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Package `MARSS`

1. If you get a warning that the solution appears to be degenerate it means that some of the elements in Qor R are going to zero and the log likelihood is changing very slowly You can either try decreas ing controlSabstol dramatically e g 1E 6 use a Newton finisher MARSSopt im MLEobj or fix the degenerate values to something very small e g 1E 8 and re estimate Try find degenerate MLEobj using the output from the MARSSkem call to find the degenerate elements Author s Eli Holmes and Eric Ward NOAA Seattle USA eli dot holmes at noaa dot gov eric dot ward at noaa dot gov References R H Shumway and D S Stoffer 2006 Chapter 6 in Time Series Analysis and its Applications Springer Verlag New York Ghahramani Z and Hinton G E 1996 Parameter estimation for linear dynamical systems Tech nical Report CRG TR 96 2 University of Totronto Dept of Computer Science Harvey A C 1989 Chapter 5 in Forecasting structural time series models and the Kalman filter Cambridge University Press Cambridge UK The user manual Holmes E E and E J Ward 2010 Analysis of multivariate time series using the MARSS package NOAA Fisheries Northwest Fisheries Science Center 2725 Montlake Blvd E Seattle WA 98112 type show doc MARSS manual to see The EM algorithm Holmes E E 2010 Derivation of the EM algorithm for constrained and un constrained multivariate autoregressive state space MARSS model
2. Topic hplot CSEGriskfigure 5 CSEGtmufigure 6 Topic package MARSS package 2 alldefaults allowed 3 allowed 3 as design is blockdiag 10 as marssm 4 53 as marssm marssm 37 checkPopWrap 3 4 53 CSEGriskfigure 5 7 CSEGtmufigure 6 6 describe marssm allowed 3 fdHess 24 find degenerate 7 31 graywhales 8 grouse graywhales 8 harborSeal 9 harborSealnomiss harborSeal 9 harborSealWA harborSeal 9 Imat is blockdiag 10 is blockdiag 10 is blockequaltri is blockdiag 10 58 is is is is LS blockunconst is blockdiag 10 design is blockdiag 10 diagonal 1s blockdiag 10 equaltri 1s blockdiag 10 fixed is blockdiag 10 is is is is is is identity is blockdiag 10 marssm 53 marssm marssm 37 marssMLE marssMLE 41 wholenumber is blockdiag 10 leRoyal graywhales 8 ivesDataLP plankton 50 kem methods allowed 3 ma AA PSP PP SEP SES gt D lakeWAplankton plankton 50 loggerhead 11 loggerheadNoisy loggerhead 11 kediag is blockdiag 10 RSS 2 4 8 12 27 28 35 40 43 45 51 53 RSS package 4 12 14 16 18 20 21 23 26 28 32 33 35 37 39 41 43 46 51 54 55 RSS package 2 RSSaic 3 18 22 RSSapplynames 20 RSSboot 3 6 19 21 27 48 49 56 RSScheckdims 23 RSScheckpar MARSScheckdims 23 RSShessian 24 48 RSSinits 25 51 RSSinnovationsboot 26
3. free VO array NA dim c m m fixed V0O array 0 dim cCc m m ml lt marssm fixed fixed free free is marssm m1 dat t harborSeal dat dat 2 nrow dat allowed is a hidden variable which specifies what model structures are allowed wrapperObj popWrap dat MARSS allowed kem method kem modelObj as marssm wrapperObj marssm class Class marssm Description marssm objects describe the multivariate autoregressive state space models used in the package MARSS package Methods print signature x marssm summary signature object marssm Author s Kellie Wills NOAA Seattle USA kellie dot wills at noaa dot gov MARSSmcinit Monte Carlo Initialization Description Performs a Monte Carlo search for optimal initial conditions iterative maximization algorithms MARSSkem and MARSSopt im This is a utility function in the MARSS package Usage MARSSmcinit MLEobj Arguments MLEob 4 An object of class marssMLE MARSSmcinit 41 Details It is recommended that initial parameter values be set using MARSSmcinit particularly if the model is not a good fit to the data This requires more compuation time but reduces the chance of the algorithm terminating at a local maximum and not reaching the true MLEs Options for MARSSmcinit may be set using MLEobj cont rol as follows MLEobj controlSnumInits Number of random initial value draws MLEobj c
4. Log likelihood 46 MARSSoptim states State estimates from the Kalman filter states se Confidence intervals based on state standard errors see caption of Fig 6 3 p 337 Shumway amp Stoffer errors Any error messages Discussion The function only returns parameter estimates To compute CIs use MARSSparamCIs but if you use parametric or non parametric bootstrapping with this function it will use the Kalman EM algorithm to compute the bootstrap parameter estimates The quasi Newton estimates are too fragile for the bootstrap routine since one often needs to search to find a set of initial conditions that work i e don t lead to numerical errors Estimates from MARSSoptim which come from optim should be checked against estimates from Kalman EM algorithm If the quasi Newton algorithm works it will tend to find parameters with higher likelihood faster than the Kalman EM algorithm However the MARSS likelihood surface can be multimodal with sharp peaks at degenerate solutions where a Q or R diagonal element equals 0 The quasi Newton algorithm tends to find and gets stuck on these peaks even when they are not the maximum Neither an initial conditions search nor starting near the known maximum or from the parameters estimates after the Kalman EM algorithm will necessarily solve this problem Thus it is wise to check against Kalman EM estimates to ensure that the BFGS estimates are close to the MLE estimates Note this is m
5. boundsInits Bounds on the uniform distributions from which initial values will be drawn if MCInit TRUE ignored otherwise MARSS 15 e silent 1 or TRUE Suppresses all printing including progress bars error messages and convergence information 0 Turns on all printing of progress bars fitting information and error messages 2 Prints a brief success failure message Details MARSS provides an interface to the base MARSS package functions and allows specification and fitting of MARSS models In MARSS package 1 0 the available estimation methods are maximum likelihood via a Kalman EM algorithm met hod kem or via a quasi Newton algo rithm provided by function optim method BFGS The function MARSS allows the user to specify models using text strings for common classes of parameter matrices via the argument constraint It allows the user to specify fixed values for matrices by passing in numeric ma trices in the constraint list If the model classes available via the constraint strings are not sufficient MARSS also allows specification using matrix pairs specified with argument fixed and free If fixed free matrices are specified for some parameters these will override any constraints for those parameters See marssm or the manual Show doc MARSS manual for documentation and instructions on specifying fixed and free matrices Valid constraints for method kem are below See the manual show doc MARSS manual for details
6. ing MLE parameter estimates from e g MARSSkem Details Uses fdHess from package nlme to numerically estimate the Hessian matrix the matrix of partial 2nd derivatives of the parameter estimates Hessian CIs are based on the asymptotic normality of ML estimates under a large sample approximation Value MARSShessian returns the marssMLE object passed in along with additional components Hessian gradient parMean and parSigma computed by the MARSShessian func tion Author s Eli Holmes NOAA Seattle USA eli dot holmes at noaa dot gov See Also MARSSparamCIs marssMLE Examples da t harborSeal dat dat 2 4 MLEobj MARSS dat MLEobj w hessian MARSShessian MLEob3 oct ct 26 MARSSinits MARSSinits Initial Values for MLE Description Sets up generic starting values for parameters for maximum likelihood estimation algorithms that use an iterative maximization routine needing starting values Examples of such algorithms are the Kalman EM algorithm in MARSSkem and Newton methods in MARSSoptim This is a utility function in the MARSS package Usage MARSSinits modelObj inits list B 1 U 0 Q 0 05 A 0 R 0 05 x0 99 VO 10 Arguments modelOb An object of class marssm MARSSinits uses three elements of the model object e data The data element is used to determine n the dimension of the y in the MARSS model e fixed The fixed matrices are used to determine whi
7. Description Utility in the MARSS package to change the defaults including default model structure for the MARSS function Usage MARSSoptions method kem Arguments A name or list of names in alldefaults To see what alldefaults looks like type MARSSoptions This is the same as MARSS alldefaults method method Estimation method MARSS 1 0 allows method kem and BFGS Author s Eli Holmes NOAA Seattle USA eli dot holmes at noaa dot gov Examples Not run Change the defaults maxit value ARSSoptions control list maxit 5000 Q hange the defaults minit maxit and abstol value setting abstol means the program default RSSoptions control list minit 100 maxit 5000 abstol 0 01 D Q hange lots of different defaults RSSoptions control list minit 100 maxit 5000 abstol 0 01 constraint list U unequal C D un how the control defaults RSSoptions control D n how all the defaults for method BFGS this doesn t change the default method RSSoptions method BFGS D End Not run 48 MARSSparamClIs MARSSparamCIs Confidence Intervals for MARSS Parameters Description Computes confidence intervals for the maximum likelihood estimates of MARSS model parame ters This is a base function in the MARSS package Usage MARSSparamCIs MLEobj method hessian alpha 0 05 nboot 1000 Arguments MLEob J An object of class mar
8. Scott 1991 Estimation of growth and extinction parame ters for endangered species Ecological Monographs 61 115 143 Fieberg J and Ellner S P 2000 When is it meaningful to estimate an extinction probability Ecology 81 2040 2047 8 find degenerate Ellner S P and E E Holmes 2008 Resolving the debate on when extinction risk is predictable Ecology Letters 11 E1 E5 See Also CSEGriskfigure Examples CSEGtmufigure N 20 u 0 1 s2p 0 01 find degenerate Find degenerate variance parameters Description A helper function to find degenerate variance parameters in Kalman EM estimates in the package MARSS package Usage find degenerate MLEobj Arguments MLEobj An object of class marssMLE as output by MARSSkem Typically after a call to MARSS MARSS data method kem Details This function plots the log of the absolute value of the variance element on the diagonal against the log iteration number Such log log plots are commonly used to assess convergence in iterative routines In state space models with both process and non process observation variance it is entirely possible that the highest likelihood occurs when one of the variance element is zero In this case that element is degenerate 0 Since the likelihood computations will generate an error this means you will not be able to compute the true likelihood Technically it is certaintly possible to compute the likelihoo
9. harborSealWA dat dat 2 4 kem MARSS dat constraint list Z factor c 1 1 1 R diagonal and unequal kem with CIs from hessian MARSSparamCIs kem kem with CIs from hessian MARSSsimulate Simulate Data from a MARSS Model and Parameter Estimates Description Generates simulated data from a MARSS model with specified parameter estimates This is a base function in the MARSS package Usage MARSSsimulate parList tSteps 100 nsim 1 silent TRU miss loc NULL miss value NULL E Arguments parList A list of parameter matrices structured like the par element of an object of class mars sMLE tSteps Number of time steps in each simulation nsim Number of simulated data sets to generate silent Suppresses progress bar miss loc Optional matrix specifying where to put missing values See Details miss value Code representing missing values in miss matrix See Details Details Argument miss loc is an array of dimensions n x tSteps x nsim specifying where to put miss ing values in the simulated data Locations where missing data appear are specified using the miss value non missing values can be specified by any other numeric value If the locations of the missing values are the same for all simulations mi ss loc can be a matrix of dim c n tSteps the original data for example If miss loc is passed in miss value must be specified The default is that there are no missing values If one
