适合指数或曲棍球棒衰减
fit exponential or hockey stick decay
我正在尝试找到适合我的数据的方程式。我认识到形状是 y=-exp(x) 但 nls(y~-a*exp(x*b)) 具有各种参数起始值失败。 y 为负，因此 log(y)~log(a)+bx 的 "easy" 拟合效果不佳。我试过 log(y+2)~a+bx 使一切都变得积极，但没有得到正确的形状。
有人可以提供一些帮助来拟合这些数据吗？谢谢！
y=瑞典夫
x=平均日期
dat2=structure(list(swediff = c(0.0379635202678687, 0.0845477936160927,
0.146010217481196, 0.0416237104326292, 0.0659140490644253, 0.134535534695029,
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0.00301157777812485, 0.19171002685605, 0.277759059448242, 0.00400780564144798,
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0.0769960292118834, 0.061783685314432, 0.0442014176783082, -0.00990798027657931,
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0.278594307094423, -0.0111994006625954, 0.0379360193757585, 6.29460162030332e-05,
0.0602068958909111, 0.173755367986025, 0.135902420389977, 0.124863098282806,
0.0706487190649132, 0.284186487140106, 0.395475978216811, 0.207437141623493,
0.125297332063683, 0.173198938943319, 0.286364692763195, 0.187181622294097,
0.0155249739392275, 0.0284811383447792, 0.3302152196822, 0.279809724823687,
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-0.267565269947471, -0.507879399175005, -0.163173363661096, -0.0301926306852119,
0.0141783247953152, -0.078676708722438), avgdate = c(107.642857142857,
108.142857142857, 111.928571428571, 101.857142857143, 80.1428571428571,
78.1428571428571, 120.214285714286, 114.785714285714, 110.428571428571,
112.5, 111.571428571429, 103.214285714286, 68.1428571428571,
85, 79.6428571428571, 78.3571428571429, 100, 99.6428571428571,
78.2142857142857, 116.285714285714, 82.5714285714286, 84.4285714285714,
87, 65.7142857142857, 54.8571428571429, 77.2142857142857, 113.214285714286,
99.7142857142857, 98.4285714285714, 116.428571428571, 128.928571428571,
102.785714285714, 96.5, 121.071428571429, 115.214285714286, 116.5,
114.785714285714, 53, 45.2142857142857, 39.5, 72.5714285714286,
84.4285714285714, 112.571428571429, 74.3571428571429, 96.8571428571429,
118.571428571429, 159.642857142857, 164.214285714286, 20.2857142857143,
49.1428571428571, 59.7142857142857, 43.5, 60.8571428571429, 117,
64.6428571428571, 31.2857142857143, 16.5714285714286, 16.5714285714286,
32.3571428571429, 33.5, 42.0714285714286, 47.4285714285714, 68.7142857142857,
113.071428571429, 135, 154.214285714286, 159.714285714286, 167.5,
167.642857142857, 143.642857142857, 97.4285714285714, 40.0714285714286,
22.2142857142857, 18.5714285714286, 39.6428571428571, 66.2857142857143,
80.3571428571429, 56.6428571428571, 28.7142857142857, 30.8571428571429,
19.8571428571429, 18.7857142857143, 85, 138.142857142857, 121.357142857143,
104.785714285714, 64.4285714285714, 147.785714285714, 161.285714285714,
171.214285714286, 173.357142857143, 168.214285714286, 170.5,
172.5, 33.5, 47.2857142857143, 134.214285714286, 101.571428571429,
66.7857142857143, 62.8571428571429, 75.8571428571429, 57.3571428571429,
135.785714285714, 131.357142857143, 140.214285714286, 167.214285714286,
171.857142857143, 157, 120.928571428571, 92.2857142857143, 90.2142857142857,
127.5, 137.285714285714, 167.785714285714, 170.857142857143,
169.714285714286, 180.714285714286, 174.857142857143, 191.071428571429,
162.857142857143, 156.142857142857, 143.642857142857, 112.071428571429,
155.571428571429, 155.928571428571, 156.714285714286, 168.142857142857,
173.5, 180.428571428571, 175.642857142857, 152.642857142857,
144.214285714286, 119, 141.428571428571, 164.714285714286, 175.142857142857,
166.428571428571, 129.571428571429, 143.071428571429, 162.571428571429,
