最大似然估计不收敛于;拼出;R中的dnorm
我使用对数似然函数估计模型参数。对于标准正态密度函数,我曾使用内置函数“dnorm”,并曾亲自指定该函数。奇怪的是,使用dnorm会导致收敛,而另一种方法不会:最大似然估计不收敛于;拼出;R中的dnorm,r,mle,R,Mle,我使用对数似然函数估计模型参数。对于标准正态密度函数,我曾使用内置函数“dnorm”,并曾亲自指定该函数。奇怪的是,使用dnorm会导致收敛,而另一种方法不会: ### Functions: u <- function(x,n) { ifelse(n!=1, util <- x^(1-n)/(1-n), util <- log(x)) return(util) } u.inv <- function(x,n) { ifelse(n !=1, inv.util
### Functions:
u <- function(x,n)
{
ifelse(n!=1, util <- x^(1-n)/(1-n), util <- log(x))
return(util)
}
u.inv <- function(x,n)
{
ifelse(n !=1, inv.util <- ((1-n)*(x))^(1/(1-n)), inv.util <- exp(x))
return(inv.util)
}
v = function(x,n){return(1/(u(maxz,n)-u(minz,n))*(u(x,n)-u(minz,n)))}
v.inv = function(x,n){return(u.inv(x*(u(maxz,n)-u(minz,n))+u(minz,n),n))}
w <- function(p,a,b){return(exp(-b*(-log(p))^(1-a)))}
### Data
z1 <- c(0.1111111, 0.1037037, 0.1222222, 0.1111111, 0.1074074, 0.1666667, 0.1333333, 0.2000000, 0.1333333, 0.1074074,
0.1037037, 0.1111111, 0.1333333, 0.2000000, 0.1222222, 0.1111111, 0.1666667, 0.1333333, 0.1111111, 0.1333333,
0.1111111, 0.1666667, 0.1074074, 0.1333333, 0.1222222, 0.2000000, 0.1037037)
z2 <- c(0.08888889, 0.06666667, 0.07777778, 0.00000000, 0.03333333, 0.09259259, 0.09629630, 0.08888889, 0.06666667,
0.03333333, 0.06666667, 0.08888889, 0.06666667, 0.08888889, 0.07777778, 0.00000000, 0.09259259, 0.09629630,
0.00000000, 0.09629630, 0.08888889, 0.09259259, 0.03333333, 0.06666667, 0.07777778, 0.08888889, 0.06666667)
p <- c(0.5, 0.9, 0.5, 0.9, 0.9, 0.1, 0.1, 0.1, 0.5, 0.9, 0.9, 0.5, 0.5, 0.1, 0.5, 0.9, 0.1, 0.1, 0.9, 0.1, 0.5, 0.1, 0.9, 0.5, 0.5, 0.1, 0.9)
zce <- c(0.11055556, 0.10277778, 0.11000000, 0.10833333, 0.10185185, 0.11666667, 0.13240741, 0.14166667, 0.13166667,
0.07222222, 0.08796296, 0.09944444, 0.09500000,0.10833333, 0.09444444, 0.05277778, 0.10925926, 0.11759259,
0.05833333, 0.10277778, 0.09277778, 0.10925926, 0.06111111, 0.08833333, 0.09222222, 0.12500000, 0.09166667)
maxz = 135
minz = 0
### Using dnorm:
LL <- function(n,a,b,s)
{
V = (v(z1,n)-v(z2,n))*w(p,a,b) + v(z2,n)
res = zce - v.inv(V,n)
ll = dnorm(res, 0, s,log=T)
return(-sum(ll))
}
### mle()
fit <- mle(LL,
start = list(n = 0.1,a=0.1,b=0.1,s=0.1),
method = "L-BFGS-B",
lower = list(n=-Inf,a = -Inf, b = 0.0001, s=0.0001),
upper = list(n=0.9999,a = 0.9999, b = Inf, s=Inf),
control = list(maxit = 500, ndeps = rep(0.000001,4)),
nobs=length(z1)
)
### Resulting coefficients saved in "fit"
Coefficients:
n a b s
0.16533414 0.65254314 0.78727084 0.01475997
问题是,我不明白为什么。如果我取起始值来生成mle将使用的第一个“res”向量,我将使用自己的规范得到对数密度向量。此外,这似乎与我使用dnorm(…log=T)时得到的向量相匹配:
有趣的是,当测试与“==”相等时,这些数字并不相同(除了一个):
以更高的精度检查这些数字表明它们与另一个略有不同:
sprintf("%.54f",ldens(res,0,s))[1]
"1.383596381246589235303190434933640062808990478515625000"
sprintf("%.54f",dnorm(res, 0, s,log=T))[1]
"1.383596381246589013258585509902331978082656860351562500"
但这不可能是为什么使用dnorm会导致收敛,而另一个不会收敛的原因?更改函数以捕获以下错误:
ldens <- function(x,mu,sig){v <- log((1/(sig*sqrt(2*pi)))*exp(-((x-mu)^2/(2*sig^2)))); if(is.infinite(sum(v))) browser(); v}
ldens这是正确的-ldens(1e18,0,1)
给出了-Inf
而dnorm(1e18,0,1,log=TRUE)
给出了-5e+35
谢谢!Browser()非常有用,我不知道这一点。我现在知道指数部分是零,因为mle()尝试了sig=0.0001(下限)。增加此下限将导致具有相似系数的收敛。或者,使用规则log(A*B)=log(A)+log(B)重写自我指定的正常密度,这将给出lden
n = a = b = s = 0.1
V = (v(z1,n)-v(z2,n))*w(p,a,b) + v(z2,n)
res = zce - v.inv(V,n)
ldens(x= res, mu=0, sig = s)
[1] 1.383596 1.383637 1.379527 1.383579 1.382617 1.320485 1.381703 1.317098 1.383168 1.325277 1.372026 1.378537 1.327294 1.139934 1.353307 1.222810 1.291415 [18] 1.379966 1.252776 1.356281 1.369575 1.291415 1.281141 1.302690 1.347586 1.242405 1.376986
dnorm(res, 0, s, log=T)
[1] 1.383596 1.383637 1.379527 1.383579 1.382617 1.320485 1.381703 1.317098 1.383168 1.325277 1.372026 1.378537 1.327294 1.139934 1.353307 1.222810 1.291415 [18] 1.379966 1.252776 1.356281 1.369575 1.291415 1.281141 1.302690 1.347586 1.242405 1.376986
ldens(x= res,mu=0,sig = s) == dnorm(res, 0, s,log=T)
[1] FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE [26] TRUE FALSE
sprintf("%.54f",ldens(res,0,s))[1]
"1.383596381246589235303190434933640062808990478515625000"
sprintf("%.54f",dnorm(res, 0, s,log=T))[1]
"1.383596381246589013258585509902331978082656860351562500"
ldens <- function(x,mu,sig){v <- log((1/(sig*sqrt(2*pi)))*exp(-((x-mu)^2/(2*sig^2)))); if(is.infinite(sum(v))) browser(); v}