R錯誤：參數而不啓動值

Question

非線性真實世界數據中，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 

我手動繪製的公式爲起點，

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，我收到一條錯誤消息：

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 

不知道我在這裏錯過了什麼。

Answer 1

我可以重現您的錯誤。 nls函數缺少其中的參數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 

現在數據df被創建並傳遞給nls函數。請確保，I()中的絕緣表達是預期的。

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 

閱讀公式手冊頁以瞭解絕緣表達式。

?formula 

的formula手冊頁說，

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，它建議使用I()防止公式運算符和算術運算符之間的模糊。

這裏爲來自公式手冊頁

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.

的另一句名言也是這人頁是值得一讀

?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.