NA, 187.357142857143, 167.285714285714, 159.642857142857, 152.785714285714,
174.142857142857, 180.357142857143, 180.357142857143, 173.642857142857,
177.642857142857, 170.357142857143, 158.928571428571, 141.357142857143,
117.571428571429, 136.571428571429, 118.714285714286, 165.785714285714,
169.5, 171.357142857143, 196.785714285714, 198.428571428571,
195.428571428571, 193.642857142857, 185, 191.928571428571, NA,
195.642857142857, 169, 168.642857142857, 162.928571428571, 147,
136.928571428571, 93.6428571428571, 105.285714285714, 130.428571428571,
139.714285714286, 145.214285714286, 160.928571428571, 164.714285714286,
171.785714285714, 174.5, 185, 187.071428571429, 191.5, 190.214285714286,
NA, 173.357142857143, 171.285714285714, 165.214285714286, 186.642857142857,
178.714285714286, 169.928571428571, 132.428571428571, 133.357142857143,
137.5, 141.357142857143, 152.642857142857, 151.428571428571,
157.142857142857, 172.142857142857, 166.714285714286, 187.785714285714,
179.857142857143, 164.428571428571, 141.357142857143, 140.357142857143,
174.357142857143, 142.214285714286, 126.285714285714, 150.571428571429,
154.571428571429, 128.857142857143, 141.785714285714, 163.5,
169, 165.714285714286, 175.071428571429, 170.285714285714, 180.071428571429,
180.5, 178.357142857143, 167.285714285714, 152.357142857143,
136.714285714286, 154.5, 162.571428571429, 168.714285714286,
164.428571428571, 164, 129.214285714286, 134.142857142857, 152.428571428571,
169, 169.5, 174.857142857143, 174.857142857143, 177.285714285714,
188.071428571429, 191.214285714286, 184.5, 176.214285714286,
170.142857142857, 162.428571428571, 174, 173.428571428571, 167.785714285714,
165.785714285714, 137.714285714286, 147, 145.642857142857, 141.571428571429,
150.5, 158.428571428571, 172.428571428571, 174.285714285714,
171.285714285714, 185.285714285714, 190.857142857143, 177.214285714286,
166.571428571429, 167.571428571429, 169.428571428571, 159.357142857143,
156.357142857143, 142.571428571429, 136.928571428571, 158.714285714286,
159.071428571429, 146.928571428571, 149.214285714286, 152.285714285714,
159.928571428571, 162.785714285714, 174, 179.285714285714, 181.571428571429,
176.428571428571, 176.071428571429, 169.285714285714, 150.428571428571,
134.785714285714, 144, 152.714285714286, 163.785714285714, 159.428571428571,
172.714285714286, 164.642857142857, 167.857142857143, 165.642857142857,
179.571428571429, 179.142857142857, 144.428571428571, 176.357142857143,
152.285714285714, 132, 129.142857142857, 139.071428571429, 161.142857142857,
171.785714285714, 161.642857142857, 171.357142857143, 172.571428571429,
172.428571428571, 180.285714285714, 180.857142857143, 175.142857142857,
164.5, 135.357142857143, 132, 144, 147.714285714286, 166.928571428571,
178.571428571429, 176.071428571429, 173.785714285714, 169.857142857143,
183.785714285714, 193.857142857143, 169.714285714286, 160.928571428571,
144, 148.785714285714, 150, 160.428571428571, 157.785714285714,
174.357142857143, 175.571428571429, 171.785714285714, 180.142857142857,
180.857142857143, 172.928571428571, 168.214285714286, 158.5,
162.214285714286, 166.928571428571, 169.071428571429, 168.5,
178.428571428571, 188.285714285714, 178.142857142857, 175.785714285714,
170.214285714286, 154.571428571429, 170.142857142857, 165.214285714286,
168.642857142857, 167.214285714286, 154.071428571429, 168.357142857143
)), row.names = c(NA, -349L), class = c("tbl_df", "tbl", "data.frame"
), .Names = c("swediff", "avgdate"))
难怪它不收敛。您的模型不允许拟合度超过 0。
