# [R] model selection with spg and AIC (or, convert list to fitted model object)

Thu Oct 11 02:11:35 CEST 2012

```Dear R Help,

I have two nested negative log-likelihood functions that I am optimizing
with the spg function [BB package].  I would like to perform model
selection on these two objective functions using AIC (and possibly
anova() too).  However, the spg() function returns a list and I need a
fitted model object for AIC(), ICtab() [bbmle package], or anova().

How can I perform AIC-based model selection on two spg-optimized
objective functions?  Alternatively, how can I convert the list returned
by spg into a fitted model object that can be run in AIC, ICtab, or anova?

Here is an example:

##########################################################################

library(BB)
library(bbmle)

# define multinomial distribution
dmnom2 <- function(x,prob,log=FALSE) {
r <- lgamma(sum(x) + 1) + sum(x * log(prob) - lgamma(x + 1))
if (log) r else exp(r)
}

# data frame y
y <- structure(list(tv = 1:20, n1 = c(17L, 18L, 16L, 18L, 16L, 16L,
18L, 18L, 20L, 16L, 20L, 16L, 17L, 17L, 18L, 19L, 18L,
16L, 17L,
17L), n2 = c(2L, 2L, 3L, 2L, 4L, 4L, 2L, 2L, 0L, 4L, 0L,
4L,
3L, 3L, 2L, 1L, 2L, 4L, 3L, 3L), n3 = c(1L, 0L, 1L, 0L,
0L, 0L,
0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L, 0L,
0L)), .Names = c("tv",
"n1", "n2", "n3"), row.names = c(NA, -20L), class =
"data.frame")

# Negative log likelihood functions
NLL1 <- function(par, y){
p1 <- par[1]
p2 <- par[2]
mu1 <- par[3]
mu2 <- par[4]
n1 <- y\$n1
n2 <- y\$n2
n3 <- y\$n3
t <- y\$tv
P1 <- (p1*((-1 + exp(sqrt((mu1 + mu2 + p1 + p2)^2 -
4*(mu2*p1 + mu1*(mu2 + p2)))*t))*((-mu2)*(mu2 - p1 + p2) +
mu1*(mu2 + 2*p2)) - mu2*sqrt((mu1 + mu2 + p1 + p2)^2 -
4*(mu2*p1 + mu1*(mu2 + p2))) -
exp(sqrt((mu1 + mu2 + p1 + p2)^2 - 4*(mu2*p1 + mu1*(mu2 + p2)))*t)*
mu2*sqrt((mu1 + mu2 + p1 + p2)^2 - 4*(mu2*p1 + mu1*(mu2 + p2))) +
2*exp((1/2)*(mu1 + mu2 + p1 + p2 + sqrt((mu1 + mu2 + p1 + p2)^2 -
4*(mu2*p1 + mu1*(mu2 + p2))))*t)*mu2*
sqrt((mu1 + mu2 + p1 + p2)^2 - 4*(mu2*p1 + mu1*(mu2 + p2)))))/
exp((1/2)*(mu1 + mu2 + p1 + p2 + sqrt((mu1 + mu2 + p1 + p2)^2 -
4*(mu2*p1 + mu1*(mu2 + p2))))*t)/(2*(mu2*p1 + mu1*(mu2 + p2))*
sqrt((mu1 + mu2 + p1 + p2)^2 - 4*(mu2*p1 + mu1*(mu2 + p2))))

P2 <- (p2*((-1 + exp(sqrt((mu1 + mu2 + p1 + p2)^2 -
4*(mu2*p1 + mu1*(mu2 + p2)))*t))*(-mu1^2 + 2*mu2*p1 +
mu1*(mu2 - p1 + p2)) - mu1*sqrt((mu1 + mu2 + p1 + p2)^2 -
4*(mu2*p1 + mu1*(mu2 + p2))) -
exp(sqrt((mu1 + mu2 + p1 + p2)^2 - 4*(mu2*p1 + mu1*(mu2 + p2)))*t)*
mu1*sqrt((mu1 + mu2 + p1 + p2)^2 - 4*(mu2*p1 + mu1*(mu2 + p2))) +
