# [ADMB Users] Linear multivariate state-space model.

H. Skaug hskaug at gmail.com
Wed Jul 3 11:15:45 PDT 2013

```Hi Dan,

Since your model is linear there are at least two approaches you can take:
1. Implement the Kalman filter (see chapter 8 in the ADMB manual)
2. Use the random effects module of ADMB in which you explicitly define
your state variable X to be a latent variable. This approach
can be generalized to nonlinear models.

I recommend doing both as an exercise to understand the possibilities that
ADMB offers. With regard to 2) there are a few tricks that people have
tpl-files for.

What is the size of your model, i.e. the dimension of X and the length of
your
time series? This info is critical for assessing which of 1 and 2 (if any)
is
the best choice. You say "spatio" which indicates that X is high
dimentional.

Hans

On Wed, Jul 3, 2013 at 6:34 PM, Dan Gladish <dan.gladish at gmail.com> wrote:

> Hello all,
>
> I am currently working on a spatio-temporal model that we are hoping to
> implement in ADMB.  Unfortunately, I am very new at ADMB and am looking for
> a little help.  Specifically, I am looking to see if there are any examples
> of code for a multivariate linear state-space model:
>
> Y(t) = X(t) + e(t), e(t) \sim N(0,s2e I)
> X(t) = M*X(t-1) + eta(t), eta(t) \sim N(0,Q)
>
> where Y(t) is the data vector, X(t) is the latent variable vector, M is
> the propagator matrix, and s2e and Q the innovation variance and latent
> covariance, respectively.
>
> There are a few examples of state-space models, but I did not see one
> using a very bare bones set-up like this.  Any help would be much
> appreciated for a lowly beginner like me.
>
> Sincerely,
>
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