# Multivariate Autoregressive State-Space Modeling

The MARSS package provides maximum-likelihood parameter estimation for constrained and unconstrained linear multivariate autoregressive state-space (MARSS) models fit to multivariate time-series data. Fitting is primarily via an Expectation-Maximization (EM) algorithm, although fitting via the BFGS algorithm (using the optim function) is also provided. MARSS models are a class of dynamic linear model (DLM) and vector autoregressive model (VAR) model. Functions are provided for parametric and innovations bootstrapping, Kalman filtering and smoothing, bootstrap model selection criteria (AICb), confidences intervals via the Hessian approximation and via bootstrapping and calculation of auxiliary residuals for detecting outliers and shocks. The user guide shows examples of using MARSS for parameter estimation for a variety of applications, model selection, dynamic factor analysis, outlier and shock detection, and addition of covariates. Online workshops (lectures, eBook, and computer labs) at < https://atsa-es.github.io/> See the NEWS file for update information.

# News

New work on MARSS before posting to CRAN is at https://nwfsc-timeseries.github.io/MARSS/''. Notes on known issues are also posted there.

Minor update to declare S3 objects if user has broom package installed. A few minor changes also made.

• Add if statement to declare S3 objects in NAMESPACE if user has broom package installed. Allows delayed loading of S3 methods for broom.
• MARSSkfss had bug on V0T line. * instead of %*%. This code is almost never called.
• MARSSkfss had bug. Did not check if G was time-varying. This code is almost never called.
• Typo in User Guide Chapter 2. R was supposed to be "diagonal and equal" in the first example.
• Changed plot.marssMLE to autoplot since it is ggplot2 based
• Created plot.marssMLE that uses only base R graphics

The main changes have to do with residuals and confidence intervals calculations.

BUGS

• Erroneous standardized residuals when Z was non-diagonal (and thus also > 1 row). Also changed residuals.MARSSMLE so it returns residuals (which would be equal to 0) when there are 0s on the diagonal of Q or R
• If t=1 and x0 was fixed, residuals were not returned.
• The wrong residuals were returned if there were any missing values. Fix involved implementing the missing values modifications for the Kalman filter described in Shumway and Stoffer.

inits functions

• in MARSSinits_marxss() function would give error if U, A, C, or D fixed and user passed in inits. inits ignored in this case so should not throw error.
• alldefaults could be updated by form. A few functions were neglecting to (re)load alldefaults or to ressign alldefaults when updated: is_marssMLE(), MARSSinits.marxss(), MARSSinits(). The variables in the pkg_globals environment should be (and only be) loaded when needed by a function and only loaded into the function environment.

kalman filter functions

• MARSSkfss() mis-counting num data points when R=0, V0=0, and tinitx=1. When Ft[,,1]=0 (e.g. when R=0, V0=0, and tinitx=1), MARSSkfss was including the y[1] associated with Ft[,,1]=0 in the # number of data points. These should be excluded since they don't affect x10.

Confidence intervals and std error for R and Q MARSSparamCIs() gave the wrong s.e. for variances and covariances when method="hessian". It also gave the wrong CIs for variances and covariances when var-cov matrix was non-diagonal. There were a series of issues related to back-transforming from the hessian of a chol-transformed var-cov matrix ( Sigma=chol%*%t(chol) ).

MARSSparamCIs(), vrs 3.9 was getting the hessian numerically using a var-cov matrix that had been transformed with a Cholesky decomposition to ensure it stays positive-definite. The upper and lower CIs were computed from the s.e.'s. I back-transformed the Hessian to the original (non-chol) scale the same way I back transformed a var-covariance matrix. But the variance of s^2 is not the var(s)^2, which is what I was doing, essentially. So the s.e. for R and Q were wrong in all cases. Note, using a Hessian to estimate CIs for variance-covariance matrices is generally a bad idea anyhow however.

For non-diagonal matrices. There was a bug in MARSShessian() in subscripting the d matrix when doing the chol transform. Caused NAs for cases with non-diagonal matrices. However, had the se been returned, they would be wrong for non-diagonal matrices because the elements of the chol transformed matrices do not correspond one-to-one to the non-transformed matrices. E.g. the untransformed [2,2]^2 is chol transformed [1,2]^2+[2,2]^2. The hessian used was for the chol-transformation and the curvature of the LL surface for the chol-transformed values is different than the curvature for the untransformed var-cov elements.

Fix: I completely abandoned working with the chol transformed variance-covariance matrices for the Hessian calculation. The chol transformation was not necessary for computing the Hessian since the Hessian is computed at the MLEs and localized.

