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This set of Matlab scripts conducts a first order MAR(1) model to estimate interactive effects, and covariate effects, on a time series of data from a community.

It uses a Gibbs sampler to estimate parameters, and currently is set up with diffuse priors on all parameters for the model. It is pretty basic at this point, but it works.

Note on the Gamma distribution:

Going back and forth between Matlab/R/WinBUGS can be confusing, because of the different parameterizations of the gamma pdf. Here's the Matlab/BUGS forms and the R equivalents:

Matlab: X ~ g(a,b) E[X] = ab

R equivalent: X ~ g(shape=a,scale=b)

BUGS: X ~ g(a,b) E[X] = a/b

R equivalent: X ~ g(shape=a,rate=b) OR

X ~ g(shape=a,scale=1/b)

We use a multivariate state-space model and a time series of yearly migration dates for sockeye salmon to estimate the heritability coef from the classic breeder's equation.

The 2 files below are the dataset and the R script.

LAMBDA is a MatLab toolkit designed to do MAR-1 based data analysis on long-term datasets and is based on the methods described in Ives et al. 2003, Ecological Monographs 73:301-330. LAMBDA is designed to allow the user to step through the entire modeling process, from importing the data, to obtaining descriptive statistics of the dataset, to, finally, performing a MAR-1 regression model and obtaining output parameters. A MAR-1 process is a Multivariate, Auto-Regressive first (1st) order process. Essentially, it is a means of estimating interactions between multiple variates from time series data, using matrix algebra. A MAR-1 model is a stochastic, non-mechanistic model that uses time series data on species numbers and co-variates to deduce inter-population interactions and the effects of covariates (e.g., physical variables) on populations.

Where does it come from?LAMBDA is a product of the Mathematical Biology program at the Northwest Fisheries Science Center in Seattle, WA, and was developed with support by NOAA/NMFS and the National Research Council. It is open-source software released under the GNU GPL license, meaning you are free to use and modify it in (almost) any way you see fit. LAMBDA was developed by Steven Viscido while on a National Research Council postdoctoral associateship with Elizabeth Holmes.

CreditsLAMBDA is based on the techniques outlined in the paper Ives et al. 2003, Ecological Monographs 73:301-330. The code for the actual MAR-1 regression was based on the "MARbasic.m" MatLab script written by Tony Ives (available at the Ecological Archives). The parameter search code was based on an unpublished script written by Tony Ives. All other code was written by Steven Viscido.

Executable versionDownload the LAMBDA executable along the installation instructions from the links below.

LAMBDA_MCR_pkg.exe 0.9.2 Warning: This is a 138 MB file!

Installation Instructions

The executable version of LAMBDA does not require MatLab. Its system requirements are Windows XP/2000, 256 MB of RAM, and 150 MB of Hard Drive Space.

If Installation hangsThis is a bug on MatLab's side. To work around it, you will need to install vcredist_x86.exe (32 bit systems) or vcredist_x64.exe (64 bit system) first and then repeat the LAMBDA installation. But read the If_Installation_Hangs.txt readme file if this happens to you. This bug affects about 20% of computers, randomly it would seem.

Matlab Source CodeThis is not needed if you are using the executable version. Current source code version is LAMBDA_0.9.2Beta.zip. The source code can be downloaded below. Requirements for running LAMBDA from the source code are

• MatLab version 7.0.1 (R14) w/service Pack 1, or later
• MatLab's Statistics and Optimization toolboxes
• At least 256 MB of RAM on your system
• 5 MB of Hard Drive space for the LAMBDA installation

This is the DEVELOPMENT site for the MARSS.  For the current MARSS  release go to CRAN or download straight from the R GUI using "Install Packages" menu.

MARSS fits mulitvariate autoregressive state-space (MARSS) models with Gaussian errors to multivariate time series data.  A MARSS model is:

x(t) = B x(t-1) + u + v(t), v(t)~MVN(0,Q)

y(t) = Z x(t) + a + w(t), w(t)~MVN(0,R)

Project news (Jan 27, 2012): MARSS 2.8 uploaded to CRAN.  2.3+ implements the algorithm for a fully unconstrained MARSS model with fixed and shared elements in all parameters.  See changes.pdf for the fixes since 2.5.  MARSS 2.9 is in the works which will allow more typical specification of covariates. I'm also working on MARSS 3.0, which implements the general EM algorithm with linear constraints on the parameter matrices. MARSS 2.8 is implementing a constrained version of the more general algorithm in the EMDerivation paper.  The change for 3.0 requires changing the 'wrappers' so user can specify the linear constraints.  The actual algorithm code (MARSSkem.r) is unchanged.

Developers: Eli Holmes, Eric Ward and Kellie Wills

Current known issues:

• lap-p models not working with method=kem since kemcheck is blocking.  Need to review EM algorithm per constraint that B subblock corresponding to diag(Q)=0 must be diagonal.    Use method="BFGS" as a work around. 
• moving average models not tested.
• The likelihood for the covariate "trick" where you want covariate to affect process only and do that by setting R=zero is wrong.  There shouldn't be a likelihood of the covariate added in, but will be since Q=1.I added a note to manual for 2.8 saying you need to subtract off that extra LL.
  
• For cross-platform compatibility with MacOS, I think all of the source files need a hard return / empty line as the last line.

A series of modules for estimation of PVA parameters from time series data. Uses kalman filters, REML, and slope methods.