10. is an extrapolated data set where missing values in the original dataset have been extrapolated so that the data set can be used to demonstrate fitting population models with different underlying structures Usage data harborSeal data harborSealnomiss data harborSealWA Format Matrix harborSeal contains columns Years StraitJuanDeFuca SanJuanIslands Eastern Bays PugetSound HoodCanal CoastalEstuaries OlympicPeninsula CA Mainland OR NorthCoast CA Channellslands and OR SouthCoast Matrix harborSealnomiss contains columns Years StraitJuanDeFuca SanJuanIslands EasternBays PugetSound HoodCanal CoastalEstu aries OlympicPeninsula OR NorthCoast and OR SouthCoast Matrix harborSealWA contains columns Years SJF SJI EBays PSnd and HC representing the same five sites as the first five columns of harborSeal Details Matrix harborSealWA contains the original 1978 1999 LOGGED count data for five inland WA sites Matrix harborSealnomiss contains 1975 2003 data for the same sites as well as four coastal sites where missing values have been replaced with extrapolated values Matrix harborSeal con tains the original 1975 2003 LOGGED data with missing values for the WA and OR sites as well as aCA Mainland and CA Channellslands time series is blockdiag 11 Source Jeffries et al 2003 Trends and status of harbor seals in Washington State
11. 1978 1999 Journal of Wildlife Management 67 1 208 219 Examples str harborSealWA str harborSealnomiss str harborSeal is blockdiag Matrix Utilities Description Matrix utilities for MARSS functions in the MARSS package Usage is blockdiag x is blockequaltri x uniqueblocks FALSI is blockunconst x uniqueblocks FALSE is diagonal x is equaltri x makediag x nrow NA takediag x is design x is fixed x is identity x El vec x unvec x dim NULL is wholenumber x tol MachineSdouble eps 0 5 as design fixed free Imat x Arguments x A matrix or vector for makedi ag dim Matrix dimensions fixed A fixed matrix per the MARSS specification for fixed matrix syntax free A free matrix per the MARSS specification for free matrix syntax nrow Number of rows tol Tolerance uniqueblocks Must blocks be unique 12 loggerhead Details is tests for various matrix properties vec x creates a column vector from a matrix per the standard vec math function unvec c dim takes the vector c and creates a matrix with the specified dimensions as design fixed free returns the fixed vector and design matrix for a fixed free pair Imat nrow returns the identity matrix of dimension nrow Value makediag x a matrix with diagonal x takediag x the diagonal from matrix x Author s Eli Holmes and Eric Ward NOAA Seattle USA eli dot holmes
12. at noaa dot gov eric dot ward at noaa dot gov loggerhead Loggerhead Turtle Tracking Data Description Data used in MARSS vignettes in the MARSS package Tracking data from ARGOS tags on eight individual loggerhead turtles 1997 2006 Usage data loggerhead data loggerheadNoisy Format Data frames loggerhead and loggerheadNoisy contain the following columns turtle Turtle name day Day of the month character month Month number character year Year character lon Longitude of observation lat Latitude of observation Details Data frame loggerhead contains the original latitude and longitude data Data frame loggerhead Noisy has noise added to the lat and lon data to represent data corrupted by errors MARSS 13 Source Gray s Reef National Marine Sanctuary Georgia and WhaleNet http whale wheelock edu whalenet stuff stop_cover_archive html Examples str loggerhead str loggerheadNoisy MARSS Interface MARSS Model Specification and Estimation Description A top level MARSS package function to perform model specification and estimation for multi variate autoregressive state space MARSS models To open the manual from the command line type show doc MARSS manual To open an overview page with package information type show doc MARSS index MARSS models take the form x t 1 B x t U w t where w t MVN 0 Q y t Z x t A v t where v t MVN
13. constraint list Q equalvarcov control list abstol 0 1 fit a model with 5 correlated hidden states abstol set rather huge and many of the Q s are not converged based on log log test kemfit MARSS dat constraint list Q unconstrained control list abstol 0 1 fit a model with 5 independent hidden states where each observation time series is independent the hidden trajectories 1 3 amp 4 5 share their U parameter kemfit MARSS dat constraint list U factor c N N N S S same model but with fixed independent observation errors kemfit MARSS dat constraint list U factor c N N N S S R diag 0 01 5 control list minit 100 fit a model with 2 hidden states north and south where observation time series 1 3 are north and 4 5 are south Make the hidden state process independent with same process var Make the observation errors different but independent Make the growth parameters U the same kemfit MARSS dat constraint list Z factor c N N N S S Q diagonal and equal R diagonal and unequal U equal control list minit 100 print the model followed by the marssMLE object kemfitSmodel kemfit simulate some new data from our fitted model sim data MARSSsimulate kemfitSpar nsim 10 tSteps 100 Not run Compute bootstrap AIC for the model this takes a long long time kemfit with AICb MARSSaic kemfit output AICbp MARS
14. control list minit 40 abstol 0 1 hess list MARSSboot kem param gen hessian nboot 5 24 MARSScheckdims no missing values boot list MARSSboot kem output all sim innovations nboot 5 Bootstrap CIs for data with missing values dat t harborSealWA dat dat 2 4 kem MARSS dat constraint list Q diagonal and equal control list minit 40 abstol 0 1 boot list MARSSboot kem output all sim parametric nboot 5 MARSScheckdims MARSS Utilities Description This is a utility function in the MARSS package for checking MARSS matrix dimensions and parameter lists Usage MARSScheckdims el target n m MARSScheckpar parList n m Arguments el Name of a MARSS list element A B Q R U VO x0 Z target List to be checked n Number of time series m Number of state processes parList MARSS parameter list Value TRUE if no problems otherwise a message describing the problems Author s Kellie Wills NOAA Seattle USA kellie dot wills at noaa dot gov MARSShessian 25 MARSShessian MARSS Parameter Variance Covariance Matrix from the Hessian Ma trix Description Calculates approximate parameter variance covariance matrix and appends it to a marssMLE ob ject This is a utility function in the MARSS package Usage MARSShessian MLEobj Arguments MLEob 3 An object of class marssMLE This object must have a Spar element contain
15. inits B constructed as diag value m Initial value s for U parameter length 1 or m x 1 If length 1 inits U constructed as matrix value nrow m ncol 1 Initial value s for Q parameter length 1 or m x m If length 1 inits Q constructed as diag value m Initial value s for Z parameter n x m Ignored in MARSS 1 0 included for MARSS 2 0 Initial value s for A parameter length 1 or n x 1 If length 1 inits U constructed as matrix value nrow n ncol 1 Initial value s for R parameter length 1 or n x n If length 1 inits R constructed as diag value n x0 Initial value s for x0 parameter length 1 or m x 1 If length 1 inits x0 constructed as matrix value nrow m ncol 1 VO Initial variance s for hidden states length 1 or m x m Ignored in MARSS 1 0 included for forward compatibility G 10 N D W Model specification using parameter constraint descriptions recommended See MARSS for details Optional model specification using matrices of fixed and free parameters See manual for details Optional model specification using matrices of fixed and free parameters See manual for details How are missing values represented in the data The method used for estimation This is needed for setting default values for control Control options for maximization algorithms minit Minimum number of EM iterations maxit Maximum number of EM iterations abstol Optional tolerance for log likel
16. of the forecast length number of time steps and forecasted decline percentage This is a function used by one of the vignettes in the MARSS package Usage CSEGtmufigure N 20 u 0 1 s2p 0 01 make legend TRUE Arguments N Time steps between the first and last population data point positive integer u Per time step decline 0 1 means a 10 decline per time step 1 means a dou bling per time step s2p Process variance Q a positive number make legend Adda legend to the plot T F Details This figure shows the region of high uncertainty in dark grey In this region the minimum 95 percent confidence intervals on the probability of quasi extinction span 80 percent of the 0 to 1 probability Green hashing indicates where the 95 percent upper bound does not exceed 5 probability of quasi extinction The red hashing indicates where the 95 percent lower bound is above 95 probability of quasi extinction The light grey lies between these two certain uncertain extremes The extinction calculation is based on Dennis et al 1991 The minimum theoretical confidence interval is based on Fieberg and Ellner 2000 This figure was developed in Ellner and Holmes 2008 Examples using this figure are shown in the manual show doc MARSS manual inthe PVA case study Author s Eli Holmes NOAA Seattle USA and Steve Ellner Cornell Univ eli dot holmes at noaa dot gov References Dennis B P L Munholland and J M
17. too long try making MLEobj controlSmaxit smaller like 500 convergence 12 MLEobj controlSabstol was reached but the log log plot test returned NAs This is an odd error and you should set cont rol trace TRUI and look at the outputted iter record to see what is wrong This value can only be output if MLEob j control abstol is passed in EJ convergence 52 The algorithm was abandoned due to numerical errors Usu ally this means one of the variances either went to zero or to all elements being equal This is not an error per se Most likely it means that your model is not very good for your data too inflexible or too many parame ters Try setting cont rol trace 1 to view a detailed error report convergence 62 The algorithm was abandoned due to errors in the log log con vergence test You should not get this error it is included for debugging purposes to catch improper arguments passed into the log log convergence test If you get it try passing in control abstol to use delta logLik as the convergence test convergence 72 Other convergence errors This is included for debugging pur poses to catch misc errors If you get it try passing in controlSabstol to use delta logLik as the convergence test logLik Log likelihood states State estimates from the Kalman filter states se Confidence intervals based on state standard errors see caption of Fig 6 3 p 337 Shumway amp Stoffer errors Any error messages Discussi
18. 0 R x 1 MVN x0 VO MARSS provides an interface to the base MARSS package functions so that users do not need to directly construct marssm and marssMLE objects Usage MARSS y inits NULL constraint NULL fixed NULL free NULL miss value 99 method kem fit TRUE silent FALSE control NULL Arguments The default settings for the optional arguments are set in MARSSsettings R and are given below in the details section A nx T matrix of n time series over T time steps ynits List with up to 7 matrices A R B U Q x0 VO specifying initial values for parameters 14 constraint fixed free miss value method fit silent control MARSS e B Initial value s for B matrix length 1 or m x m e U Initial value s for U matrix length 1 or mx 1 e Q Initial value s for process error variance s length 1 or m x m e A Initial value s for observation bias length 1 orn x 1 e R Initial value s for non process observation error variance s length 1 orn xn x0 Initial value s for hidden state s at time 1 length 1 or m x 1 VO Initial variance s for hidden state s at time 1 length 1 or m x m Model specification using parameter constraint descriptions See Details Optional model specification using matrices of fixed and free parameters See Details Optional model specification using matrices of fixed and free parameters See Details How are missing values represente
