非有限函数值积分R：线性回归与误差分解

Question

我现在正在进行线性回归，其中误差项用普通随机变量和β随机变量分解（更多细节参见例如http://www.eea-esem.com/files/papers/eea-esem/2012/405/Cardak-Johnston-Martin_20111110.pdf）。问题是，当我在R中使用maxLik执行MLE时，它会返回错误并且进程停止。这是R中的代码：

#######################DGP################
library(maxLik)
set.seed(1357)
n=1000
x1 = matrix(rnorm(n,3,1.5),n,1)
x2 = matrix(rnorm(n,1,2.5),n,1)
x3 = sample(c(0,1), n, replace = TRUE)

X = cbind(1,x1,x2)
b = matrix(c(1,2,-3),1,3)
y = X%*%t(b)+rnorm(n,0,2)
g0 = 2
g1 = 1
g2 = 1.5
g3 = 2.4
#######################
p = exp(g0+g1*x3)
q = exp(g2+g3*x3)
#cbind(p,q)
eta = rep(0,n)
for (i in 1:n){
eta[i] = rbeta(1,shape1=p[i],shape2=q[i])}
plot(density(eta))

y2 = y+eta*2
summary(lm(y~X-1))
ols = lm(y2~X-1)
summary(ols)

#######################Model specification################   


normbeta = function(u,nu,sigma2,p,q,k){
eta = (u-nu)/k
ff= dnorm(nu,0,sqrt(sigma2))*dbeta(eta,shape1=p,shape2=q)/k
return(ff)
}
obj = function(u,sigma2,p,q,k){
integrate(normbeta,u=u,lower=u-k,upper=u,sigma2=sigma2,p=p,q=q,k=k)$value
}
objv = Vectorize(obj)


############MLE#################  


loglik = function(b){
a = split(b,rep(1:7,c(3,1,1,1,1,1,1)))
beta = a[[1]]
sigma2 = a[[2]]^2
k2 = a[[3]]^2
k=sqrt(k2)


g0 = a[[4]]
g1 = a[[5]]
g2 = a[[6]]
g3 = a[[7]]


p = exp(g0+g1*x3)
q = exp(g2+g3*x3)

u = y-X%*%beta

l = objv(u=u,sigma2=sigma2,p=p,q=q,k=k)


return(log(l))
}

a = list()
a[[1]] = coef(ols)
a[[2]] = sqrt(deviance(ols)/df.residual(ols))
a[[3]] = c(1,2,1,1.5,2.4)
b = unlist(a)

sum(loglik(b))

MLE = maxLik(logLik=loglik,print.level=2,start=b,method="BHHH")
summary(MLE)

报告错误：

----- Initial parameters: -----
fcn value: -2331.714 
   parameter initial gradient free
X1  2.042012       -338.04135    1
X2  1.953121      -1008.58628    1
X3 -2.969475       -310.82131    1
    2.008750        212.29245    1
    1.000000       -161.51965    1
    2.000000        -75.76826    1
    1.000000        -29.25573    1
    1.500000         75.10844    1
    2.400000         29.20714    1
Condition number of the (active) hessian: 1.657308e+14 
Error in integrate(normbeta, u = u, lower = u - k, upper = u, sigma2 = sigma2,  : 
  non-finite function value
In addition: Warning message:
In dbeta(eta, shape1 = p, shape2 = q) : NaNs produced

我认为错误可能来自dbeta(eta, shape1 = p, shape2 = q)，β密度参数p和q应该是正数。但是我已经用exp()函数约束了它们。谁知道这里发生了什么？非常感谢。