * x3 )对模型没有任何贡献，因为它实际上为 0。
如果您像 中那样手动计算梯度nlsModel，您会得到一个不是满秩的矩阵；最后一列仅包含 0 ：
theenv <- list2env( c(df, thecoefs))
thederiv <- numericDeriv(form[[3]], names(starting_value), theenv)
thegrad <- attr(thederiv, "gradient")
这就是给你带来错误的原因。该模型对于您拥有的数据来说是过度指定的。
Gabor 建议的对数转换可以防止您的最后估计值变得太大而迫使 x3 脱离模型。由于对数变换，该算法不会很容易跳到这样的极值。为了获得与原始模型相同的估计，他的值decay_x3应该与3.2e16指定相同的模型一样高（exp(38)）。因此，对数变换可以保护您免受将任何变量的影响强制为 0 的估计。
对数变换的另一个副作用是 值的大步幅decay_x3仅对模型产生中等影响。Gabor 发现的估计值 已经是一个巨大的值1.3e7，但经过反向变换后，这仍然是 的可行16值decay_x3。如果您查看以下内容，这仍然会使模型中的 x3 变得多余：
> exp(-16*c(1,2,3))
[1] 1.125352e-07 1.266417e-14 1.425164e-21
但它不会导致导致错误的奇点。
您可以通过设置上限来避免这种情况，例如：
themod <- nlsLM(
formula = y ~ (F_initial_x2 * exp(- F_decay_x2 * x2) +
S_initial_x2 * exp(- S_decay_x2 * x2)) *
(1 + initial_x1 * exp(- decay_x1 * x1)) *
(1 + initial_x3 * exp(- decay_x3 * x3 )),
data = df,
start = starting_value,
lower = c(0, 0, 0, 0, 0, 0, 0, 0),
upper = rep(- log(.Machine$double.eps^0.5),8),
control = nls.lm.control(maxiter = 200),
trace = TRUE)
运行得很好，给你相同的估计，并再次得出结论这x3是多余的。
因此，无论您如何看待它，x3 对 y 都没有影响，您的模型过度指定，无法与手头的数据很好地拟合。