在 chol.default(K) 中出現錯誤：5 階的前導次要與 betareg 不是正定的

Question

我正在嘗試使用betareg package的betareg function將beta regression模型擬合到這些數據：

df <- data.frame(category=c("c1","c1","c1","c1","c1","c1","c2","c2","c2","c2","c2","c2","c3","c3","c3","c3","c3","c3","c4","c4","c4","c4","c4","c4","c5","c5","c5","c5","c5","c5"),
                 value=c(6.6e-18,0.0061,0.015,1.1e-17,4.7e-17,0.0032,0.29,0.77,0.64,0.59,0.39,0.72,0.097,0.074,0.073,0.08,0.06,0.11,0.034,0.01,0.031,0.041,4.7e-17,0.025,0.58,0.14,0.24,0.29,0.55,0.15),stringsAsFactors = F)

df$category <- factor(df$category,levels=c("c1","c2","c3","c4","c5"))

使用此命令：

library(betareg)
fit <- betareg(value ~ category, data = df)

我收到此error ：

Error in chol.default(K) : 
  the leading minor of order 5 is not positive definite
In addition: Warning message:
In sqrt(wpp) : NaNs produced
Error in chol.default(K) : 
  the leading minor of order 5 is not positive definite
In addition: Warning messages:
1: In betareg.fit(X, Y, Z, weights, offset, link, link.phi, type, control) :
  failed to invert the information matrix: iteration stopped prematurely
2: In sqrt(wpp) : NaNs produced

是否有任何解決方案或 beta 回歸根本無法擬合這些數據？

Answer 1

將 beta 分布擬合到類別 1 中的數據將非常具有挑戰性，因為三個觀測值基本上為零。 四舍五入為五位數：0.00000、0.00000、0.00000、0.00320、0.00610、0.01500。 我不清楚這個類別是否應該以與其他類別相同的方式建模。

在類別 4 中，還有一個數值為零的觀測值，盡管其他觀測值稍大一些：0.00000、0.01000、0.02500、0.03100、0.03400、0.04100。

省略類別 1 至少允許在沒有數值問題的情況下估計模型。 對於來自每組六個觀測值的兩個參數，漸近推理是否是一個很好的近似是另一個問題。 不過，各組之間的精度似乎並不相同。

betareg(value ~ category | 1, data = df, subset = category != "c1")
## Call:
## betareg(formula = value ~ category | 1, data = df, subset = category != 
##     "c1")
## 
## Coefficients (mean model with logit link):
## (Intercept)   categoryc3   categoryc4   categoryc5  
##      0.2634      -2.2758      -4.4627      -1.0206  
## 
## Phi coefficients (precision model with log link):
## (Intercept)  
##       2.312  
betareg(value ~ category | category, data = df, subset = category != "c1")
## Call:
## betareg(formula = value ~ category | category, data = df, subset = category != 
##     "c1")
## 
## Coefficients (mean model with logit link):
## (Intercept)   categoryc3   categoryc4   categoryc5  
##      0.2566      -2.6676      -4.0601      -0.9784  
## 
## Phi coefficients (precision model with log link):
## (Intercept)   categoryc3   categoryc4   categoryc5  
##      2.0849       3.5619      -0.2308      -0.1376