19. 2 MARSScheckdims 25 ps5 bop es bes bole eb bas a Le ee Gs 24 MARSShessian i amp sent 245 24 486 4066 2454046 56 240Gb eeSS 25 MA ROSIDI S seu dus Lis bis eww ae Bee ee hE Se eee ee ee eS 26 MARSSinnovationsboot 21 MARSSKeM e e be os e due A ar du Run a ee 29 MARSSkemcheck 33 MARSSKE SEE Da o A AA IA OO 34 MARSSLLprofile Las ads bb eek Lis 4h oe eb ba e a hip 2 36 MALSSIO acto dt a Sti EN NS M RS MN es UN EN do 38 MAFSSME CIASS wows GR dise ORR ne soute Ee See oe Ee ek eee 40 MAR DSC eg 6c das Ge dee EEE Po Oe wee ES eS 40 marssMLB 53 4 Lun sisi eG eA aR a Re ee pe 42 miarsSMILE Class is ee hk de Beth we hg te ne moe SL GE it a Soe eke 44 MARSSoptit ree e a he e Rw Ee ERR Oe ee ee ee a 44 MARSSOpUONS ooo ge ons de nan ne Me BD pepe a a den Na He RR AG A 47 MARSSparamCIs 48 MARSSSIMUIAS soe 6 Shes eR de supp Ee Se ee de oe A 49 MARSSvectorizeparam 50 plankton is poussa ee eR au sue puede EE EE eR SD al POP WAP sta eee Russes Se RES BES EARS min gb Ro 52 popWrap class 55 A Ba dt den BRAG Re he RR a 55 StdINNOV 4 dun a hee eee eee ee bee eee bea Mes 56 Index 58 MARSS package Multivariate Autoregressive State Space Model Estimation Description The MARSS package fits constrained and unconstraine
20. 48 55 56 RSSken 2 8 16 24 27 28 32 34 35 39 42 45 52 RSSkemcheck 32 RSSkf 2 8 16 29 31 33 44 45 52 55 56 RSSLLprofile 35 INDEX marssm 12 14 16 20 22 25 26 32 35 37 41 42 49 53 marssm class 39 MARSSmcinit 29 31 39 44 52 marssMLE 4 6 12 16 18 22 24 27 29 31 33 35 36 39 40 41 41 43 45 47 50 marssMLE class 43 ARSSoptim 2 3 16 25 26 31 39 41 43 ARSSoptions 46 ARSSparamCIs 3 5 24 27 36 45 47 MARSSsettings 15 A A A M RSSsettings MARSS 12 RSSsimulate 2 48 MARSSvectorizeparam 35 43 49 model elem allowed 3 M neglogLik MARSSopt im 43 nlme 24 optim 3 41 43 45 optim methods allowed 3 plankton 50 popWrap 4 37 38 51 popWrap class 54 prairiechicken graywhales 8 print marssm method marssm class 39 print marssMLE method marssMLE class 43 RShowDoc 54 show doc 54 stdInnov 27 55 summary marssm method marssm class 39 summary marssMLE method marssMLE class 43 takediag is blockdiag 10 unvec 1s blockdiag 10 vec is blockdiag 10 wilddogs graywhales 8 59
21. Lprofile The user manual Holmes E E and E J Ward 2010 Analysis of multivariate time series using the MARSS package NOAA Fisheries Northwest Fisheries Science Center 2725 Montlake Blvd E Seattle WA 98112 type show doc MARSS manual to see See Also MARSS marssm MARSSkem Examples dat t harborSeal dat dat 2 nrow dat you can use MARSS to construct a MLEobj MARSS calls MARSSinits to construct default initial values MLEobj MARSS dat fit FALSE Compute the kf output at the params used for the inits kfList MARSSkf dat MLEobj start miss value 99 MARSSLLprofile Log likelihood profiles for MARSS Parameters Description Computes log likelihood profiles for the maximum likelihood estimates of MARSS model param eters This is a base function in the MARSS package Usage MARSSLLprofile MLEobj param NULL x NULL LLlim 3 pstep 0 01 max steps 20 plot Arguments MLEob 3 An object of class marssMLE Must have a Spar element containing the MLE parameter estimates param A vector of parameter names Must match those output from MARSSvectorizeparam and output when a marssMLE object is printed If you leave this off leave NULL then profiles will be computed for all free variables x An optional vector of parameters values at which to comput the log likelihood If x is not specified then LLlim must be If you pass in x then LLlim and pstep will be ignored If you want
22. Package MARSS October 19 2010 Type Package Title Multivariate Autoregressive State Space Modeling Version 1 1 Date 2010 10 01 Depends MASS mvtnorm nlme time Author Eli Holmes Eric Ward and Kellie Wills NOAA Seattle USA Maintainer eli holmesOnoaa gov lt eli holmes noaa gov gt Description The MARSS package fits constrained and unconstrained linear multivariate autoregressive state space MARSS models to multivariate time series data Type show doc MARSS manual at the R command line to open the MARSS User Guide License GPL 2 LazyLoad yes LazyData yes Repository CRAN Date Publication 2010 10 19 07 31 06 R topics documented MARSS package alowed vos 244544 ses ri EE DR ee dde a Se CheckPOpWap gt seek GAR a BS Bao A AS Ba us dll Bh Go CSEGnskhigure ek ee bee Pe wa eR ea dur db don re CSEGtmufigure 23 2 See a SR AR ee pe find degenerate serios bode HRA ESS Ye SBA ERS de EHER ES As Oraywhales plo oe don db SEE Ge DOS RENE ee eee Ke wh e harborseali lt 3 dno e BREE SHES REE i oi e ESS IS DIGCK Cas iS ahd Sls ae SR ee ee Pas MR ee eA Re ee 2 MARSS package loggerhead s 4 3 4 485 e US ee CSR GE eH Ee Reh eae a 12 MARSS sus bb iG me a AE aod Soe AG Pate Eee 13 MARSSAIC se be Le 8h rue a Re ee a er ok eed 19 MARS SapplyDaMeS 2 8 408 Game RA ERE OGRE DER HEE Oe nee 20 MARSSb00ti34 6 ee ba Es eink 3 DEL SE EVE PER Error 2
23. S parameters using a quasi Newton algorithm via opt im ARSSaic Calculates AICc AICc and various bootstrap AICs ARSSboot Creates bootstrap MARSS parameter estimates 2 mw mw mw z MARSSparamCIs Computes confidence intervals for maximum likelihood estimates of MARSS parameters Author s Eli Holmes Eric Ward and Kellie Wills NOAA Seattle USA eli dot holmes at noaa dot gov eric dot ward at noaa dot gov kellie dot wills at noaa dot gov References The MARSS manual Holmes E E and E J Ward 2010 Analysis of multivariate time series using the MARSS package NOAA Fisheries Northwest Fisheries Science Center 2725 Montlake Blvd E Seattle WA 98112 Type show doc MARSS manual at the R command line to open the MARSS Manual Type show doc MARSS index to see all the package documentation tutorials and case study scripts 4 checkPop Wrap allowed MARSS function defaults and allowed methods Description Defaults and allowed fitting methods for the MARSS function are specified in the file MARSSsettings R These are hidden thus to see them preface with MARSS Details allowed is a list with the allowed constraints for each fitting method used in checkPopWrap allowed methods is a vector with the allowed method arguments for the MARSS function kem methods and opt im methods are vectors of method arguments that fall in each of these two categories used by MARSS alldefaults is a list that sp
24. Saic 19 kemfit with AICb End Not run MARSSaic AIC for MARSS models Description Calculates AIC AICc a parametric bootstrap AIC AICbp and a non parametric bootstrap AIC AICbb This is a base function in the MARSS package Usage MARSSaic MLEobj output c AIC AICc Options list nboot 1000 return logL star FALSE silent FALSE Arguments MLEob J An object of class marssMLE This object must have a Spar element contain ing MLE parameter estimates from e g MARSSkem output A vector containing one or more of the following AIC AICc AICbp AICbb AICi boot params See Details Options A list containing e nboot Number of bootstraps positive integer return logL star Return the log likelihoods for each bootstrap T F e silent Suppress printing of the progress bar during AIC bootstraps T F Details When sample size is small Akaike s Information Criterion AIC under penalizes more complex models The most commonly used small sample size corrector is AICc which uses a penalty term of Kn n K 1 where K is the number of estimated parameters However for time series models AICc still under penalizes complex models this is especially true for MARSS models Two small sample estimators specific for MARSS models have been developed Cavanaugh and Shumway 1997 developed a variant of bootstrapped AIC using Stoffer and Wall s 1991 bootstrap algorithm AIC
25. a different x for each parameter then pass in a list x list U c Q c Any left off parameters will use LLlim and pstep LLlim If passed in the LL profile will go from max LL LLlim to max LL to max LL LLlim The range of parameter values will keep being stepped upward or down ward to reach these limits MARSSLLprofile 37 pstep The value of step parameter x 1 parameter x 2 to use when steping towards max plot Details Computes log likelihood profiles for the free parameters specified in param for a fitted marssMLE object to the LLlim If the parameters are from Q R or VO then step is on the log scale step log parameter x 1 log parameter x 2 If you want different step val ues for different parameters pass this in as a list pstep list U 0 01 Q 1 R 2 Any parameter names left off will use the default step of 0 01 steps Since it is not guaranteed that LLlim will be reached max steps is used to spec ify the maximum number of steps to do Whether to produce a plot If FALSE then just the x values and LL values are returned using the method MLEobj method A red line is plotted at max LL 1 92 corresponding 1 degree of freedom chi square value If you want to change the control values used for computing the log likelihoods to say speed things up then change the control element of MLI param Eob3 If you have a lot of free parameters then just call MARSSLLprofile with a f
26. ainly a problem if the time series are short or very gappy If the time series are long then the likelihood surface should be nice with a single interior peak In this case the quasi Newton algorithm works well but it can still be sensitive and slow if not started with a good initial condition Thus starting it with the estimates from the Kalman EM algorithm is often desirable The VO matrix is set to a diffuse prior if x0 is estimated in which case VO must be zero to treat x0 as fixed but unknown VO is reset to zero when the final likelihood and state estimates are computed via MARSSkf See discussion in the manual and MARSSkem MARSSopt im only allows diagonal Q and R matrices if they are estimated Author s Eli Holmes NOAA Seattle USA eli dot holmes at noaa dot gov See Also MARSS MARSSkem marssMLE optim Examples dat t harborSealWA dat dat 2 nrow dat remove the year row fit a model with 1 hidden state where obs errors are iid bfgsfit MARSS dat constraint list Z factor c 1 1 1 1 1 method BFGS fit a model with Kalman EM and then use that fit as the start for BFGS MARSSoptions 47 when BFGS throws numerical errors sometimes a close initial condition will fix the problem kemfit MARSS dat constraint list Z factor c 1 1 1 1 1 bfgsfit MARSS dat constraint list Z factor c 1 1 1 1 1 inits kemfitSpar method BFGS MARSSoptions Change MARSS Defaults Utility
27. aint list Z identity A scaling R diagonal and equal B identity U unconstrained Q diagonal and unequal x0 unconstrained miss value 99 control list minit 1 maxit 5000 abstol 0 01 iter VO 10 trace 0 safe FALSE MCInit FALSE numInits 500 numInitSteps 10 boundsInits list B c 0 1 U c 1 1 logQ c log 1 0e 05 log 1 0 Z c 0 1 A c 1 1 logR c log 1 0e 05 log 1 0 For method BFGS type alldefaults BFGS to see the defaults The likelihood surface for MARSS models can be highly multimodal It is recommended that for final analyses the ML estimates are checked by using the Monte Carlo initial conditions search using MCInit TRUE in the control list This requires more computation time but reduces the chance of the algorithm terminating at a local maximum and not reaching the true MLEs Value An object of class marssMLE with the following components model MARSS model specification an object of class marssm start List with 8 matrices A R B U Q Z x0 VO specifying initial values for parameters control A list of estimation options as specified by arguments control method Estimation method If it TRUE the following are also added to the marssMLE object If fit FALSE an marssMLE object ready for fitting via the specified met hod is returned par A list with 8 matrices of estimated fixed parameter values Z A R B U Q x0 VO kf A list containing Kalman filt
28. and type al lowedS kem to see the allowed list specified in MARSSsettings R e Z identity or a vector of factors specifying which of the m hidden state time series correspond to which of the n observation time series May also be specified as a numeric n x m matrix to use a custom fixed Z e B identity or a vector of factors specifying shared diagonal elements May also be specified as anumeric m x m matrix to use custom fixed B but in this case all the eigenvalues of B must fall in the unit circle e U unconstrained equal unequal or zero May also be a vector of factors specifying shared u terms May also be specified as a numeric m x matrix to use a custom fixed U NAs can be put in this matrix to allow some elements to be fixed and others the NAs to be estimated e Q unconstrained diagonal and unequal diagonal and equal or equalvarcov May also be a vector of factors specifying shared diagonal elements May also be specified as a numeric m x m matrix to use a custom fixed Q If the matrix is diagonal off diagonals all zeros then NAs may appear on the diagonal to allow some diagonal elements to be fixed while other elements the NAs are estimated e A scaling This treats A as an intercept or zero which sets A to a fixed value of all zeros May also be specified as a numeric n x matrix to use a custom fixed A NAs can be put in this matrix to allow some elements to be fixed and others the NAs to be estimat