# 4 Added MARSSinfo(26) which discusses the reason for NAs in the Hessian.

Misc minor bugs

• MARSShatyt() was setting ytt1 (expected value of y(t) conditioned on data up to t-1) to y(t), which is incorrect. Expected value of y(t) conditioned on y up to t-1 is Z xtt1 + a
• CSEGriskfigure() panel 2 was wrong when mu>0 (increasing population).
• CSEGriskfigure() panel 2 CIs were wrong when CI method=hessian since Q had not been back transformed (so was using sqrt(Q)).
• MARSSkemcheck()'s test that fixed B is in unit circle failed when B was time-varying and some fixed and others estimated. Also when the eigenvalues were complex, it should test the real part only.
• coef.marssMLE() was not stopping when illegal "what: arg passed in. man page did not say what happens when type=parameter.
• passing in method not in allowed.methods was causing errors since model conversion and testing happening before checkMARSSinputs and model testing is algorithm dependent (some forms not allowed by BFGS). Added check for method at top of MARSS function.

IMPROVEMENTS

• w(t) and v(t) can be specified as G(t)*w(t) and H(t)*v(t) where G and H are fixed matrices (not estimated). In version 3.10, G and H are restricted to being 0 or identity, however the code is in place for other values.
• change to MARSSkem to specifiy star lists with G, H, and L (mathbb(elem) in EM Derivation)
• changed MARSSkss to use Q*=G Q t(G), R*=H R t(H) and V0*=L V0 t(L)
• added Multivariate linear regression chapter
• added chapter on estimating a Leslie matrix from stage time series using a MARSS model.
• removed the function MARSSmcinits and added chapter on searching over the initial conditions into the User Guide. As the MARSS models that MARSS() can fit expanded, MARSSmcinits was increasing obsolete and it was impossible to come up with good searching distributions. Because MARSSmcinits was removed, control$MCInits list item was removed also from defaults and from accepted input. • added default inits for c and d in marxss form so that user can pass in inits using coef(fit); was balking because this includes d and c which didn't have defaults. Removed msg referring to need that model be in marss form for inits (not true). • changed MARSS.marxss() to allow c and d to be 3D arrays. This allows one to use inits=fit to set inits and not get a d (or c) must be 2D error. • adding info to MARSSinfo(4) regarding errors about R=0 and x0 not fixed. Added info to the error warnings to direct user to MARSSinfo(). • changed order of MARSS args to be MARSS(y, model= , inits=, ...) • added pchol and psolve functions to return the chol or inverse via solve when there are 0s on the diagonal • added information to print.marssMODEL on summary.marssMODEL. Added silent argument to summary.marssMODEL to block printing to the console. • print.marssMLE(x, what="par") returned a vector of estimated values instead of the list of par. Changed to return the list. • added E[y(t), x(t+1)] to MARSShatyt output. Needed for residuals.marssMLE(). • added code to is.validvarcov() so that it returns an error if the user specifies a structurally illegal variance-covariance matrix. Added info to MARSSinfo(25). • added a model.frame method for marssMODEL and marssMLE • added broom augment, tidy and glance functions for marssMLE • added logLik method for marssMLE objects • added fitted method for marssMLE objects to return Z xtT + u (model fitted value of y) • added plot method with diagnostics MISC • moved info in MARSSsettings.R to .onLoad function. • added suppressWarnings() wrapper to KFAS call when R=0 in MARSSkfas since update to KFAS package produces warning messages when R=0. • Typo in Eqn 124 of EMDerivation.pdf. \beta should have been ^{-1}. Typo in Eqns 133 and 134. vec parentheses should have been in front of R in second summation. R in first line of eqn 133, was not referring to R (the var-cov matrix). It should have had a new symbol. Switched to T. Eqn 134 was not R but this 'T'. • added safe to control list in man file MARSS.Rd Left off accidentally. • Small change to DLM chapter to clarify that rotation matrix only exists if Z has more than 2 columns. • All subfunctions for a function moved into the main functions so they are hidden to the rest of the functions. • The logLik function was using the logLik, samp.size and df attributes from the MLE object, but this is prone to creating errors. The user may have changed the model structure or data in a MLE object and is trying to get the new logLik. Changed to recompute the logLik. • removed use of stringr package; did not need • Poor name choice. y.se was not the standardard error of ytT since sqrt(OtT) not sqrt(OtT-ytT^2) was being returned. Changed name of y.se to ytT.se ## CHANGES IN MARSS 3.9 none. resubmission due to missing file ## CHANGES IN MARSS 3.8 • added check for fun.kf value in checkMARSSinputs() • added check to print.marssMLE to make sure models are class marssMODEL. Added info to MARSSinfo() to give the user some code to convert pre-3.5 marssMLE object to the 3.5+ form. • changed summary.marssMODEL to return the list matrix instead of the marssMODEL passed in. Added tinitx to the returned (and printed) list. • removed is.blockunconst and is.blockequaltri functions. Not really used or useful and were buggy. • much of their code (assoc with identifying blocks) incorporated into a better is.validvarcov function to test for many more illegal constraints on a variance-covariance matrix. This will catch most but not all illegal constraints on Q, R and V0. It has a method argument, so method=BFGS can be passed in to check that all blocks are diagonal or unconstrained as needed by the chol transformation used in the MARSSoption() code to ensure varcov matrices stay postitive-definite. • in MARSS(). -- Switched to use MARSSkf() to return kf (so use what user requested), but set Innov, Sigma, Kt etc with MARSSkfss. -- Added row names to states.se and y.se. • in MARSSkem(). Removed adding of kf and Ey when trace>0. This happens in MARSS(). • Changed