Printing functions for MARSS MLE objects
print_marssMLE.RdMARSS() outputs marssMLE objects. print(MLEobj), where MLEobj is a marssMLE object, will print out information on the fit. However, print can be used to print a variety of information (residuals, smoothed states, imputed missing values, etc) from a marssMLE object using the what argument in the print call.
Arguments
- x
A
marssMLEobject.- digits
Number of digits for printing.
- ...
Other arguments for print.
- what
What to print. Default is "fit". If you input what as a vector, print returns a list. See examples.
- "model"
The model parameters with names for the estimated parameters. The output is customized by the form of the model that was fit. This info is in
attr(x$model, "form").- "par"
A list of only the estimated values in each matrix. Each model matrix has it's own list element. Standard function:
coef(x)- "start" or "inits"
The values that the optimization algorithm was started at. Note,
x$startshows this in form="marss" whileprintshows it in whatever form is inattr(x$model, "form").- "paramvector"
A vector of all the estimated values in each matrix. Standard function:
coef(x, type="vector"). Seecoef().- "par.se","par.bias","par.lowCIs","par.upCIs"
A vector the estimated parameter standard errors, parameter bias, lower and upper confidence intervals. Standard function:
MARSSparamCIs(x)SeeMARSSparamCIs().- "xtT" or "states"
The estimated states conditioned on all the data.
x$states- "data"
The data. This is in
x$model$data- "logLik"
The log-likelihood. Standard function:
x$logLik. SeeMARSSkf()for a discussion of the computation of the log-likelihood for MARSS models.- "ytT"
The expected value of the data conditioned on all the data. Returns the data if present and the expected value if missing. This is in
x$ytT(ytT is analogous to xtT).- "states.se"
The state standard errors.
x$states.se- "states.cis"
Approximate confidence intervals for the states. See
MARSSparamCIs().- "model.residuals"
The one-step ahead model residuals or innovations. \(\mathbf{y}_t - \textrm{E}[\mathbf{Y}_t|\mathbf{y}_1^{t-1}]\), aka actual data at time \(t\) minus the expected value of the data conditioned on the data from \(t=1\) to \(t-1\). Standard function:
residuals(x, type="tt1")SeeMARSSresiduals()for a discussion of residuals in the context of MARSS models.- "state.residuals"
The smoothed state residuals. \(\mathbf{x}_t^T- \textrm{E}[\mathbf{X}_t|\mathbf{x}_{t-1}^T]\), aka the expected value of the states at time \(t\) conditioned on all the data minus the expected value of the states at time \(t\) conditioned on \(\mathbf{x}_{t-1}^T]\). Standard function:
residuals(x, type="tT")SeeMARSSresiduals().- parameter name
Returns the parameter matrix for that parameter with fixed values at their fixed values and the estimated values at their estimated values. Standard function:
coef(x, type="matrix")$elem- "kfs"
The Kalman filter and smoother output. See
MARSSkf()for a description of the output. The full kf output is not normally attached to the output from aMARSS()call. This will run the filter/smoother if needed and return the list invisibly. So assign the output asfoo=print(x,what="kfs")- "Ey"
The expectations involving y conditioned on all the data. See
MARSShatyt()for a discussion of these expectations. This output is not normally attached to the output from aMARSS()call--exceptytTwhich is the predicted value of any missing y. The list is returned invisibly so assign the output asfoo=print(x,what="Ey").
- form
By default, print uses the model form specified in the call to
MARSS(). This information is inattr(marssMLE$model, "form"), however you can specify a different form.form="marss"should always work since this is the model form in which the model objects are stored (inmarssMLE$marss).- silent
If TRUE, do not print just return the object. If print call is assigned, nothing will be printed. See examples. If
what="fit", there is always output printed.
Value
A print out of information. If you assign the print call to a value, then you can reference the output. See the examples.
Examples
dat <- t(harborSeal)
dat <- dat[c(2,11),]
MLEobj <- MARSS(dat)
#> Success! abstol and log-log tests passed at 26 iterations.
#> Alert: conv.test.slope.tol is 0.5.
