Generalized Regression Model Pathway

Important Note

SVEM models that are defined as ensembles of Generalized Regression fits can be constructed in JMP Pro only.

The Generalized Regression pathway enables you to fit various modeling situations and provides variable selection techniques, including Lasso and Elastic Net, which address highly correlated predictors. You can specify a variety of distributions for your response variables.

Launching SVEM

To fit an ensemble model using generalized regression fits:

1. Open the Predictum menu > Self-Validating Ensemble Modeling > Generalized Regression.

   

2. If you don't have a JMP data table open, SVEM prompts you to open one from a local directory.

   The Self-Validating Ensemble Modeling - Generalized Regression window appears.

SVEM Generalized Regression Launch Window

To define the details of the model that will be generated:

1. Select one or more columns from the Select Columns list and click Y, Response. If selecting more than one response, the response columns should have the same modeling type.

   Note

   Selecting exactly two responses will give a prompt asking if the two responses represent interval censoring. You should click No.

2. Construct the model effects by selecting columns from the Select Columns list and using the model effect buttons Add, Cross, Nest, Macros, Attributes, and Transform. For details, see the JMP documentation section Construct Model Effects.

   

3. Optional: Select a numeric column for the frequency role from the Select Columns list and click Freq. For each row, the value in a Freq column reflects how many times that row should be included in the analysis. Fractional frequencies are allowed. Frequencies can be used to down-weight specific rows in a SVEM analysis. For example, if you have observations taken under uncontrolled conditions and you want to include them in a model along with observations taken under controlled conditions, you might want to assign all controlled observations a weight of one and the uncontrolled observations a weight less than one.

4. Specify a distribution for your Ys. There are many possible options.

   

5. Optional: To keep the dialog open in case you want to make changes later on, turn on the Keep dialog open checkbox.

6. Optional: To fit a model with no intercept, turn on the No Intercept checkbox. This option is useful for data from mixture experiments.

7. Optional: You can select Informative Missing from the red triangle menu for the Model Specification outline box. For more information about Informative Missing, see the JMP documentation for Informative Missing as it relates to fitting linear models.

   Note

   For more information on JMP's model dialog for Generalized Regression, see the JMP documentation for the Generalized Regression personality.

8. After specifying your model details, click Run.

   The Model Launch window appears.

Model Launch Window

You can specify fitting options for the bootstrapped models as well as SVEM settings in this window. These fitting options will apply to all responses.

Changing the Settings

You can change SVEM's settings in the SVEM settings panel box.

Number of Bootstrapped Models

In the Number of Bootstrapped Models field, enter the number of bootstrapped models that will be included in the ensemble model.

The default value is 100 for continuous responses or 50 for categorical responses, which proves adequate in many cases. However, you can increase this number if you want greater precision. Note that increasing the number of bootstrapped models also increases the runtime.

Set Random Seed

To obtain a reproducible analysis, enter an integer value in the Set Random Seed field. You can use this seed to rerun the analysis and obtain the same results. The seed is given in the Model Summary outline box in the report that is produced. Also, the seed is included in the SVEM script that you can save to the data table. See the Report Options page.

Warning

A random seed in JMP 14 will not necessarily produce the same analysis as in later versions of JMP.

Proportion of Runs to Exclude

In the Proportion of Runs to Exclude field, enter a value between 0 and 1 representing the proportion of the worst bootstrap runs to exclude from the final model. The default value is 0.5, meaning that half the bootstrap runs will be excluded. The validation root average square error (RASE) is used to determine the worst bootstrap runs to exclude. That is, the specified proportion of runs with the largest validation RASE values are excluded.

The SVEM algorithm generates an ensemble or collection of models using fractionally weighted bootstrapping that are combined to form an overall predictive model. Because of the inherent instability of all model fitting algorithms, these models generally vary considerably in terms of validation RASE. The The Proportion of Runs to Exclude strategy provides smaller and smoother prediction error estimates over the factor space.

Running SVEM

To run SVEM and generate the results in a report, click Go.

While SVEM is running, a progress dialog is displayed.

Notes

To stop the run before the specified number of bootstrapped models has been fit for each response, click the Stop Early button. The resulting report will display only the responses that have completed or partially completed their bootstrap runs at the stop time. If you close the progress dialog manually, SVEM continues running until the specified number of bootstrap runs has been completed.

Also, for some larger models, the Stop Early button will not be accessible. In this case, the only way to stop SVEM from running is to press the Esc key repeatedly. The results from the run will not be reported.

After SVEM has completed the run, the SVEM report window is displayed. The SVEM report window is described in more detail in the following section.

Notes

If your model specification is inconsistent with JMP protocols, you may receive a JMP alert that describes the issue.

Also, when SVEM starts fitting bootstrapped models, it is possible that a condition required for fitting one of the models fails. SVEM checks the first model and if this model fails to meet the condition, SVEM displays a warning message that shows the alert generated by JMP in red. For example:



To continue running the specified number of bootstrapped models despite the issue that JMP reports, click OK. Otherwise, click Cancel to cancel the run and start over with new modeling specifications.

SVEM Report Window

The SVEM report window displays the following reports.

Report Type	Example Screenshot
The Actual by Predicted plot shows observed values on the vertical axis and predicted values on the horizontal axis. If the model provides a good fit, the points are positioned close to the diagonal line y = x. Note: Not shown for categorical responses.
The Model Summary report provides details about the model fitting process, including the SVEM settings, and metrics for the final ensemble model. The random seed is provided in case you want to reproduce your analysis. The final model root average squared error (RASE) is computed from the training data, but because of the inherent self-validation capability of SVEM, it is also considered a validation metric.
The Residual by Predicted plot shows the actual values minus their predicted values. Note: Not shown for categorical responses.
The Proportion Non-Zero plot shows the proportion of bootstrapped models for which each effect has a non-zero coefficient estimate. The estimated coefficients for each bootstrap run are given in the Bootstrap Results Table, which you can obtain by selecting Show Bootstrap Results Table from the red triangle menu for the SVEM outline box.
The Parameter Estimates table shows the parameter estimates for the final model and empirically based estimates of their standard errors. The standard errors are the standard deviations of the parameter estimates of the bootstrapped models.
For categorical responses, a Receiver-Operating Characteristic (ROC) plot is shown. If the response is Nominal, as in the top plot on the right, the ROC plot shows the sensitivity and (1 - specificity) trade-off for each level of the response. Area Under the Curve (AUC) values for each level of the response are shown parenthetically in the legend of the plot. If the response is Ordinal with J levels, the ROC plot shows the sensitivity and (1 - specificity) trade-off for J-1 levels of the response. For each level shown, the ROC curve is constructed using response values greater than or equal to that level as "positives." There is no plot for the lowest level in the value ordering because all responses are greater than or equal to that level. Area Under the Curve (AUC) values for each level of the response are shown parenthetically in the legend of the plot. The bottom plot on the right is for an ordinal response with levels Low < Medium < High; in this example, J=3, and the two levels shown are Medium and High. The plot labeled Medium includes responses of both Medium and High levels (i.e, responses that are at least Medium) as positives.

Report Options

Report options are available in the SVEM report window. For details, see Report Options page.