如何根据给定的测量数据拟合曲线并确定渐近线

Question

我已经在增加的光强度下测量了光合速率，以产生单个样品的PI曲线。我想通过将模型拟合到每个样本的测量响应来确定每个曲线的渐近线。以下是数据帧的子集，其中O2_229，O2_35等是单个样本。

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")

这里是到目前为止，我可以比较单个样本（O2_229）的模型。我现在正在尝试确保找到最佳模型并确定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式对数据建模，该方程式没有明确的渐近线。我发现带有偏移量的标准几何公式“ y = a * pow（x，（b * x））+偏移量”似乎是数据的良好模型，其优点是“偏移量”参数是明确拟合的渐近线。这是我对各种数据集（O2_Blank除外）和模型图的拟合值。我注意到数据集02_36似乎向下弯曲而不是接近渐近线。

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

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

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

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