#> Test with smaller values (<0.1) to ensure convergence.
#>
#> MARSS fit is
#> Estimation method: kem
#> Convergence test: conv.test.slope.tol = 0.5, abstol = 0.001
#> Estimation converged in 26 iterations.
#> Log-likelihood: 11.74016
#> AIC: -9.480311 AICc: -6.3692
#>
#> Estimate
#> R.diag 0.0115
#> U.X.CoastalEstuaries 0.0613
#> U.X.OR.NorthCoast 0.0510
#> Q.(X.CoastalEstuaries,X.CoastalEstuaries) 0.0147
#> Q.(X.OR.NorthCoast,X.OR.NorthCoast) 0.0122
#> x0.X.CoastalEstuaries 7.3823
#> x0.X.OR.NorthCoast 6.2707
#> Initial states (x0) defined at t=0
#>
#> Standard errors have not been calculated.
#> Use MARSSparamCIs to compute CIs and bias estimates.
#>
print(MLEobj)
#>
#> MARSS fit is
#> Estimation method: kem
#> Convergence test: conv.test.slope.tol = 0.5, abstol = 0.001
#> Estimation converged in 26 iterations.
#> Log-likelihood: 11.74016
#> AIC: -9.480311 AICc: -6.3692
#>
#> Estimate
#> R.diag 0.0115
#> U.X.CoastalEstuaries 0.0613
#> U.X.OR.NorthCoast 0.0510
#> Q.(X.CoastalEstuaries,X.CoastalEstuaries) 0.0147
#> Q.(X.OR.NorthCoast,X.OR.NorthCoast) 0.0122
#> x0.X.CoastalEstuaries 7.3823
#> x0.X.OR.NorthCoast 6.2707
#> Initial states (x0) defined at t=0
#>
#> Standard errors have not been calculated.
#> Use MARSSparamCIs to compute CIs and bias estimates.
#>
print(MLEobj, what="model")
#>
#> Model form is marxss. Model Structure is
#> m: 2 state process(es) named X.CoastalEstuaries X.OR.NorthCoast
#> n: 2 observation time series named CoastalEstuaries OR.NorthCoast
#>
#> Z : design matrix with rows: X.CoastalEstuaries X.OR.NorthCoast (2 x 2)
#> A : fixed and zero (2 x 1)
#> R : diagonal and equal (2 x 2)
#> B : identity (2 x 2)
#> U : unconstrained (2 x 1)
#> Q : diagonal and unequal (2 x 2)
#> x0 : unconstrained (2 x 1)
#> V0 : fixed and zero (2 x 2)
#> D : fixed and zero (2 x 1)
#> C : fixed and zero (2 x 1)
#> d : fixed and zero (1 x 1)
#> c : fixed and zero (1 x 1)
#> G : identity (2 x 2)
#> H : identity (2 x 2)
#> L : identity (2 x 2)
print(MLEobj,what="par")
#> List of the estimated values in each parameter matrix
#> $Z
#> [,1]
#>
#> $A
#> [,1]
#>
#> $R
#> [,1]
#> diag 0.01148472
#>
#> $B
#> [,1]
#>
#> $U
#> [,1]
#> X.CoastalEstuaries 0.06134704
#> X.OR.NorthCoast 0.05099574
#>
#> $Q
#> [,1]
#> (X.CoastalEstuaries,X.CoastalEstuaries) 0.01468309
#> (X.OR.NorthCoast,X.OR.NorthCoast) 0.01218082
#>
#> $x0
#> [,1]
#> X.CoastalEstuaries 7.382266
#> X.OR.NorthCoast 6.270672
#>
#> $V0
#> [,1]
#>
#> $G
#> [,1]
#>
#> $H
#> [,1]
#>
#> $L
#> [,1]
#>
#> $C
#> [,1]
#>
#> $D
#> [,1]
#>
#> $c
#> [,1]
#>
#> $d
#> [,1]
#>
#>
#silent doesn't mean silent unless the print output is assigned
print(MLEobj, what="paramvector", silent=TRUE)
#> R.diag
