How do I find best starting values for nlimb optimization? - r

Question

I am trying to run the following code with the attached dataset. How do I solve the error of hessian matrix inversion?
library(stats4)
library(bbmle)
library(stats)
library(numDeriv)
library('bbmle')
x<- c(1.1, 1.4, 1.3, 1.7,1.9, 1.8, 1.6, 2.2, 1.7, 2.7, 4.1, 1.8, 1.5, 1.2, 1.4, 3, 1.7, 2.3, 1.6, 2.0)
hist(x)
fEHLKUMW<-function(a,b,alpha,vartheta)
{
-sum(log( (2*a*b*alpha*vartheta*(x^(vartheta-1))*(exp(-x^(vartheta)))*((1- (exp(-x^(vartheta))))^(a-1))*((1-((1-((1-(exp(-x^(vartheta))))^a))^b))^(alpha-1)))/((1-((1-(exp(-x^(vartheta))))^a))^(b*(alpha+1)))
))
}
EHLKUMW.result<-mle2(fEHLKUMW,hessian = NULL,start=list(a=0.01,b=0.01,alpha=.3,vartheta=0.01),optimizer="nlminb",lower=0)
summary(EHLKUMW.result)
I get the error as;
**
Warning messages:
1: In nlminb(start = start, objective = objectivefunction, hessian = NULL, :
NA/NaN function evaluation
2: In mle2(fEHLKUML, hessian = NULL, start = list(a = 1, b = 0.4, c = 0.5, :
couldn't invert Hessian
**

Answer 1

This is a very open question I think, so I'll present some tools and an approach to this, and maybe others can comment, etc.
First, the main part:
library(bbmle)
library(stats)
library(numDeriv)
library(bbmle)
x<- c(1.1, 1.4, 1.3, 1.7,1.9, 1.8, 1.6, 2.2, 1.7, 2.7, 4.1, 1.8, 1.5, 1.2, 1.4, 3, 1.7, 2.3, 1.6, 2.0)
hist(x)
fEHLKUMW <- function(a,b,alpha,vartheta) {
-sum(log( (2*a*b*alpha*vartheta*(x^(vartheta-1))*(exp(-x^(vartheta)))*((1- (exp(-x^(vartheta))))^(a-1))*((1-((1-((1-(exp(-x^(vartheta))))^a))^b))^(alpha-1)))/((1-((1-(exp(-x^(vartheta))))^a))^(b*(alpha+1)))
))
}
Now, we can of course run it like you've done:
EHLKUMW.result <- mle2(
fEHLKUMW,
hessian = NULL,
start = list(
a = 0.01,
b = 0.01,
alpha = .3,
vartheta = 0.01
),
optimizer = "nlminb",
lower = 0
)
But we can also run it with a distribution on each of these parameters, to get a new input all the time:
EHLKUMW.result <- mle2(
fEHLKUMW,
hessian = NULL,
start =
list(
# a = 0.01,
# a = rt(1, 10, ncp = 0.01),
a = truncdist::rtrunc(1, spec = "t", a = 0, ncp = 0.01, df = 10),
# b = 0.01,
b = truncdist::rtrunc(1, spec = "t", a = 0, ncp = 0.01, df = 10),
# alpha = .3,
alpha = truncdist::rtrunc(1, spec = "t", a = 0, ncp = 0.3, df = 10),
# vartheta = 0.01
vartheta = truncdist::rtrunc(1, spec = "t", a = 0, ncp = 0.01, df = 10)
),
optimizer = "nlminb",
lower = 0
)
I've chosen to use trundist to get a t-distribution, centralised around
the values you provided, and lower is 0 through the a = -argument.
If you know what the upper limit of these parameters, this can be done with b = -argument.
The output that I think is most relevant are the attained logLik and the coef.
library(tidyverse)
exec(fEHLKUMW, !!!list(
a = 0.01,
b = 0.01,
alpha = .3,
vartheta = 0.01
))
replicate(
250,
exec(fEHLKUMW, !!!list(
# a = 0.01,
# a = rt(1, 10, ncp = 0.01),
a = truncdist::rtrunc(1, spec = "t", a = 0, ncp = 0.01, df = 10),
# b = 0.01,
b = truncdist::rtrunc(1, spec = "t", a = 0, ncp = 0.01, df = 10),
# alpha = .3,
alpha = truncdist::rtrunc(1, spec = "t", a = 0, ncp = 0.3, df = 10),
# vartheta = 0.01
vartheta = truncdist::rtrunc(1, spec = "t", a = 0, ncp = 0.01, df = 10)
)))
I used this to fine-tune the distributions the parameters
The following is a multiple runs and their output compared to
logLik.
tibble(n = seq_len(100),
output = map(n, ~mle2(
fEHLKUMW,
hessian = NULL,
start =
list(
# a = 0.01,
# a = rt(1, 10, ncp = 0.01),
a = truncdist::rtrunc(1, spec = "t", a = 0, ncp = 0.01, df = 10),
# b = 0.01,
b = truncdist::rtrunc(1, spec = "t", a = 0, ncp = 0.01, df = 10),
# alpha = .3,
alpha = truncdist::rtrunc(1, spec = "t", a = 0, ncp = 0.3, df = 10),
# vartheta = 0.01
vartheta = truncdist::rtrunc(1, spec = "t", a = 0, ncp = 0.01, df = 10)
),
optimizer = "nlminb",
lower = 0
))) ->
outputs_df
This code gives a nice print
outputs_df %>%
mutate(coef = output %>% map(coef),
logLik = output %>% map_dbl(logLik)) %>%
unnest_wider(coef) %>%
arrange(logLik) %>%
print(n=Inf)