summary.marssMODEL to use marssMODEL attributes for par.names and model.dims, so it works on non-marss form marssMODEL objects. • added ability to handle time-varying var-cov matrices in MARSShessian() • added check that Hessian CIs are only computed for models with diagonal var-cov matrices • added ability to deal with NAs in Hessian in MARSShessian() • The OR and CA years for the harborSeal dataset were off. Fixed and added references to the man file for harborSeal. Removed the harborSealnomiss dataset as that is no longer used in the User Guide. • Rewrote the Seal Population Structure chapter and MAR(p) chapter. • bugs • in MARSSkfss. When Z was not square (num rows > num cols), OmgRVtt was not getting set. OmgRVtt sets Vtt diagonals (and corresponding cols and row) to zero when R had 0s on the diagonal. • in MARSSkfas. Was returning$Innov and $Sigma using$v and $F, but as detailed in the KFS help page (KFAS package), the ones returned by KFS are not the same as the standard innovations and Sigma for multivariate data. Now, MARSSkfas() returns a text message to use MARSSkfss to get these. • residuals.marssMLE & MARSSinnovationsboot were not running MARSSkfss to get Innov, Kt, and Sigma when R was not diagonal. Problem occurred after I changed MARSSkfss() to return text error instead of NULL for these. • bug introduced in 3.6 that printed no absol convergence when convergence=10. Should have printed abstol convergence only. • bug in MARSSoptim (method=BFGS) that lead to only diagonal var-cov matrices when anything other than a diagonal var-cov matrix was selected. • same bug affected attempt to compute CIs for non-diagonal var-cov matrices with Hessian. • bug in MARSSoptim (method=BFGS) that allowed user to specify time-varying Q and R models, which code does not allow because cannot backsolve for par in that case. • bug in MARSSoptim (method=BFGS) that allowed Q, R, and V0 structures that can't be handled by the chol transformation in that code. The transformation requires that Q, R, and V0 matrices be block unconstrained. Blocks can be identical or unique or some identical and others unique but each must be unconstrained. Note, in the context of a "block" matrix, a diagonal matrix is composed of n 1x1 blocks where n=nrows. Thus by definition, a diagonal matrix (with shared or unshared elements on the diagonal) is always block unconstrained. Dealt with with new is.validvarcov() function. • bug in convert.model.mat() when user used names like "2" or "1" and had fixed values of the same (e.g. 1,2). This is because, inexplicably, R considers 1=="1" to be TRUE (and 2=="2", etc). Replaced with sapply and identical() embedded within. • There is a check in MARSSkfss() that any 0s on the diagonal of Vtt1 have a corresponding 0 on the diagonal of Q. Was this line: Q0s=identical(which(diag.Q==0),which(diag.Vtt1==0)). But that forced a more stringent requirement, that all 0s on diag of Q were identical to 0s on diag of vtt1 rather than that 0s on diag of Vtt1 had 0 on diag on Q, but not the converse. Changed to Q0s=all(which(diag.Vtt1==0)%in%which(diag.Q==0)) so that requirement is one-way. • X names were not getting applied to states in MARSS(); default X.names would be odd for non-design Z matrices. MARSS_marss() and MARSS_marxss(). ## CHANGES IN MARSS 3.7 3.7 update required due to new version of KFAS that changed its API. • Changed dependency to new version of KFAS. Updated NAMESPACE to only import the 3 KFAS functions used. • Created a versiontest.R file for comparing output from two different versions of MARSS. It's in the doc directory. • Changes to the documentation. Mark made a few changes to the DFA chapter. Got rid of Bluegreens in the example since that was mostly missing data. Moved the info on the general MARSS equation from the Quick_Start guide to the chapter on algorithms. Added a 'Tips and Tricks' section to the Quick_Start guide. • Cryptomonas misspelled in data files • The index file was out of date with old names for R scripts. Made some minor updates to the MARSS man file. • Exported the toLatex method for making a LaTex version (and pdf) of a marssMODEL object. bugs • fixed allow.degen bug that would set elements to zero, leading to non positive definite matrices. Test if Q and R are diagonal. If not, don't allow degens to be set since that is likely to lead to non-pos def matrices. I could test if the row/col covariance are 0s but that would be costly. • fixed loglog.conv.test bug that returned NAs when logLik > 720 due to exp(LL) call. Changed to exp(LL-mean(LL)) ## CHANGES IN MARSS 3.6 3.6 is mainly concerned with speeding up MARSS() for problems with large number of time series (n > 100) and where many R elements are being estimated (e.g. R="diagonal and unequal"). This comes up in dynamic factor analyses often. The changes also improve speed for small R problems by about 25%, but speed increase is 10 fold for problems with R matrices that are 100x100 with 100 estimated R elements. • changed MARSS.marxss to speed up conversion of "unconstrained" shortcut to a matrix. Only matters if m or n is big. • speed up convert.model.matrix(). Old version was always using slow code to deal with * and + in character matrix. This made formation of the free and fixed matrices very, very slow when the matrix got big (100x100, say). • added silent==2 which gives verbose output of progress • changed is.design to not use near equality for test of element==0. This may break MARSS since R sometimes doesn't maintain "zeroness". • removed many inefficiencies in MARSSkem() code for working with large matrices. Replaced all crossproducts with crossprod() and tcrossprod() which are significantly faster for large matrices. This increases speed 2-10 fold when working with larger matrices. Largest speed increases are when R is not diagonal and equal. • Hard coded a fast diagonal test into MARSSkfss() instead of using the very slow is.diagonal() function (which is really meant for list matrices) • added set.degen to degen.test() function so that it sets