#> 0.01148472
#> U.X.CoastalEstuaries
#> 0.06134704
#> U.X.OR.NorthCoast
#> 0.05099574
#> Q.(X.CoastalEstuaries,X.CoastalEstuaries)
#> 0.01468309
#> Q.(X.OR.NorthCoast,X.OR.NorthCoast)
#> 0.01218082
#> x0.X.CoastalEstuaries
#> 7.38226633
#> x0.X.OR.NorthCoast
#> 6.27067221
tmp <- print(MLEobj, what="paramvector", silent=TRUE)
#silent means some info on what you are printing is shown whether
#or not the print output is assigned
print(MLEobj, what="paramvector", silent=FALSE)
#> vector of the estimated parameter values
#> R.diag
#> 0.01148472
#> U.X.CoastalEstuaries
#> 0.06134704
#> U.X.OR.NorthCoast
#> 0.05099574
#> Q.(X.CoastalEstuaries,X.CoastalEstuaries)
#> 0.01468309
#> Q.(X.OR.NorthCoast,X.OR.NorthCoast)
#> 0.01218082
#> x0.X.CoastalEstuaries
#> 7.38226633
#> x0.X.OR.NorthCoast
#> 6.27067221
#>
tmp <- print(MLEobj, what="paramvector", silent=FALSE)
#> vector of the estimated parameter values
#> R.diag
#> 0.01148472
#> U.X.CoastalEstuaries
#> 0.06134704
#> U.X.OR.NorthCoast
#> 0.05099574
#> Q.(X.CoastalEstuaries,X.CoastalEstuaries)
#> 0.01468309
#> Q.(X.OR.NorthCoast,X.OR.NorthCoast)
#> 0.01218082
#> x0.X.CoastalEstuaries
#> 7.38226633
#> x0.X.OR.NorthCoast
#> 6.27067221
#>
cis <- print(MLEobj, what="states.cis")
#> Approximate 95% confidence intervals for the states using 1.95*states.se.
#>
#> $up95CI
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> X.CoastalEstuaries 7.582208 7.662731 7.805439 7.974288 8.145434 8.213839
#> X.OR.NorthCoast 6.508716 6.586029 6.600061 6.726306 6.810411 6.865571
#> [,7] [,8] [,9] [,10] [,11] [,12]
#> X.CoastalEstuaries 8.452396 8.585865 8.569941 8.591932 8.743092 8.759882
#> X.OR.NorthCoast 6.891149 6.870485 6.991319 7.060527 7.132938 7.178193
#> [,13] [,14] [,15] [,16] [,17] [,18]
#> X.CoastalEstuaries 8.948957 8.966939 8.984194 9.113593 9.140259 9.103758
#> X.OR.NorthCoast 7.369163 7.495229 7.619290 7.662625 7.686318 7.837325
#> [,19] [,20] [,21] [,22] [,23] [,24]
#> X.CoastalEstuaries 9.071700 8.934430 8.955694 9.016046 9.067013 9.128120
#> X.OR.NorthCoast 7.851273 7.818153 7.771569 7.810496 7.867185 7.838241
#> [,25] [,26] [,27] [,28] [,29] [,30]
#> X.CoastalEstuaries 9.099459 9.277452 9.421406 9.550456 9.670583 9.784593
#> X.OR.NorthCoast 7.695457 7.630595 7.655370 7.792159 7.915711 8.073195
#>
#> $est
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> X.CoastalEstuaries 7.443643 7.516263 7.657249 7.818901 7.938669 8.058437
#> X.OR.NorthCoast 6.322973 6.375274 6.427575 6.484465 6.541356 6.598247
#> [,7] [,8] [,9] [,10] [,11] [,12]
#> X.CoastalEstuaries 8.304090 8.438403 8.422577 8.444578 8.595738 8.612517
#> X.OR.NorthCoast 6.655137 6.712028 6.846831 6.918080 6.990775 7.036070
#> [,13] [,14] [,15] [,16] [,17] [,18]