您的 nls 模型需要一个渐近线参数，而不是强制它为 0。
如果你尝试
nls(y~c-a*exp(x*b),start=list(a=.1,b=.1,c=0.2))
你很合身：
统计学家可能会问你为什么需要函数形式；典型的非参数回归/平滑方法*应该描述这种关系，或者稍微好一点；您可以使用交叉验证来选择 df。
* 我希望具有 3 df 加上常数项的自然三次样条会表现得很好（它有一个额外的参数，所以如果它比 nls 指数拟合更好，那就不足为奇了）
你可以很容易地做一个虚线配合包segmented:
library(segmented)
linmdl <- lm(y~x)
segmentedmdl <- segmented(linmdl, seg.Z = ~x, psi=150)
summary(segmentedmdl)
***Regression Model with Segmented Relationship(s)***
Call:
segmented.lm(obj = linmdl, seg.Z = ~x, psi = 150)
Estimated Break-Point(s):
Est. St.Err
154.173 1.962
Meaningful coefficients of the linear terms:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.1518234 0.0427016 3.555 0.00043 ***
x -0.0003317 0.0003784 -0.877 0.38134
U1.x -0.0191520 0.0015109 -12.676 NA
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.1909 on 342 degrees of freedom
Multiple R-Squared: 0.5835, Adjusted R-squared: 0.5799
Convergence attained in 2 iterations with relative change 1.425652e-16
如您所见，它在大约 154 处设置了中断，产生了这个拟合：
我正在尝试找到适合我的数据的方程式。我认识到形状是 y=-exp(x) 但 nls(y~-a*exp(x*b)) 具有各种参数起始值失败。 y 为负，因此 log(y)~log(a)+bx 的 "easy" 拟合效果不佳。我试过 log(y+2)~a+bx 使一切都变得积极，但没有得到正确的形状。
有人可以提供一些帮助来拟合这些数据吗？谢谢！
y=瑞典夫
x=平均日期
dat2=structure(list(swediff = c(0.0379635202678687, 0.0845477936160927,
0.146010217481196, 0.0416237104326292, 0.0659140490644253, 0.134535534695029,
0.0095147654468483, 0.238456044233877, 0.276025694437364, 0.29435448415394,
0.00301157777812485, 0.19171002685605, 0.277759059448242, 0.00400780564144798,
0.342605838471721, 0.236804884903432, 0.151048712082562, 0.188620966368049,
-0.0615972418208484, -0.00184933102124457, -0.0163171325413688,
0.00370250929658511, 0.30014673206306, 0.135354035472228, 0.00699671782210069,
0.0174510674253347, -0.0145499677497698, 0.0113155610814752,
-0.0683884523999768, 0.20157093417998, 0.186320361855075, -0.115609443650563,
0.069177592825418, -0.0161221161393796, 0.150181081582068, 0.0632121126749741,
0.0769960292118834, 0.061783685314432, 0.0442014176783082, -0.00990798027657931,
-0.00186219548019918, 0.0274216740478325, 0.118878480695049,
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84.4285714285714, 112.571428571429, 74.3571428571429, 96.8571428571429,
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104.785714285714, 64.4285714285714, 147.785714285714, 161.285714285714,
171.214285714286, 173.357142857143, 168.214285714286, 170.5,
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66.7857142857143, 62.8571428571429, 75.8571428571429, 57.3571428571429,
135.785714285714, 131.357142857143, 140.214285714286, 167.214285714286,
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127.5, 137.285714285714, 167.785714285714, 170.857142857143,
169.714285714286, 180.714285714286, 174.857142857143, 191.071428571429,
162.857142857143, 156.142857142857, 143.642857142857, 112.071428571429,
155.571428571429, 155.928571428571, 156.714285714286, 168.142857142857,
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144.214285714286, 119, 141.428571428571, 164.714285714286, 175.142857142857,
166.428571428571, 129.571428571429, 143.071428571429, 162.571428571429,
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174.142857142857, 180.357142857143, 180.357142857143, 173.642857142857,
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117.571428571429, 136.571428571429, 118.714285714286, 165.785714285714,
169.5, 171.357142857143, 196.785714285714, 198.428571428571,
195.428571428571, 193.642857142857, 185, 191.928571428571, NA,
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139.714285714286, 145.214285714286, 160.928571428571, 164.714285714286,
