Viewing a Sensitivity Analysis Table

One of the most powerful options for analyzing multi-variate results is to carry out a sensitivity analysis. GoldSim provides a number of statistical sensitivity analyses through the multi-variate result display option.

If you are viewing a 2D Scatter Plot (or a different type of Multi-variate display), you can view a Sensitivity Analysis Table by pressing the Sensitivity button at the top of the display.

Note: When viewing a Multi-Variate Result element, the element “remembers”the last type of view that was displayed, and displays that view when you double-click on it.

This table displays measures of the sensitivity of the first output in the list of results in the Result Properties dialog (listed at the top of the dialog) to the selected input variables (all the other outputs in the list of results in the Result Properties dialog). In the example above, the analysis is being carried out on the result R1, and the other results whose impact on R1 is being measured are A, B, C and W.

Note: If some of your Stochastics are triggered repeatedly during a simulation, selecting them for sensitivity analysis is likely not to produce meaningful results.

The order in which results appear in the list in the Result Properties dialog can be changed using the Move Up and Move Down buttons in that dialog, such that any variable in the list can be specified as the result for which the sensitivity analysis is being carried out.

Each of the measures computed in the Sensitivity Analysis Table is described below:

Coefficient of determination: This coefficient varies between 0 and 1, and represents the fraction of the total variance in the result that can be explained based on a linear (regression) relationship to the input variables (i.e., Result = aX + bY + cZ + …). The closer this value is to 1, the better the relationship between the result and the variables can be explained with a linear model.

Importance Measure: This measure varies between 0 and 1, and represents the fraction of the result’s variance that is explained by the variable. This measure is useful in identifying nonlinear, non-monotonic relationships between an input variable and the result (which conventional correlation coefficients may not reveal). The importance measure is a normalized version of a measure discussed in Saltelli and Tarantola (2002).

Correlation Coefficient: Rank (Spearman) or value (Pearson) correlation coefficients range between -1 and 1, and express the extent to which there is a linear relationship between the selected result and an input variable.

SRC (Standardized Regression Coefficient): Standardized regression coefficients range between -1 and 1 and provide a normalized measure of the linear relationship between variables and the result. They are the regression coefficients found when all of the variables (and the result) are transformed and expressed in terms of the number of standard deviations away from their mean. GoldSim’s formulation is based on Iman et al (1985).

Partial Correlation Coefficient: Partial correlation coefficients vary between -1 and 1, and reflect the extent to which there is a linear relationship between the selected result and an input variable, after removing the effects of any linear relationships between the other input variables and both the result and the input variable in question. For systems where some of the input variables may be correlated, the partial correlation coefficients represent the “unique” contribution of each input to the result. GoldSim’s formulation is based on Iman et al (1985).

You can copy the contents of a sensitivity analysis table to the clipboard. To do so, you must first select the entire table (by double-clicking on the empty cell in the upper left-hand corner of the table. After you do so, you can copy the table to the clipboard by Ctrl+C. You can subsequently paste the table into another application (such as a spreadsheet).

Like all result tables in GoldSim, this table can be sorted in ascending or descending order by selecting a column and pressing the Sort button:

The Use Ranks button determines whether the calculations use ranks of the values or the actual values. By default, this button is not pressed, and the calculations are based on actual values.

By default, Multi-Variate results operate on Final Values. That is, the analysis applies to the values at the end of each realization. However, by defining Capture Times, you can carry out the analysis at any specified time. If you have created Capture Times, an additional drop-list is added to the display window to allow you to select the set of data (i.e., the values at the specified Capture Time) that you would like to analyze.

Note: The sensitivity analyses presented here are statistical measures computed by analyzing multiple realizations of the model in which all of the Stochastic variables are simultaneously sampled each realization. GoldSim also provides a second type of sensitivity analysis in which you can vary one variable at a time, while holding all other variables constant.

Note: If you need to carry out more advanced sensitivity analyses, you can do so by exporting all results and using a third party analysis tool.