Home / Monte Carlo / Analyzing the Model / Percent Contribution / Options
Percent Contribution Options¶
Every control in the Percent Contribution dialog.
The methods¶
Every method starts ticked, except an LMG the model cannot run (below). Tick any combination. Each ticked method is one more simulation. At least one must be ticked:
Select at least one method.
The dialog carries a description beside each one, quoted here as it words them.
LMG Shapley Regression (Dominance Analysis)¶
Averages each input's marginal contribution to the explained variance over all possible orderings of the inputs, so the contributions sum exactly to the model R-Squared. LMG does not require the inputs to be independent; its attribution remains well-defined when inputs are correlated. LMG is the most computationally intensive method, and assumes the output is approximately a linear function of the inputs.
LMG has a limit of 15 declared inputs. Above that it is unavailable, and the dialog says so in words rather than only greying the box out:
LMG is not available for this model. It has 18 declared inputs and LMG allows at most 15, because it fits every combination of the inputs and the work doubles with each one added. The other two methods have no such limit.
Least Squares Regression Type I and III Sums of Squares¶
Type I (sequential) sums of squares attribute variance to each input in the order entered, each adjusted only for the inputs preceding it. Type III (partial) sums of squares attribute to each input only the variance it explains after adjusting for all other inputs. Both assume the output is approximately a linear function of the inputs.
Spearman's Method¶
Based on Spearman rank correlation. It does not assume a linear relationship between the inputs and the output, only a monotonic one, but it assumes the inputs are statistically independent.
Number of Simulations¶
One list per method, because each method is its own simulation and LMG stops at 10,000. A method's list is disabled while that method is unticked.
| Method | Offered | Starts at |
|---|---|---|
| LMG Shapley Regression (Dominance Analysis) | 1,000 / 2,000 / 5,000 / 10,000 | 10,000 |
| Least Squares Regression Type I and III Sums of Squares | 1,000 / 10,000 / 100,000 / 1,000,000 | 10,000 |
| Spearman's Method | 1,000 / 10,000 / 100,000 / 1,000,000 | 1,000,000 (100,000 on 32-bit Excel) |
The dialog notes what the number buys:
The sampling error of the Percent Contribution estimates decreases as the number of simulations increases, at the cost of run time. LMG is limited to 10,000 simulations because it fits every subset of the inputs.
On a 32-bit build of Excel the largest counts are removed, and the dialog says why:
This is a 32-bit build of Excel, so the largest run offered is ... simulations. A larger run needs more memory than a 32-bit process can hold while Excel is also loaded.
That message never affects the LMG list, which stops at 10,000 anyway.
Outputs¶
Tick the outputs to decompose. Every output starts ticked, and Select all and Unselect all tick or clear the whole list. One selection covers every method, because the same outputs are decomposed whichever method computes them. At least one is required:
Select at least one output to analyze.
Random seed¶
The Seed box starts at 0, and its hint reads:
Enter 0 for a clock-initialized random seed, or any positive integer for reproducible results. Every method uses the same seed.
An empty box counts as 0. When the seed is 0, one seed is picked from the clock and given to every
method, and the report prints it as Random Seed, so the run can be repeated by typing it in. Where
two methods use the same number of simulations, the shared seed means they are computed on identical
trials.
A negative number, or anything that is not a whole number, is refused:
The random seed must be 0 or a positive integer.
Buttons¶
Help opens the Percent Contribution help page. Cancel closes the dialog without running anything. OK runs the ticked methods; it is unavailable while one of the three refusals above (no method, no output, or a seed that is refused) is showing. The LMG and 32-bit messages do not block it.