R错误：参数而不启动值

Question

非线性真实世界数据中，n = 2600

SAMPLE 
X values 71.33 74.98 80 85.35 90.03 
Y values 119.17 107.73 99.72 75 54.59 

我手动绘制的公式为起点，

formula: y = b/x^2+a 
manual: y = 800000/x^2-39.5 
sum of residuals = 185 
correlation forecast to actual =0.79 

R中使用NLS式，我收到一条错误消息：

a_start = -39.5 
b_start = 800000 
m<-nls(y~b/(x^2)+a, start=list(a=a_start,b=b_start)) 

Error in nls(y~ b/(x^2) + a, start = list(a = a_start, b = b_start)) : 
parameters without starting value in 'data': y, x 

不知道我在这里错过了什么。

Answer 1

我可以重现您的错误。 nls函数缺少其中的参数data。

m<-nls(y ~ b/(x^2)+a, start=list(a=a_start, b=b_start)) 
# Error in nls(y ~ b/(x^2) + a, start = list(a = a_start, b = b_start)) : 
# parameters without starting value in 'data': y, x 

现在数据df被创建并传递给nls函数。请确保，I()中的绝缘表达是预期的。

df <- data.frame(x = c(71.33, 74.98 , 80 , 85.35 , 90.03), 
       y = c(119.17, 107.73 , 99.72 , 75, 54.59)) 
a_start <- -39.5 
b_start <- 800000 
m <- nls(y ~ I(b/(x^2+a)), data = df, start=list(a=a_start, b=b_start)) 
summary(m) 

# Formula: y ~ I(b/(x^2 + a)) 
# 
# Parameters: 
# Estimate Std. Error t value Pr(>|t|) 
# a -1743.2  872.5 -1.998 0.1396 
# b 412486.2 89981.4 4.584 0.0195 * 
# --- 
# Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 
# 
# Residual standard error: 9.103 on 3 degrees of freedom 
# 
# Number of iterations to convergence: 6 
# Achieved convergence tolerance: 4.371e-06 

阅读公式手册页以了解绝缘表达式。

?formula 

的formula手册页说，

The^operator indicates crossing to the specified degree. For example (a+b+c)^2 is identical to (a+b+c)*(a+b+c) which in turn expands to a formula containing the main effects for a, b and c together with their second-order interactions

此外，它建议使用I()防止公式运算符和算术运算符之间的模糊。

这里为来自公式手册页

avoid this confusion, the function I() can be used to bracket those portions of a model formula where the operators are used in their arithmetic sense. For example, in the formula y ~ a + I(b+c), the term b+c is to be interpreted as the sum of b and c.

的另一句名言也是这人页是值得一读

?AsIs 

In function formula. There it is used to inhibit the interpretation of operators such as "+", "-", "*" and "^" as formula operators, so they are used as arithmetical operators. This is interpreted as a symbol by terms.formula.