29. bar error messages and convergence information method A string specifying the estimation method MARSS 1 0 allows kem for Kalman EM and BFGS for quasi Newton par A list with 8 matrices of estimated parameter values Z A R B U Q x0 VO kf A list containing Kalman filter smoother output numIter Number of iterations which were required for convergence convergence Convergence status and errors 0 means converged successfully Anything else means an error or warning logLik Log likelihood Value TRUE if no problems otherwise a message describing the problems Author s Kellie Wills NOAA Seattle USA kellie dot wills at noaa dot gov See Also marssmMARSSkem 44 MARSSoptim marssMLE class Class marssMLE Description marssMLE objects specify maximum likelihood estimation of multivariate autoregressive state space models in the package MARSS package Methods print signature x marssMLE summary signature object marssMLE Author s Kellie Wills NOAA Seattle USA kellie dot wills at noaa dot gov MARSSoptim Parameter estimation for MARSS models using optim Description Parameter estimation for MARSS models using R s opt im function This allows access to R s quasi Newton algorithms available via the optim function The MARSSopt im is called when MARSS is called with met hod BFGS Only diagonal Q and R matrices are allowed if they are estimated This i
30. bb Holmes and Ward 2010 developed a variant on AICb AICbp using a parametric bootstrap The parametric bootstrap permits AICb calculation when there are missing values in the data which Cavanaugh and Shumway s algorithm does not allow More recently Bengtsson and Cavanaugh 2006 developed another small sample AIC estimator AICi based on fitting candidate models to multivariate white noise When out put includes both AICbp and boot params the bootstrapped parameters from AICbp will be added to MLEobj 20 MARSSapplynames Value Returns the marssMLE object that was passed in with additional AIC components added on top as specified in the output argument Author s Eli Holmes and Eric Ward NOAA Seattle USA eli dot holmes at noaa dot gov eric dot ward at noaa dot gov References Holmes E E and E J Ward 2010 Analysis of multivariate time series using the MARSS pack age NOAA Fisheries Northwest Fisheries Science Center 2725 Montlake Blvd E Seattle WA 98112 this is the user manual accesses via show doc MARSS manual Bengtsson T and J E Cavanaugh 2006 An improved Akaike information criterion for state space model selection Computational Statistics amp Data Analysis 50 2635 2654 Cavanaugh J E and R H Shumway 1997 A bootstrap variant of AIC for state space model selection Statistica Sinica 7 473 496 See Also MARSSboot Examples dat t harborSealWA dat
31. ch if any model pa rameters are fixed e miss value Used if a linear regression through the data is used to con struct inits for xO In this case the missing values are replaced by NA inits A list of up to 8 values to construct starting matrices for each parameter in a MARSSmodel Details Creates an inits parameter list for use by iterative maximization algorithms Defaults values for init s is supplied in MARSSsettings R The user can alter these and supply any of the following m is the dim of X and n is the dim of Y in the MARSS model e elem A U A numeric vector or matrix which will be constructed into init sS elem by the command array initsSelem dim c n or m 1 If elem is fixed in the model any initsSelem values will be overridden and replaced with the fixed value Default is array 0 dim c n or m 1 e elem Q R B A numeric vector or matrix If length equals the length modelObj fixed elem then inits elem will be constructed by array initsSelem dim dim modelOb j fixed elem If length is 1 or equals m or n then inits elem will be constructed into a diagonal matrix by the command diag initsSelem m or n Ifelemis fixed in the model any initsSelem values will be overridden and replaced with the fixed value Default is diag 0 05 m or n for Q and R Default is diag 1 m for B MARSSinnovationsboot 27 e x0 If inits x0 99 then starting values for xO are estimated by a linear regression through the co
32. columns Source e graywhales Gerber L R Master D P D and Kareiva P M 1999 Gray whales and the value of monitoring data in implementing the U S Endangered Species Act Conservation Biology 13 1215 1219 e grouse Hays D W Tirhi M J and Stinson D W 1998 Washington state status report for the sharptailed grouse Washington Department Fish and Wildlife Olympia WA 57 pp e isleRoyal Peterson R O Thomas N J Thurber J M Vucetich J A and Waite T A 1998 Population limitation and the wolves of Isle Royale In Biology and Conservation of Wild Canids eds D Macdonald and C Sillero Zubiri Oxford University Press Oxford pp 281 292 10 harborSeal e prairiechicken Peterson M J and Silvy N J 1996 Reproductive stages limiting productivity of the endangered Attwater s prairie chicken Conservation Biology 10 1264 1276 e wilddogs Ginsberg J R Mace G M and Albon S 1995 Local extinction in a small and declining population Wild Dogs in the Serengeti Proc R Soc Lond B 262 221 228 Examples str graywhales str grouse str isleRoyal str prairiechicken str wilddogs harborSeal Harbor Seal Population Count Data Log counts Description Data sets used in MARSS vignettes in the MARSS package These are data sets based on LOGGED count data from Oregon Washington and California sites where harbor seals were cen sused while hauled out on land harborSeallnomiss
33. cription Implements the Kalman filter smoother for MARSS models This is a base function in the MARSS package Usage MARSSkf y parList missing matrix NULL miss value NULL init state x10 debugkf FALS E Arguments y A matrix not dataframe sites rows x years columns See Details regarding handling of missing values parList A list with 8 matrices Z A R B U Q x0 VO specifying parameter values An example is the par element in a marssMLE object missing matrix Optional matrix specifying which observations are missing See Details miss value How are missing values represented in the data Either miss value or miss ing matrix must be supplied If both are supplied then miss value will be ig nored with no warning init state Is the initial state x0 treated as E x at time t 0 init state x00 or E x att 1 init state x10 Defaultis init state x10 note for Shumway and Stoffer s Kalman filter use init state x00 See De tails debugkf Return detailed error messages Details For state space models the Kalman filter and smoother provide optimal minimum mean square error estimates of the hidden states The Kalman filter is a forward recursive algorithm which computes estimates of the states x t conditioned on the data up to time t The Kalman smoother is a backward recursive algorithm which starts at time T and works backwards to t to provide estimates of the states con
34. d but the code in MARSSkf will throw an error if you try to set one of the variances to zero Value A plot where each diagonal variance element appears in a panel Converged elements with have a flat log log plot Degenerate variance elements will have a declining log log plot Typically degenerate variance parameters will show a slope of ca 1 Author s Eli Holmes NOAA Seattle USA eli dot holmes at noaa dot gov graywhales 9 See Also MARSSkem Examples dat t harborSealnomiss shorten the data set to 10 yrs in order to produce a degenerate solution in this case there is not enough data to estimate all the Q variances dat dat 2 4 1 10 For example sake it s stopped at 50 interations as it could go on for a long time trying MLEobj MARSS dat control list maxit 50 find degenerate MLEob graywhales Population Data Sets Description Example data sets for use in MARSS PVA vignettes in the MARSS package manual All are UNLOGGED population counts The data sets are matrices with year in the first column and counts in other columns Since MARSS functions require time to be across columns these data matrices must be transposed before passing into MARSS functions Usage data graywhales data grouse data isleRoyal data prairiechicken data wilddogs Format The data are supplied as a matrix with years in the first column and counts in the second and third for isleRoyal
35. d in the data Estimation method MARSS 1 0 allows method kem and BFGS TRUE FALSE Whether to fit the model to the data If FALSE a marssMLE object with only the model is returned TRUE FALSE Suppresses printing of full error messages warnings progress bars and convergence information Estimation options for the maximization algorithm The control options for method kem are minit The minimum number of iterations to do in the maximization rou tine if needed by method If method kem this is an easy way to up the iterations and see how your estimates are converging positive integer maxit Maximum number of iterations to be used in the maximization rou tine if needed by method positive integer abstol Convergence tolerance for the maximization routine default is 0 01 which is a bit high iter VO The value of VO to be used in place of O when x0 is treated as fixed and VO 0 See manual for discussion of initial state variance default is 10 which works well trace A positive integer If not 0 a record will be created during maxi mization iterations what s recorded depends on the method of maximiza tion MCInit If TRUE do a Monte Carlo search of the initial condition space T F numInits Number of random initial value draws if MCInit TRUE ig nored otherwise positive integer numInitSteps Number of EM iterations for each random initial value draw if MCInit TRUE ignored otherwise positive integer
36. d multivariate autoregressive time series models to multivariate time series data To open the manual from the command line type show doc MARSS manual To open an overview page with package information type show doc MARSS index The MARSS model is x t 1 B x t U w t where w t MVN 0 Q y t Z x t A v t where v t MVN 0 R x 1 MVN x0 VO The parameters hidden state processes x and observations y are matrices MARSS package 3 e x t ismx 1 e y t isn x 1 m lt n e Zisnxm e Bismxm e Uismxl e Qismxm e Aisnx 1 e Risnxn x0ismxl e VOismxm The package functions estimate the parameters U Q A R and x0 using a Kalman EM algorithm primarily but see MARSSopt im Parameters may be constrained to have shared elements ele ments which are constrained to have the same value or fixed elements with the other elements estimated The states and smoothed state estimates are provided via a Kalman filter and smoother Bootstrapping confidence interval estimation bias estimation model selection and simulation func tions are provided The main user interface to the package is the top level function MARSS Details Important MARSS functions MARSS Top level function for specifying and fitting MARSS models ARSSsimulate Produces simulated data from a MARSS model ARSSkem Estimates MARSS parameters using an Kalman EM algorithm IARSSk Kalman filter and smoother ARSSoptim Estimates MARS
37. dat 2 3 kem MARSS dat constraint list Z factor c 1 1 R diagonal and equal kemAIC MARSSaic kem output c AIC AICc MARSSapplynames Names for marssMLE Object Components Description Puts names on the matrix components of marssMLE and marssm objects This is a utility function in the MARSS package and is not directly accessible Use MARSS MARSSapplynames to access Usage MARSSapplynames obj Y names NA X names NA x0 names NA VO names NA U names NA A names NA R names NA Q names NA B names NA Z names NA rows TRUE cols TRUE MARSSapplynames Arguments obj Y names X names x0 names VO names U names A names R names Q names B names Z names rows cols Details 21 An object of class marssMLE or marssm Vector of names for observed time series Vector of names for the hidden state trajectories Vector of names for MLEobj par x0 MLEobjSstart x0 MLEobj model fixed x0 and MLEobj model freeS x0 Names for Names for Names for Names for Names for Names for L L L L Eob 4 Eob Eob Eob Eob Eob Sparsvo Sparsu SparsA SparsR Spar Q SparSB Row and col names for MLEobjSpar Z Add row names Add column names to B Q R and VO matrices Default behavior will use names rownames of data if available and if not Y1 Y2 for the Ys and all matrices that a
