Model Browser User's Guide

Selecting the Two-Stage Model

Recall how two-stage models are constructed: two-stage modeling partitions the variation separately between tests and within tests, by fitting local and global models separately. A model is fitted to each test independently (local models). These local models are used to generate global models that are fitted across all tests.

For each sweep (test) of spark against torque, you fit a local model. The local model in this case is a spline curve, which has the fitted response features of knot, max, Bhigh_2 and Blow_2. The result of fitting a local model is a value for knot (and the other coefficients) for each test. The global model for knot is fitted to these values (that is, the knot global model fits knot as a function of the global variables). The values of knot from the global model (along with the other global models) are then used to construct the two-stage model

The global models are used to reconstruct a model for the local response (in this case, torque) that spans all input factors. This is the two-stage model across the whole global space, derived from the global models.

Now you can use the model selection features to view the fit of this two-stage model in various ways, to compare it with both the data and the local model fit.

Within this tutorial, you use the following:

• Tests View
• Response Surface View

For more detailed help on all the views available in the Model Selection window, see Selecting Models in the GUI reference.

Note    To construct a two-stage model from the local and global models, you click the local node in the model tree (with the house icon) and click the Select button. This is the next step in the tutorial.

Once you are satisfied with the fit of the local and global models, it is time to construct a two-stage model from them. Return to the Local Model view by clicking the local node PS22 in the Model Browser tree. The Model Browser should look like the following example.

Click Select in the Response Features list pane, and the Model Selection window appears. This window is intended to help you select a Best Model by comparing several candidate models. There are a number of icons in the toolbar that enable you to view the fit of the model in various ways. By default the Tests view appears. These plots show how well the two-stage model agrees with the data.

Tests View

Scroll though the tests using the left/right arrows or the Select Test button at the top left. The plots show the fit of the two-stage model for each test (green open circles and line), compared with the fit of the local model (black line) and the data (blue dots). You can left-click (and hold) to see information on each test or zoom in on points of interest by Shift-click-dragging or middle-click-dragging. Double-click to return the plot to the original size.

Response Surface View

You view the model as a surface by clicking the Response Surface icon in the toolbar. You can rotate the plot by click-dragging it.

1. Click Movie in the Display Type list to see the surface (torque against spark and speed) vary through different values of load.

   

2. Dismiss the Model Selection pane, and accept the best model by clicking Yes in the Model Selection dialog (it is the only two-stage model so far).
3. The MLE dialog appears, prompting you to calculate the maximum likelihood estimate (MLE) for the two-stage model. Click Cancel. You can calculate MLE later.

Verifying the Global Model

Comparing the Local Model and the Two-Stage Model