Learn more about Model-Based Calibration

MLE

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Calculating MLE MLE Settings

Calculating MLE

For an ordinary (univariate) two-stage model, the global models are created in isolation without accounting for any correlations between the response features.

• Using MLE (maximum likelihood estimation) to fit the two-stage model takes account of possible correlations between response features.

• In cases where such correlations occur, using MLE significantly improves the two-stage model.

When you close the Model Selection window, a dialog box asks if you want to calculate MLE. If you click Cancel at this point, you can calculate MLE later as follows:

1. From the local node, click the MLE icon in the toolbar .

   Alternatively, choose Model > Calculate MLE.

2. The MLE dialog box appears. Click Start.

   You can alter various MLE settings on this dialog box.

3. After you click Start a series of progress messages appears, and when finished a new Two-Stage RMSE (root mean square error) value is reported.

4. You can perform more iterations by clicking Start again to see how the RMSE value changes, or you can click Stop at any time.

5. Clicking OK returns you to the Model Browser, where you can view the new MLE model fit.

   Note   After calculating MLE, you will notice that the plots and the icons in the model tree for the whole two-stage model (response node, local node, and all response feature nodes) have turned purple. See Icons: Blue Backgrounds and Purple Worlds.

You can select all response features in turn to inspect their properties graphically; the plots are all purple to symbolize MLE. At the local node the plots show the purple MLE curves against the black local fit and the blue data.

• From the response feature nodes, at any time, click the MLE toolbar icon to recalculate MLE and perform more iterations.

• From the local node, you can click Select to enter the Model Selection window, compare the MLE model with the previous univariate model (without correlations), and choose the best. Here you can select the univariate model and click Assign Best to "undo" MLE and return to the previous model.

  Note   If there are exactly enough response features for the model, you can go straight to MLE calculation after model setup without going through the Select process. The MLE toolbar button and the Model > Calculate MLE menu item are both active in this case. If you add new response features, you cannot create MLE until you go through model selection to choose the response features to use.

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MLE Settings

Algorithm

The algorithm drop-down menu offers a choice between two covariance estimation algorithms, Quasi-Newton and Expectation Maximization. These are algorithms for estimating the covariance matrix for the global models.

Quasi-Newton is recommended for smaller problems (< 5 response features and < 100 tests). Quasi-Newton usually produces better answers (smaller values of -logL) and hence is the default for small problems.

Expectation Maximization is an iterative method for calculating the global covariance (as described in Davidian and Giltinan (1995); see References in Two-Stage Models for Engines). This algorithm has slow convergence, so you might want to use the Stop button.

Tolerance

You can edit the tolerance value. Tolerance is used to specify a stopping condition for the algorithm. The default values are usually appropriate, and if calculation is taking too long you can always click Stop.

Initialize with previous estimate

When you recalculate MLE (that is, perform more iterations), there is a check box you can use to initialize with the previous estimate.

Predict missing values

The other check box (selected by default) predicts missing values. When it is selected, response features that are outliers for the univariate global model are replaced by the predicted value. This allows tests to be used for MLE even if one of the response features is missing. If all the response features for a particular test are missing or the check box is unselected, the whole test is removed from MLE calculation.

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Selecting Models

Response Level

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