R help - Oct 2011 - simultaneously maximizing two independent log likelihood functions using mle2

Hello,

I have a log likelihood function that I was able to optimize using 
mle2.  I have two years of the data used to fit the function and I would 
like to fit both years simultaneously to test if the model parameter 
estimates differ between years, using likelihood ratio tests and AIC.  
Can anyone give advice on how to do this?

My likelihood functions are long so I'll use the tadpole predation 
example from Ben Bolker's book, Ecological Data and Models in R (p. 
268-270).

library(emdbook)
data(ReedfrogFuncresp)
attach(ReedfrogFuncresp)
# Holling Type II Equation
holling2.pred = function(N0, a, h, P, T) {
   a * N0 * P * T/(1 + a * h * N0)
}
# Negative log likelihood function
NLL.holling2 = function(a, h, P = 1, T = 1) {
   -sum(dbinom(Killed, prob = a * T * P/(1 + a * h * Initial),
   size = Initial, log = TRUE))
}
# MLE statement
FFR.holling2 = mle2(NLL.holling2, start = list(a = 0.012,
   h = 0.84), data = list(T = 14, P = 3))

I have my negative log likelihood function setup similarly to the above 
example.  Again, my goal is to simultaneously estimate parameters from 
the same function for two years, such that I can test if the parameters 
from the two years are different.  Perhaps an important difference from 
the above example is that I am using a multinomial distribution (dmnom) 
because my data are trinomially distributed.

Any help would be greatly appreciated.
Adam Zeilinger

-- 

Adam Zeilinger
Ph. D Candidate
Conservation Biology Program
University of Minnesota
Saint Paul, MN
www.linkedin.com/in/adamzeilinger

Adam Zeilinger <zeil0006 <at> umn.edu> writes:
> I have a log likelihood function that I was able to optimize using 
> mle2.  I have two years of the data used to fit the function and I would 
> like to fit both years simultaneously to test if the model parameter 
> estimates differ between years, using likelihood ratio tests and AIC.  
> Can anyone give advice on how to do this?
> 
> My likelihood functions are long so I'll use the tadpole predation 
> example from Ben Bolker's book, Ecological Data and Models in R (p. 
> 268-270).
> 
> library(emdbook)
> data(ReedfrogFuncresp)
> attach(ReedfrogFuncresp)
> # Holling Type II Equation
> holling2.pred = function(N0, a, h, P, T) {
>    a * N0 * P * T/(1 + a * h * N0)
> }
> # Negative log likelihood function
> NLL.holling2 = function(a, h, P = 1, T = 1) {
>    -sum(dbinom(Killed, prob = a * T * P/(1 + a * h * Initial),
>    size = Initial, log = TRUE))
> }
> # MLE statement
> FFR.holling2 = mle2(NLL.holling2, start = list(a = 0.012,
>    h = 0.84), data = list(T = 14, P = 3))
> 
> I have my negative log likelihood function setup similarly to the above 
> example.  Again, my goal is to simultaneously estimate parameters from 
> the same function for two years, such that I can test if the parameters 
> from the two years are different.  Perhaps an important difference from 
> the above example is that I am using a multinomial distribution (dmnom) 
> because my data are trinomially distributed.

  The most convenient way to do this would be to use the
'parameters' argument to mle2.  For example,

FFR.holling2.byyear <- mle2(NLL.holling2, start = list(a = 0.012,
    h = 0.84), data = c(list(T = 14, P = 3), ReedfrogFuncresp),  
    parameters=list(a~year, h~year))

-- or you could fit a model where only one or the other of the
parameters varied between years.
   R should automatically construct a set of parameters (in 
this case 'a for year 1', 'delta-a between year 1 and year 2',
'h for year 1', 'delta-h between year 1 and year 2'); it
sets the starting values of the 'delta' variables to zero
by default.  (Things get a little bit tricky if you also 
want to set lower and upper bounds.)  [See section 6.6.1 of
the book for more details.]

   Note that I have included ReedfrogFuncresp in the data list.
I now regret using attach() in the book examples.

  Ben Bolker