a flag to TRUE if any var-cov diagonals set to 0. If so, do the updates otherwise skip. • Improved speed of parmat() by testing if d and f matrices are not time-varying. In which case, don't subset the array, but rather rest the "dim" attribute. Much, much faster for big d and f matrices. • Improved sub3D() to make it a bit faster by using x[,,t] when both nrow and ncol are >1 • Improved vec() to make it 3x faster by setting dim attr instead of using matrix() when matrix is 2D • lakeWAplankton datasets were saved as data.frame. Changed to matrix. • Created R files for all the 'application' chapters in the user guide. bugs • fixed bug in building A matrix for A="scaling" which would throw warning if zero columns were in Z. No error but just unnecessary warnings. • MARSS() didn't print out marssMLE object when convergence=12 (maxit set below min for conv test). • If there were duplicated rownames in the data, R and U would use those to set shared values. This was a bug. Added a test for duplicated rownames, and add "-1", "-2" etc to duplicated name to distinguish them. ## CHANGES IN MARSS 3.5 3.5 is mainly concerned with formalizing the internal structure of model objects. marssMODEL objects have been formalized with attributes. A form definition along with associated form functions have been defined. This won't be noticeable to users but makes writing functions that use marssMODEL objects easier and more versatile. • The original Lake Washington dataset was added as lakeWAplanktonRaw. Month^2 dropped and month not z-scored. Original raw data for the counts. • changed MARSS.dfa to allow B and Q setting to "diagonal and equal" or "diagonal and unequal" • added better message reports when model list elements are not allowed • fixed the printing of model structure so it shows the form that the user called rather than base form • added basic predict function (note, not exported to users in 3.5. accessible to users via MARSS:::predict.marssMLE(). Further development will be done before exporting to users.) • removed MARSSvectorizeparam and MARSSapplynames from the exported list. The former has been replaced by coef(marssMLEObj, type="vector"). The latter is an internal utility function. • changed MARSSkfas to return Innov and Sigma when R is diagonal. When R is not diagonal, the user is directed to use MARSSkfss since MARSSkfas and MARSSkfss do not agree when R is not diagonal (and I think the error is in KFAS as the Sigma looks off when R not diagonal). • updated the help files • changed MARSShessian to use a Cholesky transformation on any variances so that the variance covariance matrices stay positive definite • change above required update to MARSSparamCIs • added more items to MARSSinfo() • miss.value is now deprecated. The user is instructed to replace missing values with NAs before passing data to MARSS(). • created an global environment (pkg_globals) specific to the package environment, so that all functions have access to these package-specific globals. This is assigned in a new onLoad() function. • Added check in MARSSkfas.R for version of KFAS. API changes in KFAS 1.0.0, and a line of coded was added to use the correct API if KFAS 0.9.11 versus 1.0.0 is installed. MARSS will work with both versions of KFAS. • added dynamic linear model case study • revamped and extended the covariates case study • condensed the errors print-out to 10 errors; added more error info to MARSSinfo() • restructured the NAMESPACE and DESCRIPTION files to better control imports and dependencies so that user cannot break the package by detaching needed libraries or redefining needed base and stats functions. bugs • MARSSboot was out of date with newest version of MARSShessian's returned arguments. • fixed bug in is.blockunconst which made it break on certain diagonal list matrices ## CHANGES IN MARSS 3.3 and 3.4 (1-16-2013) This version update is mainly concerned with adding generic functions (coef, residuals, predict), hooking back up KFAS package filters into MARSS functions, and customizing print functions for different model forms. added features • linked the KFAS package to MARSS • MARSSkfas() was changed to work with the new KFAS version released July 2012. This led to a 10-20 fold decrease in computation time for method="BFGS" and 2 fold for method="kem". • MARSSkf() changed to MARSSkfss(); MARSSkf() is now a utility function that picks MARSSkfas() or MARSSkfss() based on MLEobj$fun.kf
• Added a lag-one covariance smoother to the output of MARSSkfas() using the algorithm given on page 321 in Shumway and Stoffer (2000), Time Series Analysis and Its Applications (note the 2000 edition not 2006). The algorithm is given in the User Guide also. The EM Algorithm requires the lag-one covariance smoother but this is not one of the outputs of the KFS() function in the KFAS package.
• Changed the Kalman filter output in MARSSkfas to be strictly 0 when it is supposed to be (when R has 0 on the diagonals); KFS output has ~0 not actually 0.
• Changed the print function for marssMLE objects so that printing can be customized for model form.
• Added coef() method for marssMLE objects. Added $coef to marssMLE object. • Changed parmat() to be hidden (not exported). Instead its functionality is through the standard R function for this purpose, coef(). • Added residuals() method for marssMLE objects by changing MARSSresids() to residuals.marssMLE(). • Added predict() method for marssMLE objects. • added$call, $alt.forms to marssMLE objects so that printing (and coef and other functions for model objects) can be customized to form. • Added the standard error of the missing y values. MLEobj$y.se. Edited .Rd file to reflect changes.
• Added utility function all.equal.vector to test for equality in vectors and matrices _ changed fixed.free.to.formula to allow 3D matrices; returns array if fixed/free indicated time-varying parameter
• added toLatex.marssMODEL function to create latex and pdf output of models
• various changes to NAMESPACE in conjunction with the above changes.

