如何拟合曲线和确定给定测量数据的渐近线

Question

我测量了在增加光强的情况下的光合作用速率，以产生单个样品的PI曲线。我想通过对每个样本的测量响应拟合一个模型来确定每条曲线的渐近线。下面是数据帧的一个子集，其中O2_229、O2_35等是单独的样本。

A <- structure(list(LightIntensity = c(0, 112, 180, 272, 351, 430, 
482, 541, 609), O2_229 = c(-0.44673102313958, 0.0205958989967557, 
0.475351137678564, 0.640026082127451, 0.753504162148724, 
0.804818094545302, 0.84640533715284, 0.864374368585184, 
0.905709184251358), O2_35 = c(-0.302567249367208, 
0.181032510348939, 0.376659543810537, 0.496560233238315, 
0.540322247837853, 0.521608765794946, 0.528669387756481, 
0.516887809093099, 0.514844068198885), 
O2_230 = c(-0.542179874878379, 0.110661210104475, 
0.331450283334161, 0.568762984387555, 0.752938666550757, 
0.88143509214304, 0.945109493908027, 1.04005672006219, 
1.10246315337637), O2_36 = c(-0.510663216304597, 
0.509412237512078, 0.888867356301998, 1.18011410170533, 
1.28838854392113, 1.21645059640005, 1.29459817366225, 
1.02604605624222, 0.620845429599006), 
O2_Blank = c(-0.0291830039468955, -0.010410546520055, 
0.0414968296661793, 0.0398063330176891, -0.00945808361433628, 
-0.039882102158536, -0.0447402714742525, -0.0283811043764061, 
-0.0365212803552079)), row.names = c(NA, -9L), class = 
"data.frame")

以下是迄今为止我用来比较单个样本(O2_229)的模型。我现在正在努力确保我找到了最好的模型，并确定了每个样本曲线的渐近线。

A <- Data_9.20
linear.model <-lm(O2_229 ~ LightIntensity, A)
summary(linear.model)
plot(A$LightIntensity, A$O2_229)
abline(lm(O2_229 ~ LightIntensity, A))

light2 <- A$LightIntensity^2
quadratic.model <-lm(O2_229 ~ LightIntensity + light2, A)
summary(quadratic.model)
lightvalues <- seq(0, 700, 100)
predictedcounts <- 
predict(quadratic.model,list(LightIntensity=lightvalues, light2 = 
lightvalues^2)) 
plot(A$LightIntensity, A$O2_229)
lines(lightvalues, predictedcounts)

Answer 1

我看到您正在使用二次方程对数据进行建模，它没有显式的渐近线。我发现一个带有偏移量的标准几何方程"y =a* pow(x，(b*x)) +偏移量“似乎是一个很好的数据模型，优点是”偏移量“参数是显式拟合的渐近线。以下是我对各种数据集(O2_Blank除外)和模型图的拟合值。我注意到数据集02_36似乎是曲线下降，而不是接近渐近线。

data set O2_229:
a = -1.3851681272467806E+00
b = -1.0364478100088784E-03
Offset =  9.1626307846861987E-01

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data set O2_35:
a = -8.4182899434390634E-01
b = -1.7580233358644494E-03
Offset =  5.3416172364897729E-01

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data set O2_230:
a = -1.6587794258648598E+00
b = -7.2532639452267352E-04
Offset =  1.1581944009325142E+00

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data set O2_36:
a = -1.6368370242440751E+00
b = -2.1647786145736897E-03
Offset =  1.1086452557429154E+00

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