非线性数据拟合-nls

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在许多实际问题中，回归模型中响应变量和预测变量之间的关系可能是复杂的非线性函数。这时就需要采取非线性回归方法来建立模型。非线性回归是在对变量的非线性关系有一定认识前提下，对非线性函数的参数进行最优化的过程，最优化后的参数会使得模型的RSS（残差平方和）达到最小。 在R语言中最为常用的非线性回归建模函数是nls，下面以米氏方程为例，介绍一下这个函数。

米氏方程（Michaelis-Menten equation）表示一个酶促反应的起始速度与底物浓度关系的速度方程。在酶促反应中，在低浓度底物情况下，反应相对于底物是一级反应（first order reaction）；而当底物浓度处于中间范围时，反应（相对于底物）是混合级反应（mixed order reaction）。当底物浓度增加时，反应由一级反应向零级反应（zero order reaction）过渡。\(v_0 = \frac{V_{max}[S]}{K_m+[S]}\)这个方程称为Michaelis-Menten方程，是在假定存在一个稳态反应条件下推导出来的，其中\(K_m\)值称为米氏常数，\(V_{max}\)是酶被底物饱和时的反应速度，\([S]\)为底物浓度。

米氏方程拟合实例

例如：已知底物浓度数据和相应的速率，求米氏常数\(K_m\)和酶被底物饱和时的反应速度\(V_{max}\)。使用nls函数时，需要指定函数形式，并且指定参数的初始值；此外，还有一种更为简便的方法就是采用内置自启动模型(self-starting Models)， 此时只需要指定函数形式，而不需要指定参数初始值。

数据设定

conc <- c(2.856829, 5.005303, 7.519473, 22.101664, 27.769976, 39.198025, 45.483269, 203.784238) #底物浓度
rate <- c(14.58342, 24.74123, 31.34551, 72.96985, 77.50099, 96.08794, 96.96624, 108.88374) #速率
L.minor <- data.frame(conc, rate)
knitr::kable(head(L.minor,8))

conc	rate
2.856829	14.58342
5.005303	24.74123
7.519473	31.34551
22.101664	72.96985
27.769976	77.50099
39.198025	96.08794
45.483269	96.96624
203.784238	108.88374

数据拟合

使用nls函数拟合实验数据，指定函数形式：M-M动力学方程，初始值设置为K=20，Vm=120。

L.minor.m1 <- nls(rate ~ Vm * conc/(K + conc), data = L.minor, #采用M-M动力学方程
                  start = list(K = 20, Vm = 120), #初始值设置为K=20，Vm=120
                  trace = TRUE) #占线拟合过程

## 624.3282 :   20 120
## 244.5458 :   15.92382 124.57149
## 234.5196 :   17.25299 126.43878
## 234.3593 :   17.04442 125.96181
## 234.3531 :   17.08574 126.04671
## 234.3529 :   17.07774 126.03017
## 234.3529 :   17.0793 126.0334
## 234.3529 :   17.07899 126.03276

summary(L.minor.m1)

##
## Formula: rate ~ Vm * conc/(K + conc)
##
## Parameters:
##    Estimate Std. Error t value Pr(>|t|)
## K    17.079      2.953   5.784  0.00117 **
## Vm  126.033      7.173  17.570 2.18e-06 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 6.25 on 6 degrees of freedom
##
## Number of iterations to convergence: 7
## Achieved convergence tolerance: 8.137e-06

#确定x轴范围并构建数据集
min <- range(L.minor$conc)[1]
max <- range(L.minor$conc)[2]
line.data <- data.frame(conc = seq(min, max, length.out = 1000))
#用模型预测数据构建数据集
line.data$p.predict <- predict(L.minor.m1, newdata = line.data)

可视化-判断拟合效果

非线性回归模型建立后需要判断拟合效果，因为有时候参数最优化过程会捕捉到局部极值点而非全局极值点。最直观的方法是在原始数据点上绘制拟合曲线。

require(ggplot2)

## Loading required package: ggplot2

ggplot() +
  geom_point(aes(x = conc, y = rate), data = L.minor,
             alpha = 0.5, size = 5, color = "red") +
  geom_line(aes(x = conc, y = p.predict), data = line.data,
            size = 1, color = "blue") +
  scale_x_continuous(
    name = expression(Substrate ~~ concentration(mmol ~~ m^3)),#采用expression来表示数学公式
    breaks = seq(0, 200, by = 25)) +
  scale_y_continuous(
    name = "Uptake rate (weight/h)",
    breaks = seq(0, 120, by = 10)) +
  geom_text(aes(x = 100, y = 60),
            label = "bolditalic(f(list(x, (list(K, V[m])))) == frac(V[m]%.%x, K+x))",
            #注意 geom_text中如果用expression()来进行表达，必须开启parse = TRUE
            #同时以字符串""的形式表示，不能使用expression
            parse = TRUE,
            size = 5, family = "times"
            ) +
  theme_bw() +
  theme(
        axis.title.x=element_text(size=16),
        axis.title.y=element_text(size=16),
        axis.text.x=element_text(size=12),
        axis.text.y=element_text(size=12))

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" title alt width="672" />

残差诊断

和线性回归类似，非线性回归假设误差是正态、独立和同方差性。为了检测这些假设是否成立我们用拟合模型的残差来代替误差进行判断。

plot(fitted(L.minor.m1),resid(L.minor.m1),pch=20,type="b",cex=0.6*round(abs(resid(L.minor.m1))),col="#00EEEE",xlab = "拟合数", ylab="残差")

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" title alt width="672" />

通过散点图中点的大小可以判断出拟合数据的优劣。

<embed src="http://www.zzsky.cn/flash/flash/200951029516379.swf"width="150" height="110">

Author：shangfr

邮箱：shangfr@foxmail.com