#> X.CoastalEstuaries 8.801495 8.818632 8.828792 8.906824 8.984857 8.955451
#> X.OR.NorthCoast 7.227045 7.353112 7.477173 7.520508 7.544201 7.695205
#> [,19] [,20] [,21] [,22] [,23] [,24]
#> X.CoastalEstuaries 8.924236 8.787051 8.808212 8.867583 8.91033 8.913168
#> X.OR.NorthCoast 7.709134 7.675877 7.628308 7.660308 7.67418 7.688052
#> [,25] [,26] [,27] [,28] [,29] [,30]
#> X.CoastalEstuaries 8.916006 8.977353 9.038700 9.100047 9.161394 9.222741
#> X.OR.NorthCoast 7.552186 7.488249 7.512726 7.646429 7.749249 7.800245
#>
#> $low95CI
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> X.CoastalEstuaries 7.305077 7.369794 7.509059 7.663514 7.731904 7.903036
#> X.OR.NorthCoast 6.137230 6.164519 6.255088 6.242624 6.272301 6.330923
#> [,7] [,8] [,9] [,10] [,11] [,12]
#> X.CoastalEstuaries 8.155783 8.290940 8.275212 8.297225 8.448385 8.465153
#> X.OR.NorthCoast 6.419126 6.553571 6.702344 6.775632 6.848612 6.893946
#> [,13] [,14] [,15] [,16] [,17] [,18]
#> X.CoastalEstuaries 8.654032 8.670325 8.673390 8.700055 8.829454 8.807144
#> X.OR.NorthCoast 7.084927 7.210994 7.335056 7.378391 7.402083 7.553085
#> [,19] [,20] [,21] [,22] [,23] [,24]
#> X.CoastalEstuaries 8.776771 8.639671 8.660730 8.719120 8.753647 8.698216
#> X.OR.NorthCoast 7.566995 7.533601 7.485048 7.510121 7.481175 7.537863
#> [,25] [,26] [,27] [,28] [,29] [,30]
#> X.CoastalEstuaries 8.732552 8.677253 8.655993 8.649637 8.652205 8.660889
#> X.OR.NorthCoast 7.408916 7.345903 7.370082 7.500698 7.582788 7.527295
#>
#>
cis$up95CI
#> [,1] [,2] [,3] [,4] [,5] [,6]
#> X.CoastalEstuaries 7.582208 7.662731 7.805439 7.974288 8.145434 8.213839
#> X.OR.NorthCoast 6.508716 6.586029 6.600061 6.726306 6.810411 6.865571
#> [,7] [,8] [,9] [,10] [,11] [,12]
#> X.CoastalEstuaries 8.452396 8.585865 8.569941 8.591932 8.743092 8.759882
#> X.OR.NorthCoast 6.891149 6.870485 6.991319 7.060527 7.132938 7.178193
#> [,13] [,14] [,15] [,16] [,17] [,18]
#> X.CoastalEstuaries 8.948957 8.966939 8.984194 9.113593 9.140259 9.103758
#> X.OR.NorthCoast 7.369163 7.495229 7.619290 7.662625 7.686318 7.837325
#> [,19] [,20] [,21] [,22] [,23] [,24]
#> X.CoastalEstuaries 9.071700 8.934430 8.955694 9.016046 9.067013 9.128120
#> X.OR.NorthCoast 7.851273 7.818153 7.771569 7.810496 7.867185 7.838241
#> [,25] [,26] [,27] [,28] [,29] [,30]
#> X.CoastalEstuaries 9.099459 9.277452 9.421406 9.550456 9.670583 9.784593
#> X.OR.NorthCoast 7.695457 7.630595 7.655370 7.792159 7.915711 8.073195
vars <- print(MLEobj, what=c("R","Q"))
#> Parameter matrix R
#> [,1] [,2]
#> [1,] 0.01148472 0.00000000
#> [2,] 0.00000000 0.01148472
#>
#> Parameter matrix Q
#> [,1] [,2]
#> [1,] 0.01468309 0.00000000
#> [2,] 0.00000000 0.01218082
#>