bugs

• fixed bug in MARSS.dfa that did not allow user to pass in Z as matrix.
• fixed bug in parmat(). When t was a vector, parmat only returned the value at max(t).
• fixed bug in MARSSkemcheck that crashed when the test "when u^{0} or xi^{0} are estimated, B adjacency matrix must be time invariant" was started.
• fixed bug in MARSS_marxss that caused error when Z was passed in as a matrix and A="scaling"
• fixed bug in describe.marss that caused diagonal matrices with 1 estimated value and fixed values to not be identified as diagonal

## CHANGES IN MARSS 3.2 (08-28-2012)

• some edits to the case studies and the User Guide to fix typos and stuff noted in the August workshop
• added data to the Isle Royale dataset including covariates (temperature and precipitation)
• added isleRoyal.Rd man file for Isle Royale data and covariates.
• fixed bug that prevented MCInit from working.
• moved .Rinstignore to the top-level
• fixed misspelling in DESCRIPTION

## CHANGES IN MARSS 3.0 (07-10-2012)

Note, the changes are extensive but are internal and should be largely invisible to users of MARSS 2.X. The MARSS() 3.0 call is backwards compatible to 2.9 except that kf.x0 changed to tinitx and moved from control list to model list. Use of KFAS remains disabled until I can update to the new version of KFAS. This slows down method="BFGS", but does not affect method="kem".

