`nls`无法估算我模型的参数 [英] `nls` fails to estimate parameters of my model

问题描述

我正在尝试估计堆定律的常数。
我有以下数据集 novels_colection ：

I am trying to estimate the constants for Heaps law. I have the following dataset novels_colection:

  Number of novels DistinctWords WordOccurrences
1                1         13575          117795
2                1         34224          947652
3                1         40353         1146953
4                1         55392         1661664
5                1         60656         1968274

然后我建立下一个函数：

Then I build the next function:

# Function for Heaps law
heaps <- function(K, n, B){
  K*n^B
}
heaps(2,117795,.7) #Just to test it works

所以 n =出现单词和 K 和 B 是应该为常量而定的值，以便找到我对Distinct的预测

So n = Word Occurrences, and K and B are values that should be constants in order to find my prediction of Distinct Words.

我尝试过，但这给了我一个错误：

I tried this but it gives me an error:

fitHeaps <- nls(DistinctWords ~ heaps(K,WordOccurrences,B), 
    data = novels_collection[,2:3], 
    start = list(K = .1, B = .1), trace = T)

错误= numericalDeriv（form [[3L]]，names（ind），env）中的错误：
求值时缺少值或无穷大模型

关于如何解决此问题或方法以适合函数并获取 K值的任何想法和 B ？

Any idea in how could I fix this or a method to fit the function and get the values for K and B?

推荐答案

如果在 y = K * n ^ B 的两边进行对数变换，得到 log（y）= log（K）+ B * log（ n）。这是 log（y）和 log（n）之间的线性关系，因此您可以拟合线性回归模型查找 log（K）和 B 。

If you take log transform on both sides of y = K * n ^ B, you get log(y) = log(K) + B * log(n). This is a linear relationship between log(y) and log(n), hence you can fit a linear regression model to find log(K) and B.

logy <- log(DistinctWords)
logn <- log(WordOccurrences)

fit <- lm(logy ~ logn)

para <- coef(fit)  ## log(K) and B
para[1] <- exp(para[1])    ## K and B

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