适合指数或曲棍球棒衰减(fit exponential or hockey stick decay)
我试图找到一个方程来适合我的数据。 我认识到形状是y=-exp(x)但是具有各种参数起始值的nls(y~-a*exp(x*b))失败。 y是负数，所以log（y）〜log（a）+ b x的“简单”拟合效果不佳。 我试过log（y + 2）〜a + b x使一切都变正，但是没有得到正确的形状。
有人能为这些数据提供一些帮助吗？ 谢谢！
Y = swediff
X = avgdate
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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"))I'm trying to find an equation to fit my data. I recognize the shape to be y=-exp(x) but nls(y~-a*exp(x*b)) with various parameter start values fail. y is negative so the "easy" fit of log(y)~log(a)+bx doesn't work well. I tried log(y+2)~a+bx to make everything positive but that didn't result in the right shape.
Can someone provide some help for fitting this data? Thanks!
y=swediff
x=avgdate
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, 0.0592089915185285, -0.00823096478874009, 0.120750948230554, 0.278594307094423, -0.0111994006625954, 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难怪它不会收敛。 你的模型不允许配合超过0。
您需要在您的nls模型中使用渐近线参数，而不是强制为0。
如果你尝试类似的东西
nls(y~c-a*exp(x*b),start=list(a=.1,b=.1,c=0.2))你得到一个合理的合适：
统计人员可能会问你为什么需要功能表单; 典型的非参数回归/平滑方法*应该描述关系也好或略好; 您可以使用交叉验证来选择df。
*我希望有一个自然的立方样条，其中有3个df加上常数项会很好（它有一个额外的参数，所以如果它比nls指数拟合好的话，
您可以使用segmented包简单地进行折线：
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正如你所看到的，它将突破点设置在154点附近，
It's little wonder it doesn't converge. Your model doesn't allow the fit to go above 0.
You need an asymptote parameter in your nls model rather than forcing it to be 0.
If you try something like
nls(y~c-a*exp(x*b),start=list(a=.1,b=.1,c=0.2))you get a reasonable fit:
A statistician will probably ask you why you need a functional form; typical nonparametric regression / smoothing approaches* should describe the relationship as well or slightly better; you could use cross-validation to choose the df.
* I'd expect that a natural cubic spline with say 3 df plus the constant term would do pretty well (it has an extra parameter so that would be little surprise if it does better than the nls exponential fit)
You can do a broken line fit easily with the package 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-16As you see it placed the break at about 154, producing this fit:
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