2*exp((1/2)*(mu1 + mu2 + p1 + p2 + sqrt((mu1 + mu2 + p1 + p2)^2 -
4*(mu2*p1 + mu1*(mu2 + p2))))*t)*mu1*
sqrt((mu1 + mu2 + p1 + p2)^2 - 4*(mu2*p1 + mu1*(mu2 + p2)))))/
exp((1/2)*(mu1 + mu2 + p1 + p2 + sqrt((mu1 + mu2 + p1 + p2)^2 -
4*(mu2*p1 + mu1*(mu2 + p2))))*t)/(2*(mu2*p1 + mu1*(mu2 + p2))*
sqrt((mu1 + mu2 + p1 + p2)^2 - 4*(mu2*p1 + mu1*(mu2 + p2))))
P3 <- 1 - P1 - P2
p.all <- c(P1, P2, P3)
-sum(dmnom2(c(n1, n2, n3), prob = p.all, log = TRUE))
}

NLL2 <- function(par, y) {
p1 <- par[1]
p2 <- p1
mu1 <- par[2]
mu2 <- mu1
n1 <- y\$n1
n2 <- y\$n2
n3 <- y\$n3
t <- y\$t
P1 <- (p1*((-1 + exp(sqrt((mu1 + mu2 + p1 + p2)^2 -
4*(mu2*p1 + mu1*(mu2 + p2)))*t))*((-mu2)*(mu2 - p1 + p2) +
mu1*(mu2 + 2*p2)) - mu2*sqrt((mu1 + mu2 + p1 + p2)^2 -
4*(mu2*p1 + mu1*(mu2 + p2))) -
exp(sqrt((mu1 + mu2 + p1 + p2)^2 - 4*(mu2*p1 + mu1*(mu2 + p2)))*t)*
mu2*sqrt((mu1 + mu2 + p1 + p2)^2 - 4*(mu2*p1 + mu1*(mu2 + p2))) +
2*exp((1/2)*(mu1 + mu2 + p1 + p2 + sqrt((mu1 + mu2 + p1 + p2)^2 -
4*(mu2*p1 + mu1*(mu2 + p2))))*t)*mu2*
sqrt((mu1 + mu2 + p1 + p2)^2 - 4*(mu2*p1 + mu1*(mu2 + p2)))))/
exp((1/2)*(mu1 + mu2 + p1 + p2 + sqrt((mu1 + mu2 + p1 + p2)^2 -
4*(mu2*p1 + mu1*(mu2 + p2))))*t)/(2*(mu2*p1 + mu1*(mu2 + p2))*
sqrt((mu1 + mu2 + p1 + p2)^2 - 4*(mu2*p1 + mu1*(mu2 + p2))))

P2 <- (p2*((-1 + exp(sqrt((mu1 + mu2 + p1 + p2)^2 -
4*(mu2*p1 + mu1*(mu2 + p2)))*t))*(-mu1^2 + 2*mu2*p1 +
mu1*(mu2 - p1 + p2)) - mu1*sqrt((mu1 + mu2 + p1 + p2)^2 -
4*(mu2*p1 + mu1*(mu2 + p2))) -
exp(sqrt((mu1 + mu2 + p1 + p2)^2 - 4*(mu2*p1 + mu1*(mu2 + p2)))*t)*
mu1*sqrt((mu1 + mu2 + p1 + p2)^2 - 4*(mu2*p1 + mu1*(mu2 + p2))) +
2*exp((1/2)*(mu1 + mu2 + p1 + p2 + sqrt((mu1 + mu2 + p1 + p2)^2 -
4*(mu2*p1 + mu1*(mu2 + p2))))*t)*mu1*
sqrt((mu1 + mu2 + p1 + p2)^2 - 4*(mu2*p1 + mu1*(mu2 + p2)))))/
exp((1/2)*(mu1 + mu2 + p1 + p2 + sqrt((mu1 + mu2 + p1 + p2)^2 -
4*(mu2*p1 + mu1*(mu2 + p2))))*t)/(2*(mu2*p1 + mu1*(mu2 + p2))*
sqrt((mu1 + mu2 + p1 + p2)^2 - 4*(mu2*p1 + mu1*(mu2 + p2))))
P3 <- 1 - P1 - P2
p.all <- c(P1, P2, P3)
-sum(dmnom2(c(n1, n2, n3), prob = p.all, log = TRUE))
}

# Optimization with spg
spg1 <- spg(par = c(2, 0.3, 0.001, 0.001), fn = NLL1, y = y,
lower = c(0.0001, 0.0001, 0.0001, 0.0001),
control = list(maxit = 5000, trace = FALSE))

spg2 <- spg(par = c(2, 0.001), fn = NLL2, y = y,
lower = c(0.0001, 0.0001),
control = list(maxit = 5000, trace = FALSE))

# Model selection with ICtab; currently gives an error
ICtab(spg1, spg2)

##########################################################################

Any suggestions would be greatly appreciated.