The Variable Importance report calculates indices that measure the importance of factors in a model in a way that is independent of the model type and fitting method. The fitted model is used only in calculating predicted values. The method estimates the variability in the predicted response based on a range of variation for each factor. If variation in the factor causes high variability in the response, then that effect is important relative to the model.
Note: In some platforms, Assess Variable Importance is not available for categorical responses with more than two levels.
Assess Variable Importance can also be accessed in the Prediction Profiler that is obtained through the Graph menu.
For statistical details, see Statistical Details for Assess Variable Importance. See also Saltelli (2002).
Note: Assess Variable Importance requires that all columns reside in the same data table.
The Assess Variable Importance menu has the following options that address the methodology used in constructing importance indices:
Independent Uniform Inputs
For each factor, Monte Carlo samples are drawn from a uniform distribution defined by the minimum and maximum observed values. Use this option when you believe that your factors are uncorrelated and that their likely values are uniformly spread over the range represented in the study. This is the appropriate option for designed experiments that do not involve constraints or mixture factors.
Independent Resampled Inputs
For each factor, Monte Carlo samples are obtained by resampling its set of observed values. Use this option when you believe that your factors are uncorrelated and that their likely values are not represented by a uniform distribution.
Dependent Resampled Inputs
Factor values are constructed from observed combinations using a k-nearest neighbors approach, in order to account for correlation. This option treats observed variance and covariance as representative of the covariance structure for your factors. Use this option when you believe that your factors are correlated. Note that this option is sensitive to the number of rows in the data table. If used with a small number of rows, the results can be unreliable.
Note: The Independent Resampled Inputs and Dependent Resampled Inputs options are intended for observational studies. The Independent option is faster than the Dependent option, but the Dependent option handles multicollinearity better and does not extrapolate into regions far away from the data.
Linearly Constrained Inputs
For each factor, Monte Carlo samples are drawn from a uniform distribution over a region defined by linear constraints. The linear constraints can be defined in the Prediction Profiler or constructed in connection with a designed experiment. In addition, the samples are restricted to fall within the minimum and maximum observed values. Use this option in the presence of linear constraints, when you believe that these constraints impact the distribution of the inputs.
The speed of these algorithms depends on the model evaluation speed. In general, the fastest option is Independent Uniform Inputs and the slowest is Dependent Resampled Inputs. You have the option to Accept Current Indices when the estimation process is unable to complete instantaneously.
Note: Variable importance indices are constructed using Monte Carlo sampling. For this reason, you can expect some variation in importance index values from one run to another.
Each Assess Variable Importance option presents a Summary Report and Marginal Model Plots. When the Assess Variable Importance report opens, the factors in the Prediction Profiler are reordered according to their Total Effect importance indices. When there are multiple responses, the factors are reordered according to the Total Effect importance indices in the Overall report. When you run several Variable Importance reports, the factors in the Prediction Profiler are ordered according to their Total Effect indices in the most recent report.
For each response, a table displays the following elements:
Column
The factor of interest.
Main Effect
An importance index that reflects the relative contribution of that factor alone, not in combination with other factors.
Total Effect
An importance index that reflects the relative contribution of that factor both alone and in combination with other factors. The Total Effect column is displayed as a bar chart. See Weights.
Main Effect Std Error
The Monte Carlo standard error of the Main Effect’s importance index. This is a hidden column that you can access by right-clicking in the report and selecting Columns > Main Effect Std Error. By default, sampling continues until this error is less than 0.01. Details of the calculation are given in Variable Importance Standard Errors. (Not available for Dependent Resampled Inputs option.)
Total Effect Std Error
The Monte Carlo standard error of the Total Effect’s importance index. This is a hidden column that you can access by right-clicking in the report and selecting Columns > Total Effect Std Error. By default, sampling continues until this error is less than 0.01. Details of the calculation are given in Variable Importance Standard Errors. (Not available for Dependent Resampled Inputs option.)
Weights
A plot that shows the Total Effect indices, located to the right of the final column. You can deselect or reselect this plot by right-clicking in the report and selecting Columns > Weights.
Proportion of function evaluations with missing values
The proportion of Monte Carlo samples for which some combination of inputs results in an inestimable prediction. When the proportion is nonzero, this message appears as a note at the bottom of the table.
Note: When you have more than one response, the Summary Report presents an Overall table followed by tables for each response. The importance indices in the Overall report are the averages of the importance indices across all responses.
The Marginal Model Plots report (Figure 3.43) shows a matrix of plots, with a row for each response and columns for the factors. The factors are ordered according to the size of their overall Total Effect importance indices.
For a given response and factor, the plot shows the mean response for each factor value, where that mean is taken over all inputs to the calculation of importance indices. These plots differ from profiler plots, which show cross sections of the response. Marginal Model Plots are useful for assessing the main effects of factors.
Note that your choice of input methodology impacts the values plotted on marginal model plots. Also, because the plots are based on the generated input settings, the plotted mean responses might not follow a smooth curve.
The red triangle menu options enable you to show or hide the following aspects of the plots:
Estimate
A smoothed estimate of the mean of the simulated values calculated as a function of the factor values.
Note: The estimates of the mean are simulated, so the values change when you rerun the analysis.
Confidence Interval
Shows or hides a 95% confidence band for the simulated means. This band is often narrow and might not be visible unless you expand the scale. Not available for Dependent Resampled Inputs.
Note: The confidence bounds are simulated, so the bands change when you rerun the analysis.
Data
The actual (unsimulated) values of the response plotted against the factor values.
The Variable Importance red triangle menu contains the following options:
Reorder factors by main effect importance
Reorders the cells in the Prediction Profiler in accordance with the importance indices for the main effects (Main Effect).
Reorder factors by total importance
Reorders the cells in the Prediction Profiler in accordance with the total importance indices for the factors (Total Effect).
Colorize Profiler
Colors cells in the profiler by Total Effect importance indices using a red to white intensity scale.
Note: You can click rows in the Summary Report to select columns in the data table. This can facilitate further analyses.