Part 3. Outputs
Part 3 discusses how to get outputs from marssMLE objects which are the class of object resulting from a call to fit <- MARSS(). Specifically:
- Estimated states
- Model fits
- Parameter estimates
- Kalman filter and smoother output
- Residuals
- Confidence intervals
- Predictions and forecasts
- Bootstrap resamples: parametric and innovations
- Simulated data
MARSS models are used in many many different ways and different users will want different types of output. MARSS functions will give you every type of output but the trick is to figure out what it is you want. Because MARSS models are used in so many different ways, what is standard output in one field or application might never be used in another field or application.
The notation in the MARSS package follows these conventions:
tTexpectation of something at \(t\) conditioned on all the data.tt1expectation of something at \(t\) conditioned on the data up to \(t-1\).ttexpectation of something at \(t\) conditioned on the data up to \(t\).- fitted means the expected value of the right side of a MARSS \(\mathbf{x}\) or \(\mathbf{y}\) equation without the error term (\(\mathbf{w}\) or \(\mathbf{v}\)). Probably not what you want if you are trying to get states or \(\mathbf{x}\) estimates. Fitted values can be computed using any of the time conditionals listed above. Probably what you want if you are trying to get expected values of \(\mathbf{y}\) or model estimates.
- smoothed and filtered means the expected values including the error terms (\(\mathbf{w}\) or \(\mathbf{v}\)). Probably what you want if you are trying to get states or \(\mathbf{x}\) estimates and not what you want if you are trying to get model or \(\mathbf{y}\) estimates.