• meaning of fixed and free changed. fixed is the f matrix in the EM derivation and free is the D matrix. Originally, I used a fixed/free pair with NAs. The new form closely follows the derivation and leads to more unified code. This required changes in most files to deal with new meaning of fixed and free.
• added model list to model object so that what the user passed in with the MARSS() call is retained (for reference).
• allow user to spec linear constraints. The main point of 3.0 is so that users can spec intercept + beta_1 p_1 + beta_2 p_2 ... constraints. Users do this with the usual list matrices using something like "theta+phi" or "2+2*theta+phi". I added a function to interpret basic math like that with + and *.
• added parmat function. This returns a parameter matrix when given a MLEobj.
• changed par element of MLEobj. It is a vector of only the estimated elements now. This required changes to user manual where I show specific parameters. If par is fixed, par element is matrix(0,0,1).
• changed kf.x0 and t.x0 to tinitx. This standardized the naming a bit and the name now stands for "t at initial x" which will hopefully be easier to remember. Removed "x00" and "x10" at least where user will see it. They are still in the internal code. tinitx is passed in in the model list.
• changed the way the marssm objects are created. Before the code locked one into a MAR-1 state-space form. However many different types of time series models can be rewritten in MAR1SS form. This rewriting is onerous for users and I don't want them to have to do that. Also I wanted to make it easier to write functions to write different time series models in MAR-1 SS form. Now MARSS() looks for a function called MARSS."form", where form is something like "mar1ss" or "dlm". This function takes the MARSS inputs (all of them) and transforms the input into a marssm object ready for the fitting functions as the function writer wishes. All that the function has to do is to return a valid marssm object from the model element of the MARSS() call. This allows me (or anyone else) to use whatever parameter names they want in the model element. This way the user can use familiar names for parameters can set some parameters to specific values (like 0). Or the user could do something totally different with the model element and just have it be a text string like model="my.ts.model.1" or model="my.ts.model.2". The only constraint is that the function output a proper marssm object and that the control, inits, and MCbounds arguments for MARSS are properly specified.
• removed popWrap.r, checkPopWrap.r, MARSSoptions.r. Became obsolete with above changes
• added checkMARSSInputs.r and checkModelList.r. These replaced the functionality of popWrap.r and checkPopWrap.r
• added MARSS.marxss.r This is the first MARSS.form() function. This is a standardized format for so that I can add other forms easily.
• changed MARSSkf.r so that K (Kalman gain) is 0 when tinitx=1 and V0=0. Changed MARSSkf.r to allow some of diagonals of V0 to be 0 and others non zero. Got rid of many of the OMGs. Added pcholinv function to diaghelpers.r which deals with matrices with 0s on diagonals. This streamlined the filter code.
• Totally revamped the EMDerivations.pdf to allow time-varying models.
• Rewrote (again) the section on degenerate models in EMDerivation.pdf to allow B structures that imply both total deterministic X and indirectly stochastic x. The latter is required to allow one to rewrite a MAR-p model as a MAR-1 model. Time-varying params meant that the matrix geometric function no longer could be used, but I found a simplier recursion. Improved the presentation so only 1 x0 and U update equation is given rather than 5 special cases. Rewrote x0 and U update sections in MARSSkem. Removed the OMGs from MARSSkem since no longer needed given the new pcholinv() function.
• Rewrote many sections of MARSSkem.r to allow time-varying parameters. see EMDerivations.pdf
• Added fun argument to MARSShessian and MARSSparamCIs to allow one to specify the function used to compute the log-likelihood.
• Moved diffuse from control element to model element of MLEobj since it is part of the model specification. Required changes to MARSSsettings, MARSS.marxss, is.marssm, is.marssMLE.
• Changed MARSSkem and MARSShatyt to allow some diag.V0=0 and others not 0, so user can mix stochastic and fixed initial x states.

----Bug fixes----

• Bug in MARSSkem that meant that the maxit-1 kf and logLik were returned when algorithm stopped due to hitting maxit. Par was correct.

## CHANGES IN MARSS 2.9 (2012-03-20)

• updated the DFA example in the manual.
• changed the column headings in the L WA plankton dataset slightly to have uniform capitalization.
• fixed MARSSboot so that MLE objects with method=BFGS can be used; changed the param.gen argument to take "MLE" and "hessian" instead of "KalmanEM" and "hessian". Updated MARSSboot.R and MARSSboot.Rd.
• fixed MARSSaic and MARSSparamCIs so that MARSSboot call uses param.gen="MLE". This fixes the bug that stopped MLE objects from BFGS calls to fail.
• temporarily disabled calls to MARSSkfas until MARSS can be made compatible with new version of KFAS package. Removed importFrom(KFAS, kf) and importFrom(KFAS, ks) from the NAMESPACE. Removed MARSSkfas from the export list in NAMESPACE. Removed KFAS in the depends line of DESCRIPTION.