171.785714285714, 174.5, 185, 187.071428571429, 191.5, 190.214285714286,
NA, 173.357142857143, 171.285714285714, 165.214285714286, 186.642857142857,
178.714285714286, 169.928571428571, 132.428571428571, 133.357142857143,
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179.857142857143, 164.428571428571, 141.357142857143, 140.357142857143,
174.357142857143, 142.214285714286, 126.285714285714, 150.571428571429,
154.571428571429, 128.857142857143, 141.785714285714, 163.5,
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180.5, 178.357142857143, 167.285714285714, 152.357142857143,
136.714285714286, 154.5, 162.571428571429, 168.714285714286,
164.428571428571, 164, 129.214285714286, 134.142857142857, 152.428571428571,
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150.5, 158.428571428571, 172.428571428571, 174.285714285714,
171.285714285714, 185.285714285714, 190.857142857143, 177.214285714286,
166.571428571429, 167.571428571429, 169.428571428571, 159.357142857143,
156.357142857143, 142.571428571429, 136.928571428571, 158.714285714286,
159.071428571429, 146.928571428571, 149.214285714286, 152.285714285714,
159.928571428571, 162.785714285714, 174, 179.285714285714, 181.571428571429,
176.428571428571, 176.071428571429, 169.285714285714, 150.428571428571,
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172.714285714286, 164.642857142857, 167.857142857143, 165.642857142857,
179.571428571429, 179.142857142857, 144.428571428571, 176.357142857143,
152.285714285714, 132, 129.142857142857, 139.071428571429, 161.142857142857,
171.785714285714, 161.642857142857, 171.357142857143, 172.571428571429,
172.428571428571, 180.285714285714, 180.857142857143, 175.142857142857,
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178.571428571429, 176.071428571429, 173.785714285714, 169.857142857143,
183.785714285714, 193.857142857143, 169.714285714286, 160.928571428571,
144, 148.785714285714, 150, 160.428571428571, 157.785714285714,
174.357142857143, 175.571428571429, 171.785714285714, 180.142857142857,
180.857142857143, 172.928571428571, 168.214285714286, 158.5,
162.214285714286, 166.928571428571, 169.071428571429, 168.5,
178.428571428571, 188.285714285714, 178.142857142857, 175.785714285714,
170.214285714286, 154.571428571429, 170.142857142857, 165.214285714286,
168.642857142857, 167.214285714286, 154.071428571429, 168.357142857143
)), row.names = c(NA, -349L), class = c("tbl_df", "tbl", "data.frame"
), .Names = c("swediff", "avgdate"))
难怪它不收敛。您的模型不允许拟合度超过 0。
您的 nls 模型需要一个渐近线参数，而不是强制它为 0。
如果你尝试
nls(y~c-a*exp(x*b),start=list(a=.1,b=.1,c=0.2))
你很合身：
统计学家可能会问你为什么需要函数形式；典型的非参数回归/平滑方法*应该描述这种关系，或者稍微好一点；您可以使用交叉验证来选择 df。
* 我希望具有 3 df 加上常数项的自然三次样条会表现得很好（它有一个额外的参数，所以如果它比 nls 指数拟合更好，那就不足为奇了）
你可以很容易地做一个虚线配合包segmented:
library(segmented)
linmdl <- lm(y~x)
segmentedmdl <- segmented(linmdl, seg.Z = ~x, psi=150)
summary(segmentedmdl)
***Regression Model with Segmented Relationship(s)***
Call:
segmented.lm(obj = linmdl, seg.Z = ~x, psi = 150)
Estimated Break-Point(s):
Est. St.Err
154.173 1.962
Meaningful coefficients of the linear terms:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.1518234 0.0427016 3.555 0.00043 ***
x -0.0003317 0.0003784 -0.877 0.38134
U1.x -0.0191520 0.0015109 -12.676 NA
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 0.1909 on 342 degrees of freedom
Multiple R-Squared: 0.5835, Adjusted R-squared: 0.5799
Convergence attained in 2 iterations with relative change 1.425652e-16
如您所见，它在大约 154 处设置了中断，产生了这个拟合：