38. ditioned on all data Missing values in the data may be handled in one of two ways 1 Missing values may be replaced with zeroes prior to passing to MARSSkf Argument missing matrix must then be a matrix of the same dimensions as the data with 0 in the positions of observed values and in the positions of missing values 2 Data containing missing values may be passed in Argument miss value must then be the code used to represent missing values The function requires that you specify either a missing matrix or a miss value If there are no missing values just set miss value toa value that is not in your data like 99 MARSSkf 35 The expected value of the initial state x0 is an estimated parameter or treated as a prior This E initial state can either be treated in two different ways One can treat it as x00 meaning E x at t 0 y at t 0 and then compute x10 meaning E x at t 1 y at t 0 from x00 Or one can simply treat the initial state as x10 meaning E x at t 1 y at t 0 The approaches are equivalent but the likelihood is written slightly differently in each case sum over 2 to T versus to T and you need your likelihood calculation to correspond to how the initial state is treated in your model either x00 or x10 The EM algorithm in the MARSS package MARSSkem follows Ghahramani s derivation and uses x10 while Shumway and Stoffer uses x00 The init state argument spec ifies whether x00 init state x00 or x10 in
39. done before the data is passed in fixed A list with 8 matrices Z A R B U Q x0 VO specifying which elements of each parameter are fixed See Details free A list with 8 matrices Z A R B U Q x0 VO specifying which elements of each parameter are to be estimated See Details miss value How are missing values represented in the data modelOb An object of class marssm wrapperoObj An object of a wrapper class popWrap Details A marssm object is an R representation of a MARSS model along with the data Data for marssm consists of multivariate time series data in which time is across columns and the n observed time series are in the n different rows The MARSS model is x t 1 B x t U w t where w t MVN 0 Q y t Z x t A v t where v t MVN 0 R x 1 MVN x0 VO In the marssm object the MARSS model is specified by fixed free pairs of matrices for each pa rameter B U Q Z A R x0 VO The dimensions for fixed and free matrices must be Z nx m m lt n Bmxm Umxl marssm 39 Qmxm A nx R nxn x0 mx VO mxm The matrices in fixed and free work as pairs to specify the fixed and free elements for each parameter In fixed fixed elements must be numbers values that are not fixed i e are to be esti mated should be denoted NA Elements in free will be interpreted as names for the free elements even if they are numbers Identical elements within a parameter matrix will be constrained t
40. ecifies the defaults for MARSS argu ments if they are not passed in used by checkPopWrap model elemand model elem w VO specify the parameters names used in lists such are par lists checkPopWrap Check Arguments to popWrap Description Checks inputs for wrapper object popWrap creation to ensure that the wrapper object can be handled by as marssm This is a utility function in the MARSS package Usage checkPopWrap wrapperObj wrapper el allowed silent FALS Gl Arguments wrapperObj An object of class popWrap wrapper el Wrapper elements generally set by MARSS allowed Allowed constraints This changes depending on the fitting method the user has specified in MARSS or in the marssMLE object Lists of for al lowed for dif ferent fitting methods is set in MARSSsettings R Use MARSS allowed to view since al lowed is hidden silent Suppresses errors and warnings printing Details Called by popWrap to ensure that user inputs are valid and can be handled by as marssm CSEGriskfigure 5 Value TRUE if object passes all checks Author s Kellie Wills NOAA Seattle USA kellie dot wills at noaa dot gov See Also popWrap as marssm Examples Not run Error dat t harborSeal dat dat 2 nrow dat wrapperObj popWrap dat allowed MARSS allowedSkem constraint list Z wrong End Not run CSEGriskfigure Plot Extinction Risk Metrics Descript
41. ed Note all NAs in A would mean all A elements are estimated and would typically result in an under constrained and unsolveable model at least one A element per X state needs to be fixed e R unconstrained diagonal and unequal diagonal and equal or equalvarcov May also be a vector of factors specifying shared diagonal elements May also be specified as a numeric n x n matrix to use a custom fixed R If the matrix is diagonal off diagonals all zeros then NAs may appear on the diagonal to allow some diagonal elements to be fixed while other elements the NAs are estimated 16 MARSS e x0 unconstrained equal unequal or zero May also be a vector of factors specifying shared initial state values May also be specified as a numeric m x 1 matrix to use a custom fixed x0 NAs can be put in this matrix to allow some elements to be fixed and others the NAs to be estimated Valid constraints for met hod BFGS are the same as for met hod kem except that the Q and R matrices must be diagonal if estimated Thus unconstrained and equalvarcov are not allowed for Q or R Type al lowedS BFGS to see the allowed list specified in MARSSsettings The default estimation method method kem is the Kalman EM algorithm described in the manual The default settings for the optional arguments are set via alldefaults kem in MARSSsettings For this method they are inits list B 1 U 0 Q 0 05 A 0 R 0 05 x0 99 VO 10 constr
42. er each individual pa rameter update rather than only after all parameters are updated The latter is slower and unnecessary for many models but in some cases the safer and slower algorithm is needed because the ML parameter matrices have high condition numbers MLEobj control MCInit If TRUE Monte Carlo initialization will be performed by MARSSmcinit MLEobj control numIinits Number of random initial value draws to be used with MARSSmcinit Ignored if cont rolSMCInit FALSE MLEobj controlSnumInitSteps Maximum number of EM iterations for each random ini tial value draw to be used with MARSSmcinit Ignored if control MCInit FALSE MLEobj control boundsInits Length 6 list Each component is a length 2 vector of bounds on the uniform distributions from which initial values will be drawn to be used with MARSSmcinit Ignored if control MCInit FALSE See Examples MLEobj control silent Suppresses printing of progress bars error messages warnings and convergence information Value The mar ssMLE object which was passed in with additional components method String kem kf Kalman filter output iter record IfMLEobj control trace TRUE a list with par a record of each estimated parameter over all EM iterations and logLik a record of the log likelikelihood with VO set to the value of iter VO Note this is different than the log likelihood with VO 0 which is the final log likelih
43. er smoother output from MARSSkf numlter Number of iterations required for convergence convergence Convergence status 0 means converged successfully Anything else is a warning or error 2 means the MLEobj has an error the MLEobj is returned so you can debug it The other numbers are errors during fitting The error code depends on the fitting method See MARSSkem and MARSSopt im MARSS 17 logLik Log likelihood AIC Akaike s Information Criterion AICC Sample size corrected AIC Author s Eli Holmes and Kellie Wills NOAA Seattle USA eli dot holmes at noaa dot gov kellie dot wills at noaa dot gov References The user manual Holmes E E and E J Ward 2010 Analysis of multivariate time series using the MARSS package NOAA Fisheries Northwest Fisheries Science Center 2725 Montlake Blvd E Seattle WA 98112 type show doc MARSS manual to see See Also marssmmarssMLE MARSSkemMARSSoptimMARSS package Examples harborSealWA is a n 5 matrix of logged population counts dat t harborSealWA dat dat 2 nrow dat remove the year row fit a model with 1 hidden state and 5 observation time series kemfit MARSS dat constraint list Z factor c 1 1 1 1 1 R diagonal and equal kemfitSmodel This gives a description of the model print kemfit model same as kemfit model summary kemfit model This shows the model structure show kemfit model shows the raw object Look at the log log convergence p
44. ew eters at a time Otherwise the function will try to plot all of them in one plot and you ll get a plot margin error Value MARSSLLprofile returns a list of x values and LL profile values for each parameter in param Author s Eli Holmes NOAA Seattle USA eli dot holmes at noaa dot gov References Holmes E E and E J Ward 2010 Analysis of multivariate time series using the MARSS pack age NOAA Fisheries Northwest Fisheries Science Center 2725 Montlake Blvd E Seattle WA 98112 this is the user manual accesses via show doc MARSS manual See Also MARSSparamCls Examples dat t harborSealnomiss dat dat 2 3 kem MARSS dat constraint list Z factor c 1 1 R diagonal and equal Q matrix 0 01 profLL MARSSLLprofile kem c R 1 U 1 pstep list U 0 01 R 0 1 38 marssm marssm Model Objects Description These are model objects and utility functions for model objects in the package MARSS package marssm creates multivariate autoregressive state space model objects is marssm ensures model consistency as marssm attempts to coerce its argument to a marssm object Usage marssm data NULL fixed free miss value 99 is marssm model0b3 as marssm wrapperOb Arguments data An optional matrix not dataframe sites rows x years columns of observed population abundances If the algorithm is to be applied to log abundance the log transformation should be
45. gton story Interaction strengths in a planktonic food web Limnology and Oceanography 51 2042 2051 Examples str ivesDataLP str lakeWAplankton popWrap Wrapper Objects Description Wrapper objects are used by the function MARSS in the package MARSS package popWrap creates a wrapper object containing specifications and options for estimation of a multivariate au toregressive state space model Usage popWrap y allowed inits NULL constraint NULL fixed NULL free NULL miss value NULL control NULL method NUL silent FALS un E fs Arguments y A matrix not dataframe observations rows x time steps columns of data allowed Allowed constraints This is determined by the method used for parameter esti mation allowed ken specified in MARSSsettings is the set of allowed constraints for the Kalman EM algorithm under MARSS 1 0 allowed BFGS are the allowable constraints for BFGS inits List with up to 8 matrices Z A R B U Q x0 VO specifying initial values for parameters to use in iterative ML estimation algorithms such as Kalman EM and quasi Newton methods These are ignored if the specified parameter is not being estimated If not passed in by the user MARSS creates generic inits using MARSSinits popWrap constraint fixed free miss value method control silent 53 w Initial value s for B parameter length 1 or m x m If length 1
46. ihood change If log likelihood changes less than this amount relative to the previous iteration the algorithm exits iter VO This is the value to which VO will be set during the algorithm itera tions 0 See MARSSkem trace Positive integer If not 0 a record will be created of each variable over the maximization iterations The information recorded depends on the max imization method safe If TRUE MARSSkem will rerun MARSSkf after each individual param eter update rather than only after all parameters are updated MCInit Use Monte Carlo initialization See discussion in MARSSkem and MARSSmcinit numInits Number of random initial value draws numInitSteps Number of EM iterations for each random initial value draw boundsInits Bounds on the uniform distributions from which initial values will be drawn Note that bounds for the covariance matrices Q and R which require positive values are specified in logs Suppresses printing of progress bars error messages warnings and convergence information 54 pop Wrap Details Wrapper functions e g MARSS call popWrap to create a popWrap object then is marssm to coerce this object to class marssm for the estimation function The popWrap function calls checkPopWrap to check user inputs If arguments inits constraint or control are not provided by the user they will be set by the alldefaults method object specified in MARSSsettings Argument constraint is a conve