## CHANGES IN MARSS 2.8 (2012-01-23)

• added NEWS file, .Rinstignore in inst\doc
• added example of lag-p model to the manual.
• fixed bug in MARSSkf when R=0, kf.x0=x10, and V0=0. The algorithm was not setting x(1) via y(1) in this special case.
• In MARSSinits, got rid of the linear regression to get inits for x0; using instead solution of pi from y(1)=Z*(D*pi+f)+A; This stops MARSS from complaining about no inits when Z is not a design matrix. NOTE NB: This means the default initial x0 are different for 2.7 and 2.8, which leads to slightly different answers for MARSS(dat) in 2.7 and 2.8. The answers are not really different, just they started with slightly different initial values so have slightly different values when the algorithm reaches its convergence limit.
• added warning in the covariate section. The error-free covariate section in the manual did not clarify that the log-likelihood of the covariates with the dummy state model would be included in the MARSS output. MARSS version 2.9 will allow error-free covariates in a more standard manner.
• removed dependency on time package. The progressBar function was moved into MARSS since the time package is no longer maintained.
• changed MARSSkemcheck to allow lag-p models. I worked on the derivation of the degenerate models (with 0 on diag of Q) to better define the needed constraints on B.0 and B.plus sub matrices. This led to changes in MARSSkemcheck.r so that lag-p models written as MARSS model are now allowed. There are still problems though in x0 estimation in the EM algorithm when there are zeros on R and B diagonals, so best to method=BFGS'' until I redo the degenerate EM algorithm.
• bug in MARSSoptim did not allow unconstrained Q or R. The problem had to do with temporarily resetting the upper triangle of tmp fixed matrices to 0 when using tmp.par as chol matrix.
• error in MARSSkf when there were 0s on diagonal of Q. The algorithm only worked if B was diagonal. Fix required changes to Kalman smoother bit of MARSSkf. I rewrote the pertinent section in EMDerivation.pdf.
• cleaned up degenerate derivation in EMDerivation.pdf
• edited MARSSmcinit to improve random B generation. There is nothing to guarantee that random Bs in mcinit routine will be within the unit circle, however it is probably a good idea if they are. Default bounds for B changed to -1,1 and random B matrix rescaled by dividing by max(abs(Re(eigen(B)))/runif(1) to get the max abs eigenvalue between 0 and 1. This works unless the user has fixed some B values to non-zero values. This required change to is_marssMLE.r also to remove constraint that B bounds be greater than 0.
• edited MARSSmcinit to allow fixed and shared values in random Qs and Rs. The random Wishart draw is rescaled based on the fixed and shared structure in R or Q. As part of this, I cleaned up how fixed and shared values are specified in the random draws of other parameters. This change doesn't change the end effect, but the code is cleaner.

## CHANGES IN MARSS 2.7 and 2.6 (2011-10-21)

-added sections on covariates and lag-p model to the user guide.

• MCInit was not working for non-diagonal R and Q. I replaced the function for randomly drawing matrices with a random draw from a Wishart distribution.
• m not getting assigned in MARSSPopWrap. Some of the allowable cases for Z and m were missing.
• added more info re R or Q not positive-definite in error messages. If the user specifies an illegal variance covariance structure from a general estimation perspective (nothing to do with MARSS), they can get the "not positive-definite" error. Added some text in Troubleshooting section to help if they get this error.
• fixed MARSSsimulate bug. MARSSsimulate was broken for multivariate simulation since I forgot that rmvnorm returns a 1 x p matrix even if the mean is p x 1. Wrapped the rmvnorm call in a array() to fix the dim setting.
• error in x0 update when R=0 and x0 fixed. If x_1 has fixed elements, estimates should not used for those elements. Code was missing some d\$x0 bits. This means that the user can fix x_1 when R=0 to a value not equal to the corresponding y_1 value. This would mean an illogical model so a check was added to stop and give warning if that happens.

## CHANGES between MARSS 2.2 and 2.5

• factor option for all but Z removed. Same functionality is now provided via list matrices
• removed fixed/free args from MARSS(). Same functionality is provided via list matrices
• constraint arg changed to model in MARSS(). Just the name of the argument was changed to be more intuitive
• rewrote user guide to reflect above changes
• added case studies to user guide on dynamic factor analysis and species interactions with covariates

## CHANGES between MARSS 2.0 and 2.2

• added diffuse priors for method="BFGS" and kf.x0="x10"
• incorporated KFAS package. Their Kalman filter is faster but only for x10. Added MARSSkfas function.
• changed Q/R estimation in optim to allow off-diagonal terms.
• added V0 estimation option. This works like other parameters now
• LL calc when R=0 fixed. LL calc in MARSSkfas to deal with 0s on diag of Ft[,,1] so can do R=0
• replaced show.doc() with RShowDoc()
• default miss.value changed NA where NA is as.numeric(NA) rather than logical.

