Qualtrics’ MaxDiff projects produce an output called “Preference Share”. It is defined as:
The Preference Share is a measurement of the distribution of preference that respondents have for the tested attributes of the maxdiff. The preference shares sum to 100 and can be understood as the likelihood that the attribute truly is the most preferred item.
My assumption is that Qualtrics is probably taking the “Average Feature Utility” it produces and passing it through a softmax function to converts the utilities into probabilities that sum to 1.
However, when I applied a softmax function (i.e., exp(Value)/sum(exp(Value)) ) to the Average Feature Utility values, they do not produce identical values to what Qualtrics produces. See below:
| Average Feature Utility | 1.87602 | 0.891439 | 1.004267 | 0.197074 | -0.65923 | -0.65549 | 0.068604 | -1.63446 | 0.47346 | -0.01903 | -0.08351 | -1.80165 | -2.01015 | 0.082374 | 2.715848 |
| Softmax of Average Feature Utility | 0.185307 | 0.06923 | 0.077499 | 0.034573 | 0.014684 | 0.014739 | 0.030405 | 0.005537 | 0.045579 | 0.027854 | 0.026114 | 0.004685 | 0.003803 | 0.030826 | 0.429165 |
| Qualtrics Preference Share | 0.113599 | 0.086067 | 0.055882 | 0.041274 | 0.025717 | 0.028783 | 0.050811 | 0.032024 | 0.038879 | 0.039782 | 0.028486 | 0.030358 | 0.026629 | 0.05372 | 0.34799 |
Does anyone have an explanation of how Qualtrics is estimating / deriving it’s Preference Shares and why they may deviate from what you see when passing Feature Utilities through a Softmax?