47. ilt from scatch but are easier to construct using MARSS with MARSS fit FALSE Options for MARSSkem may be set using MLEobj control as follows MLEobj controlSminit Minimum number of EM iterations You can use this to force the algorithm to do a certain number of iterations This is helpful if your soln is not converging MLEob j controlSmaxit Maximum number of EM iterations MLEobj control min iter conv test The minimum number of iterations before the log log convergence test will be computed If cont rol maxit is set less than this then convergence will not be computed and the algorithm will just run for maxit iterations MLEobj control conv test deltaT The number of iterations to use in the log log con vergence test This defaults to 9 MLEobj control abstol Tolerance for log likelihood change for the delta logLik conver gence test If log likelihood changes less than this amount relative to the previous iteration the EM algorithm exits This is normally default set to NULL and the log log convergence test is used instead MLEobj control iter VO This is the value to which VO will be set during the EM algorithm 0 See Details MLEobj control trace A positive integer If not 0 a record will be created of each variable over all EM iterations and detailed warning messages if appropriate will be printed 30 MARSSkem MLEobj control safe If TRUE MARSSkem will rerun MARSSk f aft
48. ion Generates a six panel plot of extinction risk metrics used in Population Viability Analysis PVA This is a function used by one of the vignettes in the MARSS package Usage CSEGriskfigure data te 100 absolutethresh FALSE threshold 0 1 datalogged FALSE silent FALSE return model FALSE CI method hessian CI sim 1000 Arguments data A data matrix with 2 columns time in first column and counts in second column Note time is down rows which is different than the base MARSS package functions te Length of forecast period positive integer absolutethresh Is extinction threshold an absolute number T F threshold Extinction threshold either as an absolute number if absolutethresh TRUE or as a fraction of current population count if absolutethresh FALSE 6 CSEGriskfigure datalogged Are the data already logged T F silent Suppress printed output T F return model Return state space model as marssMLE object T F CI method Confidence interval method hessian parametre innovations or none See MARSSparamCIs CI sim Number of simulations for bootstrap confidence intervals positive integer Details Panel 1 Time series plot of the data Panel 2 CDF of extinction risk Panel 3 PDF of time to reach threshold Panel 4 Probability of reaching different thresholds during forecast period Panel 5 Sample projections Panel 6 TMU plot uncertainty as a function
49. it state x10 is used The default is init state x10 Value A list with the following components n is the number of state processes Names ending in T are estimates from the Kalman smoother J is also smoother output Other components are output from the Kalman filter xtT State estimates E x t y 1 T n x T matrix VET State covariances E V t y 1 T n x n x T array VEELT Conditional error covariances E V t t 1 Y L T n x n x T xOT Initial state mean estimates n x 1 VOT Estimate of initial state covariance matrix n x n J nxnxT xtt1 Forecasts E x t Y t 1 n x T vtt State covariance estimates E V t y 1 0 nx n x T VEEL Conditional error covariances E V t t 1 y 1 t n x n x T Kt Kalman gain n x n x T Innov Innovations y t E y t Y t 1 nx T a x nx T Sigma Innovations variances logLik Log likelihood computed from ms sm params and innovations errors Any error messages due to ill conditioned matrices Author s Eli Holmes and Eric Ward NOAA Seattle USA eli dot holmes at noaa dot gov eric dot ward at noaa dot gov References P J Brockwell and R A Davis 1991 Time Series Theory and Methods A C Harvey 1989 Chapter 5 Forecasting Structural Time Series Models and the Kalman Filter Cambridge University Press R H Shumway and D S Stoffer 2006 Chapter 6 Time Series Analysis and its Applications Springer Verlag New York 36 MARSSL
50. kellie dot wills at noaa dot gov show doc Documentation Utility Description Utility in the MARSS package to open documentation for R packages This is used to open files and show the directory of the doc directory of a package This is similar but a bit more flexible than that R utility RShowDoc Usage show doc pkg filename dir doc Arguments pkg The name of an R package Need not be in quotes filename A file name or manual index or dir Need not be in quotes Using manual index and dir has special behavior no quotes required man ual opens tries to open the file manual pdf index tries to open the file index html dir lists the files in the directory specified by the dir argument dir The package subdirectory in which the file is located Typically documenta tion is in the doc subdirectory and this is the default However other package directories can be specified Use dir to see the directories available Author s Eli Holmes eli dot holmes at noaa dot gov See Also See Also RShowDoc 56 stdInnov Examples Not run ARSS is used as the package in these examples but you can replace it with any package name you have loaded into R show doc is not MARSS specific list the files in the doc subdirectory show doc MARSS dir show the file manual pdf in the doc subdirectory show doc MARSS manual show the index html file in the doc s
51. ll data at time t are missing Value A list containing the following components boot states Array dim is m x tSteps x nboot of simulated state processes boot data Array dim is n x tSteps x nboot of simulated data model MARSS model mode1 element of the marssMLE object nboot Number of bootstraps performed m is the number state processes x in the MARSS model and n is the number of observation time series y in the MARSS model Author s Eli Holmes and Eric Ward NOAA Seattle USA eli dot holmes at noaa dot gov eric dot ward at noaa dot gov References Stoffer D S and K D Wall 1991 Bootstrapping state space models Gaussian maximum like lihood estimation and the Kalman filter Journal of the American Statistical Association 86 1024 1033 See Also stdInnov MARSSparamCIs MARSSboot MARSSkem 29 Examples dat t harborSealnomiss dat dat 2 nrow dat MLEobj MARSS dat constraint list U equal Q diagonal and equal boot obj MARSSinnovationsboot MLEobj MARSSkem Maximum Likelihood Estimation for Multivariate Autoregressive State Space Models Description MARSSkem performs maximum likelihood estimation using an EM algorithm for constrained and unconstrained MARSS models This is one of the base functions in the MARSS package Usage MARSSkem MLEob Arguments MLEob J An object of class marssMLE Details Objects of class marssMLE may be bu
52. lots for the variances find degenerate kemfit Increase the number of iterations to ensure convergenc kemfit100 MARSS dat constraint list Z factor c 1 1 1 1 1 R diagonal and equal control list minit 100 find degenerate kemfit100 now check log logconvergence of variances plot is flat that s good fit the model using quasi Newton algorithm Not run takes a long time bfgsfit MARSS dat constraint list Z factor c 1 1 1 1 1 R diagonal and unequal method BFGS End Not run add CIs to a marssMLE object default uses an estimated Hessian matrix kem with hess CIs MARSSparamCIs kemfit100 18 MARSS kem with hess CIs print with se s and CIs estimate CIs using a parametric bootstrap tmp kemfit tmp controlSabstol 0 01 kem with boot CIs MARSSparamCIs tmp method parametric nboot 10 nboot should be more like 1000 but set low for example sake kem with boot Cls print with se s CIs and bias est fit a model with 5 hidden states default kemfit MARSS dat silent TRUE suppress printing kemfit print information on the marssMLE object show kemfit look at the raw marssMLE object fit a model with 5 correlated hidden states with one variance and one covariance using the delta logLik convergence test by setting abstol This is fast but does not actually test convergence i e that log param value versus log iteration is flat kemfit MARSS dat
53. ltis diag 10 m Value A list with 8 matrices A R B U Q x0 VO Z specifying initial values for parameters in a MARSS model Author s Eli Holmes NOAA Seattle USA eli dot holmes at noaa dot gov See Also marssm MARSSkem MARSSoptim MARSSinnovationsboot Bootstrapped Data using Stoffer and Wall s Algorithm Description Creates bootstrap data via sampling from the standardized innovations matrix This is a base func tion in the MARSS package Usage MARSSinnovationsboot MLEobj nboot 1000 minIndx 3 28 MARSSinnovationsboot Arguments MLEob J An object of class marssMLE This object must have a Spar element contain ing MLE parameter estimates from e g MARSSkem or MARSS This algorithm may not be used if there are missing datapoints in the data nboot Number of bootstraps to perform minIndx Number of innovations to skip Stoffer amp Wall suggest not sampling from inno vations 1 3 Details Stoffer and Wall 1991 present an algorithm for generating CIs via a non parametric bootstrap for state space models The basic idea is that the Kalman filter can be used to generate estimates of the residuals of the model fit These residuals are then standardized and resampled and used to generate bootstrapped data using the MARSS model and its maximum likelihood parameter estimates One of the limitations of the Stoffer and Wall algorithm is that it cannot be used when there are missing data unless a
54. manual for a discussion of the setting of diffuse priors for iterative parts of the maximization algorithms silent Suppresses printing of progress bar Details Approximate confidence intervals CIs on the model parameters can be calculated by numerically estimating the Hessian matrix the matrix of partial 2nd derivatives of the parameter estimates The Hessian CIs are based on the asymptotic normality of ML estimates under a large sample approximation Cls that are not based on asymptotic theory can be calculated using parametric and non parametric bootstrapping Stoffer and Wall 1991 present an algorithm for generating CIs via a non parametric bootstrap for state space models sim innovations The basic idea is that the Kalman filter can be used to generate estimates of the residuals of the model fit These residuals are then standardized and resampled and used to generate bootstrapped data using the MARSS model and its maximum likelihood parameter estimates One of the limitations of the Stoffer and Wall algorithm is that it MARSSboot 23 cannot be used when there are missing data unless all data at time t are missing An alternative ap proach is a parametric bootstrap sim parametric in which the ML parameter estimates are used to produce bootstrapped data directly from the state space model Value A list with the following components boot params Matrix number of params x nboot of parameter estimates from the bootst
55. n functions and to set MLEobj par using a vector of parameter values only the estimated values Value If parvec NA a vector of estimated parameters Otherwise a marssMLE object with par set by parvec Author s Eli Holmes and Kellie Wills NOAA Seattle USA eli dot holmes at noaa dot gov eric dot ward at noaa dot gov See Also marssMLE Examples dat t harborSealWA dat dat 2 3 kem MARSS dat paramvec MARSSvectorizeparam kem paramvec plankton Plankton Data Sets Description Example data sets for use in MARSS vignettes for the MARSS package The lakeWAplankton plankton counts have been standardized to a mean of zero and variance of Z score transforma tion The second column in lakeWAplankton is simply a index for the count Columns 3 and 4 are month and month but they have also been Z score transformed Since MARSS functions re quire time to be across columns these data matrices must be transposed before passing into MARSS functions Usage data ivesDataLP data lakeWAplankton Format The data are provided as a matrix with time running down the rows 52 popWrap Source e ivesDataLPlves A R Dennis B Cottingham K L Carpenter S R 2003 Estimating com munity stability and ecological interactions from time series data Ecological Monographs 73 301 330 e lakeWAplanktonHampton S E Scheuerell M D Schindler D E 2006 Coalescence in the Lake Washin
