[ADMB Users] MAR(1) -needing Var operator and Kronecker product

[H. Skaug]

Mollie,

Previous email sent prematurely.

kronecker.cpp contains a function "inv_sym_posdef" which inv()
for positive definite matrices. I am not sure if your matrix is pos.def.
You are right that a general inv(df1b2matrix) is missing.

>I was told that there is a way to fit the latent states as regular parameters
>instead of RE.

This could be what I am working on now. It would be good if you wanted to
test it but I need a bit more time to finish things up.

Hans

On Mon, Oct 22, 2012 at 8:42 PM, Mollie Brooks <mbrooks at ufl.edu> wrote:
> Thanks Hans!
> This will really help the progress of ADMB in the area of state-space models. I'll take a look at it and be an alpha tester.
>
> I ran into another issue with the MAR(1) model... Calculating the mean of the stationary distribution involves taking the inverse of a df1b2matrix. mu=inv(identity_matrix(1,n)-B)*A
> error: no matching function for call to ‘inv(df1b2matrix)’
> I was about to add this to Redmine, but had trouble signing in.
>
> It seems this function is not defined for RE models. Do you plan to add this function or is there an alternative? I was told that there is a way to fit the latent states as regular parameters instead of RE.
>
> cheers,
> Mollie
>
> On 22 Oct 2012, at 3:25 PM, H. Skaug wrote:
>
>> Hi Mollie,
>>
>> I am actually working on a library for kronecker products right now,
>> as I see that as the right approach to space time models. It is mostly
>> geared towards sparse matrices, but at least I have kronecker(sparse,dense)
>> which should be good staring point. About vec(A) I think is
>> already in the admb source, but it was lacking for random effects,
>> so I wrote that.
>>
>> I attaching my current code which is in constant development,
>> so you can use it as a template for your own work.
>>
>> Hans
>>
>>
>>
>> On Mon, Oct 22, 2012 at 6:30 PM, Mollie Brooks <mbrooks at ufl.edu> wrote:
>>> Hi ADMB community,
>>> I'm working on an MAR(1) model. I need to compute the variance of the
>>> stationary distribution using the Vec operator and the Kronecker or direct
>>> matrix product.
>>> I'm tying to compute equation 17 from the paper "ESTIMATING COMMUNITY
>>> STABILITY AND ECOLOGICAL INTERACTIONS FROM TIME-SERIES DATA" by A.R. Ives,
>>> B. Dennis, K. L. Cottingham, and S.R. Carpenter (2003)
>>> It defines these as follows...
>>>
>>> "The operation Vec(A) creates a column vector out of any matrix A by
>>> stacking columns of A on top of each other, with the first column on the top
>>> and the last column on the bottom. The often-handy algebra of the Vec
>>> operator is reviewed by Searle (1982)"
>>>
>>> "The Kronecker or direct matrix product of M and N is formed by scalar
>>> multiplying N in turn by each element of M and arranging the results into a
>>> large matrix."
>>>
>>> I was wondering, has anyone in the community written code for these
>>> operators, and or coded an MAR(1) model? Would you be willing to share?
>>> thanks,
>>> Mollie
>>>
>>> Mollie Brooks
>>> Postdoctoral Researcher, Ponciano Lab
>>> Biology Department, University of Florida
>>> http://people.biology.ufl.edu/mbrooks
>>>
>>>
>>>
>>> _______________________________________________
>>> Users mailing list
>>> Users at admb-project.org
>>> http://lists.admb-project.org/mailman/listinfo/users
>>>
>> <kronecker.cpp>
>