## CHANGES between MARSS 1.1 and 2.0

• MARSSkem algorithm changed to allow B and Z estimation. This was the main objective of MARSS 2.0
• MARSSkem algorithm changed to allow constrained B and Z estimation. This was the second main objective of MARSS 2.0. This allows you to have fixed values or shared values in your B or Z matrices.
• allow more types of element sharing in the Q and R estimation. In MARSS 1.1, you were limited to diagonal, equal var-cov, and unconstrained. Now various types of block-diagonal matrices are allowed.
• allow some Q or R variances to be set to 0. This allows partially deterministic systems (Q=0) and systems with no observation error (R=0)
• fixed the V0=0 case. I was using a work-around to do the fixed x at t=0 case (V0=0). I derived the solution and added this to MARSSkem. There is no iter.V0 control element anymore.
• changed logLik conv test. I was doing the log-log test against logLik instead of log(logLik). I think the test works better using the log of the log-likelihood. -detect degeneracy and set Q or R element to zero] Now instead of the variance walking to log(negative infinity) in an infinite number of iterations, the algorithm detects that a variance is going to zero and tries setting it to zero.
• MARSSkem changed to a more general way to deal with missing values. This is described in the EMDerivation.pdf. It doesn't affect the user, but allows the code to be expanded to more types of models much more easily.
• changed to using list matrices to describe models. Now you can essentially write the way your model looks on paper (in matrix form) as a list matrix in R and it will run. No more fixed and free matrices---at least from the user's perspective.
• added some code optimization. I cleaned up some of the things that really slowed down 1.1. 2.0 is now about as fast as 1.0 was.
• big revamp of EMDerivations.pdf. I cleaned up my derivation a lot. I'm especially happy with the sections on dealing missing values part of the derivation. It's much more elegant and logical now. The sections on degenerate matrices are cluttered and the notation is painful, but I will leave them be for awhile.
• bug in miss.value=NA. When miss.value=NA, class for NA was logical. Needed to be numeric.

## CHANGES between MARSS 1.0 and 1.1

• fixed formatting issues with error messages.
• allow NA and NaN to be used for miss.value
• fixed bug in MARSSmcinit. MCMC init function would crash for anything except the default model.
• fixed ungraceful exiting when minit > maxit
• fixed ungraceful exiting when method=BFGS threw error
• added more info to ?MARSS and help(MARSS-package''). Changed MARSS.Rd and MARSS-package to have reference to user guide, index, and MARSS-package help page.
• changed convergence test. In the convergence diagnostics test, we check that the slope of logLik vs (log iteration num) is close to zero. This is a standard convergence test. But Shumway and Stoffers code uses a delta logLik test which checks that the logLik.new-logLik.old is less than some absolute (user specified) tolerance. This turns out to be a bad convergence test because the log-log plot (described above) can still have a fairly clear slope. I switched over to using the log-log test as the default test, but I allow the user to specify a abstol (delta logLik) if they want that instead. This change slows down model fitting considerably but model fits that are actually converged.\
• fixed is.design() function. A design matrix must have more or equal rows than columns.
• R was changing dims on some matrices in MARSSkf. R has a flaw in terms of how it behaves when you subscript a matrix and the new matrix has a dimension length of 1 for one (or more dimensions). For example, if a=array(0,dim=c(1,2,4)), then a[,,1] is no longer a matrix but instead is a vector and dim(a[,,1]) is NULL. This can cause all sorts of mysterious bugs. Sometimes adding drop=FALSE will prevent this unpleasant behavior. If b=matrix(0,2,2), dim(b[,1,drop=FALSE]) is c(2,1) while dim(b[,1]) is NULL. drop=FALSE works great with 2-dimensional matrices, but with 3-dimensional matrices it doesn't work. If a=array(0,dim=c(1,2,4)), dim(a[,,1,drop=FALSE]) is c(1,2,1) instead of c(1,2) which is what you want if a[,,1] is what is going to appear in some matrix operation. This problem came up in the Kt[, , t] %% innov[, t] line in MARSSkf. Normally Kt[,,t] is square and a square matrix or a scalar is returned, but if Kt[,,t] happened to be something like dim=c(1,3,20) then Kt[,,t] returned a VECTOR of length 3. In this case, Kt[, , t] %% innov[, t] crashed the code. I had to use a kluge to force R to keep the dimensions after subscripting. This bug only occurred in models where Z is not a design matrix.
• fixed formatting issues in summary(marssm object). The naming of elements in the model matrices did not match summary(marssMLE object).

# Reference manual

3.11.4 by Elizabeth Holmes - NOAA Federal, a month ago

Authors: Elizabeth Eli Holmes , Eric J. Ward , Mark D. Scheuerell , and Kellie Wills

Documentation:   PDF Manual