56. nient way to specify model structure for certain common cases If fixed is included it provides matrices for some parameters these will override any constraints for those parameters See marssm or the manual for instructions on how to specify fixed and free matrices Value An object of class popWrap data Data supplied by user m Number of hidden state trajectories constraint A list with up to 8 elements Z A R B U Q x0 VO unless some of these are specified in fixed See MARSS for details on what values are allowed fixed A list with up to 8 matrices Z A R B U Q x0 VO free A list with up to 8 matrices Z A R B U Q x0 VO inits A list specifying initial values for parameters to be used at iteration in iterative maximum likelihood algorithms miss value Specifies missing value representation method The method used for estimation control See Arguments Author s Kellie Wills NOAA Seattle USA kellie dot wills at noaa dot gov See Also MARSS marssm checkPopWrap as marssm Examples dat t harborSeal dat dat 2 nrow dat wrapperObj popWrap dat allowed MARSS allowed kem method kem pop Wrap class 55 popWrap class Class popWrap Description popWrap objects are wrapper object containing specifications and options for estimation of multi variate autoregressive state space models in the package MARSS package Author s Kellie Wills NOAA Seattle USA
57. o have the same value Non free i e fixed values should be denoted with NA not 0 since the code will interpret O as 0 and assume that the user wants those parameters to be coded with the name 0 and to be estimated See the manual show doc MARSS manual for many examples of MARSS models and their specification Value An object of class marssm data Data supplied by user fixed A list with 8 matrices Z A R B U Q x0 VO free A list with 8 matrices Z A R B U Q x0 VO M An array of dim n x n x t ann x n missing values matrix for each time point Each matrix is diagonal with 0 at the i i value if the i th value of y is missing and 1 otherwise miss value Specifies missing value representation Default is 99 Author s Kellie Wills NOAA Seattle USA kellie dot wills at noaa dot gov See Also popWrap Examples n gt m 5 fixed fr vector list free Q array seq l mxm free R array NA dim c n n diag freesSR 1 fixed R array 0 dim c n n diag fixed R NA free Z array NA dim c m m fixed Z array 0 dim c m m diag fixed Z 1 freeSU array seq 1 m dim c m 1 fixed U fixedSA matrix NA n 1 freeSA dim c m m fixedSQ array NA dim c m m array NA dim c m 1 matrix 1 n n 1 40 MARSSmcinit freeSB array NA dim c m m fixedSB array 0 dim c m m diag fixed B 1 free x0 array seq 1 m dim c m 1 fixed x0 array NA dim cC m 1
58. of the forecast Value If return mode1l TRUE an object of class mars sMLE Author s Eli Holmes NOAA Seattle USA eli dot holmes at noaa dot gov References Holmes E E and E J Ward 2010 Analysis of multivariate time series using the MARSS pack age NOAA Fisheries Northwest Fisheries Science Center 2725 Montlake Blvd E Seattle WA 98112 this is the user manual accesses via show doc MARSS manual theory behind the figure Holmes E E J L Sabo S V Viscido and W F Fagan 2007 A statistical approach to quasi extinction forecasting Ecology Letters 10 1182 1198 CDF and PDF calculations Dennis B P L Munholland and J M Scott 1991 Estimation of growth and extinction parameters for endangered species Ecological Monographs 61 115 143 TMU figure Ellner S P and E E Holmes 2008 Resolving the debate on when extinction risk is predictable Ecology Letters 11 E1 E5 See Also MARSSboot marssMLE CSEGtmufigure Examples d harborSeal 1 2 kem CSEGriskfigure d datalogged TRUE CSEGtmufigure 7 CSEGtmufigure Plot Forecast Uncertainty Description Plot the uncertainty in the probability of hitting a percent threshold quasi extinction for a single random walk trajectory This is the quasi extinction probability used in Population Viability Anal ysis The uncertainty is shown as a function of the forecast where the forecast is defined in terms
59. on To ensure that the global maximum likelihood values are found it is recommended that initial parameter values be set using Monte Carlo initialization MLEobj cont rol MCInit TRUE particularly if the model is not a good fit to the data This requires more compuation time but reduces the chance of the algorithm terminating at a local maximum and not reaching the true MLEs For many models this is unnecessary but answers should be checked using an initial conditions search before reporting final values MARSSkem calls a Kalman filter smoother MARSSkf for hidden state estimation The algo rithm allows two options for the initial state conditions x at t 1 Either x0 is treated as fixed but unknown estimated in this case fixed VO 0 and x0 is estimated This is the default behav ior In the second case the initial conditions are specified with a known prior fixed x0 and fixed VO and x0 is not estimated In the first case x0 fixed but unknown and to be estimated VO 0 but the algorithm cannot be run with this since x0 would never move from its initial value at iteration 1 Instead during the EM iterations a diffuse prior is used This is done by setting MLEobj control iter VO to a large value say 10 A small value will cause the algorithm to converge very slowly and O will generate an error Before reporting the final log likelihood MARSSkem runs the Kalman filter with the maximum likelihood parameter estimates using the diff
60. ontrolSnumInitSteps Maximum number of EM iterations for each random ini tial value draw MLEobj control boundsInits Length 6 list Each component is a length 2 vector of bounds on the uniform distributions from which initial values will be drawn See Examples The default values for these are given in MARSSsettings R and listed in MARSS Value A list with 8 matrices Z A R B U Q x0 VO specifying initial values for parameters for iteration 1 of the EM algorithm Author s Eli Holmes and Eric Ward NOAA Seattle USA eli dot holmes at noaa dot gov eric dot ward at noaa dot gov References The user manual Holmes E E and E J Ward 2010 Analysis of multivariate time series using the MARSS package NOAA Fisheries Northwest Fisheries Science Center 2725 Montlake Blvd E Seattle WA 98112 type show doc MARSS manual to see See Also MARSSkem marssMLE MARSS how the inits that were used t2 start ignore the values for Z B and VO those parameters are fixed Examples Not run Note doing a Monte Carlo search takes a long long time dat t harborSeal dat dat 2 nrow dat fit1 MARSS dat control list MCInit TRUE fitl Show the inits that were used fitlSstart Try fewer initial start locations but more iterations fit2 MARSS dat control list MCInit TRUE numInits 10 numInitSteps 100 Lt2 S i f 42 marssMLE End Not run marssMLE Maximum Likelih
61. ood MARSS Estimation Object Description An object in the MARSS package that has all the elements needed for maximum likelihood esti mation of multivariate autoregressive state space model the data model estimation methods and any control options needed for the method If the model has been fit and parameters estimated the object will also have the MLE parameters Other functions add other elements to the marssMLE object such as CIs s e s AICb and hessian Usage is marssMLE MLEobj Arguments MLEob J An object of class marssMLE See Details Details The is marssMLE function checks components model start and control which must be present for estimation by functions e g MARSSkem Components returned from estimation must include at least method par kf numIter convergence and logLik Additional compo nents e g AIC may be returned as described in function help files model MARSS model specification an object of class marssm start List with 7 matrices A R B U Q x0 VO specifying initial values for parameters to be used if needed by the maximization algorithm B Initial value s for B matrix m x m U Initial value s for U matrix m x 1 Q Initial value s for Q variance covariance matrix m x m A Initial value s for A matrix n x 1 R Initial value s for R variance covariance matrix n x n x0 Initial value s for initial state vector m x 1 VO Initial variance s fo
62. ood value numlter Number of iterations needed for convergence convergence Did estimation converge successfully convergence 0 Converged in less than MLEob j control maxit iterations and no evidence of degenerate solution using the log log plot test convergence 1 Maximum number of iterations MLEobjScontrolSmaxit was reached before MLEobj controlSabstol condition was satisfied This value can only be output if MLEobj controlSabstol is passed in If the default log log convergence test is being used convergence 10 is returned when maxit is reached convergence 2 No convergence diagnostic were computed because there are problems with the MLE object convergence 3 No convergence diagnostic were computed because MLEobj control maxit was set to less than control min iter conv test This is not an error convergence 10 Some of the parameter estimates did not converge based on the log log plot test before MLEobj control maxit was reached This 1s not an error per se Degenerate solutions are fine but the MARSS algo rithm will not compute the proper likelihood for a degenerate solution convergence 11 Some of the parameter estimates did not converge based on the log log plot test even though MLEobj controlSabstol was reached MARSSkem 31 This value can only be output if MLEobj controlSabstol is passed in Try not setting MLEob3j control abstol so that the log log con vergence test is used instead If it takes
63. r initial state variance m x m control A list specifying estimation options The following options are needed by MARSSkem Other control options can be set if needed for other estimation methods e g the control options listed for opt im for use with MARSSopt im The default values for control options are set in alldefaults method which is specified in MARSSsettings R minit The minimum number of iterations to do in the maximization routine if needed by method marssMLE 43 maxit Maximum number of iterations to be used in the maximization routine if needed by method abstol Optional convergence tolerance for the maximization routine iter VO The value of VO to be used in place of O when x0 is treated as fixed and VO 0 See manual for discussion of initial state variance trace A positive integer If not 0 a record will be created during maximization iterations what s recorded depends on method of maximization MCInit If TRUE do a Monte Carlo search of the initial condition space numInits Number of random initial value draws if MCInit TRUE ignored otherwise numInitSteps Number of EM iterations for each random initial value draw if MCInit TRUE ignored otherwise boundsInits Bounds on the uniform distributions from which initial values will be drawn if MCInit TRUE ignored otherwise silent Suppresses printing of progress bar error messages and convergence information silent Suppresses printing of progress
64. rap boot data Array n x t x nboot of simulated or bootstrapped data if requested and ap propriate model The marssm object that was passed in via MLEobj model nboot Number of bootstraps performed output Type of output returned sim Type of bootstrap param gen Parameter generation method hessian or KalmanEM Author s Eli Holmes and Eric Ward NOAA Seattle USA eli dot holmes at noaa dot gov eric dot ward at noaa dot gov References Holmes E E and E J Ward 2010 Analysis of multivariate time series using the MARSS pack age NOAA Fisheries Northwest Fisheries Science Center 2725 Montlake Blvd E Seattle WA 98112 this is the user manual accesses via show doc MARSS manual Stoffer D S and K D Wall 1991 Bootstrapping state space models Gaussian maximum like lihood estimation and the Kalman filter Journal of the American Statistical Association 86 1024 1033 Cavanaugh J E and R H Shumway 1997 A bootstrap variant of AIC for state space model selection Statistica Sinica 7 473 496 See Also marssMLE marssmMARSSaic Examples nboot is set low in these examples in order to run quickly normally nboot would be gt 1000 at least dat t harborSealnomiss dat dat 2 4 normally one would not use the delta logLik test for convergence abstol but used here with big abstol and minit to speed up the example kem MARSS dat constraint list U equal Q diagonal and equal
