3 Ways to Improve Your Regression
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1 3 Ways to Improve Your Regression Introduction This tutorial will take you through the steps demonstrated in the 3 Ways to Improve Your Regression webinar. First, you will be introduced to a dataset about compressive strength of concrete. Then, you will walk through the steps of building four models: 1) Standard linear regression 2) MARS (Multivariate Adaptive Regression Splines) 3) TreeNet Gradient Boosting 4) Random Forests The last three techniques offer different approaches to handling problems standard linear regression cannot, such as missing values, interactions, and nonlinearities. A final comparison of the models and pros/cons for each will help you tackle your next big regression project. Tutorial Begin by opening Salford Predictive Modeler (SPM):
2 From the menu, select File > Open > Data File or click the folder shortcut: Locate Concrete.xls 1 and click Open. 1 I-Cheng Yeh, "Modeling of strength of high performance concrete using artificial neural networks," Cement and Concrete Research, Vol. 28, No. 12, pp (1998)
3 The Activity Window, pictured below, will appear: On the left side of the window, the variables in the data file are listed. STRENGTH will be our target variable and measures compressive strength of concrete (MPa). The remaining eight variables are components/characteristics of concrete and will act as predictors of strength. On the right, you can see there are 1030 records and 9 numeric variables. In the row of buttons at the bottom of the Activity Window, click View Data. This feature simply displays a spreadsheet, below, for easy viewing of the data.
4 From the Activity Window (View > Activity Window), click Model. Or, use the Model shortcut:
5 This is where you will set up your first model, a standard linear regression. Select Regression as the Analysis Engine in the bottom right corner of the Model Setup window. Choose STRENGTH in the Target column and the remaining component variables in the Predictor column. Click the Testing tab: Choose No independent testing exploratory model. This is common practice for a linear regression. Click Start.
6 The Regression Results window, below, will appear with summary statistics on the completed model. The two measures you will be comparing for all of the models are MSE and R 2. For this standard linear regression, the MSE is with an R 2 of %. The other tabs in this results window will show you information about the model, such as outliers and coefficients. Method MSE R 2 Linear Regression % MARS - - TreeNet - - Random Forests - -
7 Re-open the Model Setup window: Change the Analysis Engine to MARS. Check that the Target Type is Regression and that all of the variables are correctly selected.
8 Click the Testing tab at the top of the window: Select V-fold cross-validation for 10 folds as a testing method.
9 Click the Options and Limits (MARS) tab: Enter 40 in the Max Basis Functions field. This will create more opportunities for nonlinearities in the data, if necessary. Additionally, you can change the Maximum Interactions field to allow for higher order interactions. Click Start.
10 The MARS Results window, below, will appear with the completed model: The graph shows the number of basis functions in the model plotted against both the GCV and MSE. Click the Summary button at the bottom of the window:
11 This will bring up a Summary Results window similar to the linear regression model. Here, you can see the model achieves an MSE of and an R 2 of %. Method MSE R 2 Linear Regression % MARS % TreeNet - - Random Forests - - This result is a drastic improvement from the previous linear regression. There are several other features in this window that give insight to the model and pose an advantage over regression. Click the Variable Importance tab:
12 Here, you can see AGE and CEMENT contributed most to building the MARS model, while COARSE_AGGREGATE was least important. Click the Basis Functions tab: This tab holds equations for all basis functions in addition to the final model. For those modelers who prefer the traditional output of a regression model, this tab may prove useful to you.
13 To see these basis functions in action, click the Plots tab: These are the 2D plots of the basis functions for each predictor. Click Show All.
14
15 Each variable is plotted against its contribution to the response variable, STRENGTH. The nonlinear functions are clearly depicted. For example, AGE exhibits a steep increase in contribution to strength during the first 50 days, then levels off. Re-open the Model Setup window: Change the Analysis Engine to TreeNet Gradient Boosting. Again, check the Target Type and Variable Selection.
16 Click the Testing tab: You will also use 10-fold cross-validation in this model for accurate comparisons.
17 Click the TreeNet tab: This tab holds a lot of fine-tuning parameters for adjusting your model. The default option is to grow 200 trees, but you will enter 500 for this particular exercise.
18 Click the Plots and Options tab: Select both one variable and two variable dependence plots for the top 3 variables. (In earlier versions, plots can be created after the model building process by clicking Create Plots in the results window.) Click Start.
19 The TreeNet results window, below, will appear with the completed model: In this results window, you will see the number of trees in the model plotted against either the MSE, MAD, MAPD, or R 2. Click the Summary button to bring up all of these measures for the optimal model:
20 For the Test sample, the TreeNet model achieved an MSE of and an R 2 of %. Method MSE R 2 Linear Regression % MARS % TreeNet % Random Forests This model performs slightly better than MARS, but the important thing to note is the drastic improvement over linear regression. Return to the Results window and click the Display Plots button: This brings up a list of the plots you created during the Model Setup process:
21 Click Show All. The plots above are called partial dependency plots. Each predictor is plotted against its contribution to the response variable, after averaging over contributions from all other predictors. For example, WATER has a positive contribution to STRENGTH over the values 120 to 175, at which it crosses over into negative contribution. Essentially, too much water weakens the concrete. In addition, you will see 3D plots that model the interactions between the top 3 important variables, pictured below.
22 Double-click the individual plots to open in a separate window. From here, you can manipulate the positioning of the 3D graph along with the picture details (mesh, colors, etc.).
23 Re-open the Model Setup window: Change the Analysis Engine to RandomForests.
24 Click the Testing tab: Random Forests uses a bootstrapping technique to build an ensemble of trees. Therefore, there is a built-in test sample, called out-of-bag data, which is a result of unchosen data during bootstrapping. Choose this method for testing. Click Start.
25 The RF Results window, below, will appear: This results window shows the number of trees built in the RF model plotted against the MSE. Click the Summary button:
26 You achieved an MSE of and an R 2 of 90.84%. Method MSE R 2 Linear Regression % MARS % TreeNet % Random Forests % Overall, you were able to decrease the mean error of your model from about 10 to around 5. Additionally, you explored a few different techniques that offered a variety of analysis tools, such as plots and variable rankings. Keep in mind, these results will vary depending on the model-building parameters you choose. Conclusion Now that you ve seen 3 alternate approaches to a regression model, which should you use? This is a tricky question because it depends on your data and modeling needs. All three engines handle missing values, interactions, and nonlinearities; our suggestion is that you try all of them to see which performs best with your data. MARS may be the best choice if you re looking for a traditional regression equation. If you prefer decision trees, try TreeNet or RandomForests. If you re stuck, send us an at support@salfordsystems.com and we ll help you make your decision! Resources Ask for Help! About MARS About TreeNet About RandomForests
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