6.22. Which Sensitivity Measure to Use?

The change in output statistic, added in @RISK 6, is an interesting, differencing approach to sensitivity. You can select mean, mode, or a particular percentile: click the % icon at the bottom of the Sensitivity Analysis window, or the tornado icon at the bottom of the Browse Results window and select Settings.

The Change in Output Statistic tornado displays a degree of difference for just the two extreme bins, but the spider shows more information: the direction of the relationship, and the degree of difference for every bin.

Regression coefficients and regression mapped values are just scaled versions of each other. Correlation coefficients are rank-order correlation, which works well for linear or non-linear correlations. In the Sensitivity Analysis window, when you select Display Significant Inputs Using: Regression (Coefficients), @RISK will display R² ("RSqr") in each column. You can use R² to help you decide between correlation coefficients and regression coefficients:

• A low value of R² means that a linear regression model is not very good at predicting the output from the indicated inputs. In this case, you would focus more on correlation coefficients, because rank-order correlation doesn't depend on the two distributions having similar shape or being linearly related.
• If R² is high, a linear regression model is a good fit mathematically. But even here, you should look at the variables to assure yourself that they are reasonable and to rule out a problem with multicollinearity. This would be signaled, for example, when @RISK reports a significant positive relationship between two variables in the regression analysis, and a significant negative correlation between those variables in the rank-order correlation analysis.

For a more detailed explanation of correlation and regression, see Correlation Tornado versus Regression Tornado and How @RISK Computes Rank-Order Correlation.

R² is a measure of the percentage of the variance in a given output can be traced to the inputs — as opposed to measurement errors, sampling variation, and so on. @RISK adds input variables to a regression one by one, and each variable's contribution to variance is simply bow much larger R² grows as that input is added. In other words, a regression equation should predict output values from a set of input values. A variable's contribution to variance measures how much better the equation becomes as a predictor when that input is added to the regression. Unlike a regression coefficient, this measurement is unaffected by the magnitude of the input. For more about this, see Calculating Contribution to Variance.