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## Estimation Report

### What is an Estimation Report?

The estimation report contains information about the results and options used for a model estimation. This report is stored in the `Report` property of the estimated model. The exact contents of the report depend on the estimator function you use to obtain the model.

Specifically, the estimation report has the following information:

• Status of the model — whether the model is constructed or estimated

• How the initial conditions are handled during estimation

• Termination conditions for iterative estimation algorithms

• Final prediction error (FPE), percent fit to estimation data, and mean-square error (MSE)

• Raw, normalized, and small sample-size corrected Akaike Information Criteria (AIC) and Bayesian Information Criterion (BIC)

• Type and properties of the estimation data

• All estimated quantities — parameter values, initial states for state-space and grey-box models, and their covariances

• The option set used for configuring the estimation algorithm

You can use the report to:

### Access Estimation Report

This example shows how to access the estimation report.

The estimation report keeps a log of information such as the data used, default and other settings used, and estimated results such as parameter values, initial conditions, and fit.

After you estimate a model, use dot notation to access the estimation report. For example:

```load iddata1 z1; np = 2; sys = tfest(z1,np); sys_report = sys.Report```
```sys_report = Status: 'Estimated using TFEST' Method: 'TFEST' InitializeMethod: 'iv' N4Weight: 'Not applicable' N4Horizon: 'Not applicable' InitialCondition: 'estimate' Fit: [1x1 struct] Parameters: [1x1 struct] OptionsUsed: [1x1 idoptions.tfest] RandState: [] DataUsed: [1x1 struct] Termination: [1x1 struct] ```

Explore the options used during the estimation.

`sys.Report.OptionsUsed`
```Option set for the tfest command: InitializeMethod: 'iv' InitializeOptions: [1x1 struct] InitialCondition: 'auto' Display: 'off' InputOffset: [] OutputOffset: [] EstimateCovariance: 1 Regularization: [1x1 struct] SearchMethod: 'auto' SearchOptions: [1x1 idoptions.search.identsolver] WeightingFilter: [] EnforceStability: 0 OutputWeight: [] Advanced: [1x1 struct] ```

View the fit of the transfer function model with the estimation data.

`sys.Report.Fit`
```ans = struct with fields: FitPercent: 70.7720 LossFcn: 1.6575 MSE: 1.6575 FPE: 1.7252 AIC: 1.0150e+03 AICc: 1.0153e+03 nAIC: 0.5453 BIC: 1.0372e+03 ```

### Compare Estimated Models Using Estimation Report

This example shows how to compare multiple estimated models using the estimation report.

`load iddata1 z1;`

Estimate a transfer function model.

```np = 2; sys_tf = tfest(z1,np);```

Estimate a state-space model.

`sys_ss = ssest(z1,2);`

Estimate an ARX model.

`sys_arx = arx(z1, [2 2 1]);`

Compare the percentage fit of the estimated models to the estimation data.

`fit_tf = sys_tf.Report.Fit.FitPercent`
```fit_tf = 70.7720 ```
`fit_ss = sys_ss.Report.Fit.FitPercent`
```fit_ss = 76.3808 ```
`fit_arx = sys_arx.Report.Fit.FitPercent`
```fit_arx = 68.7220 ```

The comparison shows that the state-space model provides the best percent fit to the data.

### Analyze and Refine Estimation Results Using Estimation Report

This example shows how to analyze an estimation and configure another estimation using the estimation report.

Estimate a state-space model that minimizes the 1-step ahead prediction error.

```load(fullfile(matlabroot,'toolbox','ident','iddemos','data','mrdamper.mat')); z = iddata(F,V,Ts); opt = ssestOptions; opt.Focus = 'prediction'; opt.Display = 'on'; sys1 = ssest(z,2,opt);```

`sys1` has good 1-step prediction ability as indicated by >90% fit of the prediction results to the data.

Use `compare(z,sys1)` to check the model's ability to simulate the measured output `F` using the input `V`. The model's simulated response has only 45% fit to the data.

Perform another estimation where you retain the original options used for `sys1` except that you change the focus to minimize the simulation error.

Fetch the options used by `sys1` stored in its `Report` property. This approach is useful when you have saved the estimated model but not the corresponding option set used for the estimation.

`opt2 = sys1.Report.OptionsUsed;`

Change the focus to simulation and re-estimate the model.

```opt2.Focus = 'simulation'; sys2 = ssest(z,sys1,opt2);```

Compare the simulated response to the estimation data using `compare(z,sys1,sys2)`. The fit improves to 53%.

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