65. re n x and use X1 X2 for the Xs and all matrices that are mx Value The object passed in with row and column names on matrices as specified Author s Eli Holmes and Kellie Wills NOAA Seattle USA eli dot holmes at noaa dot gov kellie dot wills at noaa dot gov See Also FA marssML marssm 22 MARSSboot MARSSboot Bootstrap MARSS Parameter Estimates Description Creates bootstrap parameter estimates and simulated or bootstrapped data if appropriate This is a base function in the MARSS package Usage MARSSboot MLEobj nboot 1000 output parameters sim parametric param gen KalmanEM control NULL silent FALSE Arguments MLEob 4 An object of class marssMLE Must have a par element containing MLE parameter estimates nboot Number of bootstraps to perform output Output to be returned data parameters or all sim Type of bootstrap parametric or innovations See Details param gen Parameter generation method hessian or KalmanEM control The options in MLEobj control are used by default If supplied here must contain all of the following max iter Maximum number of EM iterations tol Optional tolerance for log likelihood change If log likelihood decreases less than this amount relative to the previous iteration the EM algorithm exits iter VO The value of VO to be used in place of 0 when x0 is treated as fixed and VO 0 See
66. s type show doc MARSS Holmes2010 to see See Also MARSSmcinit MARSSkf marssMLE MARSSoptim find degenerate MARSSkemcheck 33 Examples dat t harborSeal dat dat 2 nrow dat you can use MARSS to construct a proper marssMLE object MLEobj MARSS dat constraint list Q diagonal and equal U equal fit FALSE Use MARSS to do the fit kemfit MARSSkem MLEob see what a Newton method would find wrapped in try because it tends to throw numerical errors bfgsfit kemfit bfgsfitSmethod BFGS bfgsfit try MARSSoptim bfgsfit look for degenerat stimates this will make a plot that will show if the vars converged plot should be flat if not try setting minit higher or using higher conv test slope tol find degenerate kemfit MARSSkemcheck Model Checking for MLE objects passed to MARSSkem Description This is a helper function in the MARSS package that checks that the model can be handled by the MARSSken algorithm Usage MARSSkemcheck modelObj method kem Arguments modelOb An object of class marssm method The method to be used Currently only method kem is available Value A list with of the model elements A B Q R U x0 Z VO specifying the structure of the model using text strings Author s Eli Holmes NOAA Seattle USA eli dot holmes at noaa dot gov See Also marssmMARSSkem 34 MARSSkf MARSSkf Kalman Filtering and Smoothing Des
67. s Length 6 list Each component is a length 2 vector of bounds on the uniform distributions from which initial values will be drawn to be used with MARSSmcinit Ignored if cont rolSMCInit FALSE See Examples MLEobj control silent Suppresses printing of progress bars error messages warnings and convergence information Value The marssMLE object which was passed in with additional components method kf iter record numIter convergence logLik String BFGS Kalman filter output If MLEobj control trace TRUE then this is the message value from optim Number of iterations needed for convergence Did estimation converge successfully convergence 0 Converged in less than MLEobj control maxit iterations and no evidence of degenerate solution convergence 1 Maximum number of iterations MLEobj control maxit was reached before MLEobj controlSabstol condition was satisfied convergence 10 Some of the variance elements appear to be degenerate T convergence 52 The algorithm was abandoned due to errors from the L BFGS B method convergence 53 The algorithm was abandoned due to numerical errors in the likelihood calculation from MARSSk f This happens frequently with BFGS and can sometimes be helped with a better initial condition Try using the Kalman EM algorithm first method kem and then using the param eter estimates from that to as initial conditions for met hod BFGS
68. s a base function in the MARSS package neglogLik is a helper function for MARSSopt im that returns the negative log likelihood given a vector of the estimated parameters and a marssMLE object Usage MARSSoptim MLEobj neglogLik x MLEob Arguments MLEob 4 An object of class marssMLE x An vector of the estimated parameters as output by MARSSvectorizeparam MARSSoptim Details 45 Objects of class marssMLE may be built from scratch but are easier to construct using MARSS with MARSS fit FALSE method BFGS Options for opt im are passed in using MLEob j cont rol See opt im for a list of that function s control options If Lower and upper for opt im need to be passed in they should be passed in as part of control as control lower and controlSupper Additional control arguments affect printing and initial conditions MLEob jScontrol algorithm must not be equal to 0 See Details MLEobj control LSiter VO This is the value to which VO will be set during the maximization LSMCInit IfTRUE Monte Carlo initialization will be performed by MARSSmcinit MLEob3j control numInits Number of random initial value draws to be used with MARSSmcinit Ignored if controlSMCInit FALSE MLEobj controlSnumInitSteps Maximum number of EM iterations for each random ini tial value draw to be used with MARSSmcinit Ignored if control MCInit FALSE LEobj control boundsInit
69. s data has missing values in it and one want to replicate those locations in the simulated data miss loc can simply be set to the original data see examples 50 MARSSvectorizeparam Value sim states Array dim m x tSteps x nsim of state processes simulated from parameter estimates sim data Array dim n x tSteps x nsim of data simulated from parameter estimates par The list of parameter matrices from which the data were simulated miss loc Matrix identifying where missing values are located tSteps Number of time steps in each simulation nsim Number of simulated data sets generated Author s Eli Holmes and Eric Ward NOAA Seattle USA eli dot holmes at noaa dot gov eric dot ward at noaa dot gov See Also marssmmarssMLE MARSSboot Examples do a parametric bootstrap Same length as original data and same location of missing data d harborSeal 2 4 dat t d MLEobj MARSS dat sim obj MARSSsimulate parList MLEobj par tSteps dim d 1 nsim 10 MARSSvectorizeparam Vector to Parameter Matrix Conversion Description Converts MLEobj Spar to a vector of the estimated parameter elements and vice versa This is a utility function in the MARSS package Usage MARSSvectorizeparam MLEobj parvec NA Arguments MLEob J An object of class marssMLE parvec NA or a vector See Value plankton 51 Details Utility function to generate parameter vectors for optimizatio
70. ssMLE Must have a Spar element containing the MLE parameter estimates method Method for calculating the standard errors hessian parametric and inno vations implemented currently alpha alpha level for the 1 alpha confidence intervals nboot Number of bootstraps to use for parametric and innovations methods Details Approximate confidence intervals CIs on the model parameters may be calculated from the Hes sian matrix the matrix of partial 2nd derivatives of the parameter estimates or parametric or non parametric innovations bootstrapping using nboot bootstraps The Hessian CIs are based on the asymptotic normality of MLE parameters under a large sample approximation Bootstrap estimates of parameter bias are reported if method parametric or innovations is specified Value MARSSparamCIs returns the marssMLE object passed in with additional components par se par upCI par lowCI par Cl alpha par Cl method par CI nboot andpar bias if method is parametric or innovations Author s Eli Holmes NOAA Seattle USA eli dot holmes at noaa dot gov References Holmes E E and E J Ward 2010 Analysis of multivariate time series using the MARSS pack age NOAA Fisheries Northwest Fisheries Science Center 2725 Montlake Blvd E Seattle WA 98112 this is the user manual accesses via show doc MARSS manual MARSSsimulate 49 See Also MARSSboot MARSSinnovationsboot MARSShessian Examples dat t
71. ubdirectory show doc MARSS index Open the file Case _ study _2 R in the doc subdirectory A s A RSS Case_study_2 R ubdirectories in the package directory RSS dir dir show doc show the show doc End Not run stdInnov Standardized Innovations Description Standardizes Kalman filter innovations This is a helper function called by MARSSinnovationsboot in the MARSS package Usage stdInnov SIGMA INNOV Arguments SIGMA n x n x T array of Kalman filter innovations variances This is output from MARSSKf INNOV n x T matrix of Kalman filter innovations This is output from MARSSkf Details n number of observation y time series T number of time steps in the time series Value n x T matrix of standardized innovations Author s Eli Holmes and Eric Ward NOAA Seattle USA eli dot holmes at noaa dot gov eric dot ward at noaa dot gov stdInnov 57 References Stoffer D S and K D Wall 1991 Bootstrapping state space models Gaussian maximum like lihood estimation and the Kalman filter Journal of the American Statistical Association 86 1024 1033 See Also MARSSboot MARSSkf MARSSinnovationsboot Examples Not run std innovations stdInnov kfList Sigma kfList Innov End Not run Index Topic Classes marssm class 39 marssMLE class 43 popWrap class 54 Topic datasets graywhales 8 harborSeal 9 loggerhead 11 plankton 50
72. unt data assuming A 0 This will be a poor start if inits A is not 0 If inits x0 is a numeric vector or matrix inits x0 will be constructed by the command array inits x0 dim c m 1 If x0 is fixed in the model any inits x0 values will be overridden and replaced with the fixed value Default is inits x0 99 e Z If Z is fixed in the model inits 2 set to the fixed value If Z is not fixed then the user must supply inits Z There is no default e elem V0 MARSSkem and MARSSopt im will override init s VO and use a diffuse prior set with marssMLEScontrolSiter V0 if any x0 are estimated and will use mode10b3 fixed VO if xO is fixed The first case corresponds to xO fixed but unknown and treated as an estimated parameter with VO 0 The diffuse prior for VO is used only during the iterations of max imization to all x0 estimation and then VO is reset to O for the final likelihood calculation The second case corresponds to using a prior for the initial state Although inits VO is ignored by the fitting algorithm in MARSS 1 0 it is set here for forward compatibility If inits V0 is a vector or matrix with length equal to the length mode10b3 fixed V0 then initsS SVO will be constructed by the command array inits V0 dim cCc m m If length is 1 or equal to m then inits VO will be constructed into a diagonal matrix by the command diag inits V0 m If x0 is fixed in the model inits VO values will be overridden and replaced with model0b3 fixed VO Defau
73. use prior and VO 0 to obtain the correct likelihood This approach works well and is easy to implement However when one fits a model with x0 having shared values AND an unconstrained R 32 MARSSkem matrix an ill conditioned matrix tends to appear in one of the steps of the Kalman filter algorithm because VO must have elements with 100 percent correlation if you say that some x0 s have the same value MARSSkem will report warnings and errors if this happens Switching to a diago nal R or an unconstrained xO will fix the ill conditioning problems See the manual for discussion about how VO is treated in the algorithm If you get errors it generally means that the solution involves an ill conditioned matrix For exam ple your Q or R matrix is going to a value in which all elements have the same value for example zero If for example you tried to fit a model with fixed and high R matrix and the variance in that R matrix was much higher than what is actually in the data then you might drive Q to zero Also if you try to fit a structurally inadequate model then it is not unusual that Q will be driven to zero For example if you fit a model with hidden state trajectory to data that clearly have 2 quite different hidden state trajectories you might have this problem Comparing the likelihood of this model to a model with more structural flexibility should reveal that the structually inflexible model is inadequate much lower likelihood

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