The short answer is that our headline odds ratio (OR) on the number of meat-free meals was pretty close to one associated with your random choice example. But the absolute increase in meat-free meal selections arising from an extra veg option (around 12pp) was lower than in the random choice example (20pp). That inconsistency reflects the high number of meat-free meal selections made by participants in the study even when there were only two meat-free options.
Detail
In the random selection example you provided (meat-free selections increasing from 40% to 60%), the OR would be 2.25:
That’s just below our estimate for the OR (2.33) on the additional meat-free meal coefficient, but well within the 90% CI (1.81 to 2.99).
When interpreting results presented in odds ratio space, its important to bear in mind that odds ratios don’t translate linearly into pp changes—the starting odds/probability matters. An OR of 2.25 is associated with a 20pp increase for a baseline probability of 40%, but only a 10pp increase for a baseline probability of 80%.
The last column of Table 10 in the full write-up on the RP website provides the results of a linear regression model, which is easier to interpret in probability space. That model suggests 56% of meal selections were meat-free in a theoretical menu containing two (non-analogue) meat-free options, and three (red) meat-based dishes. Adding an additional (non-analogue) meat-free option would increase meat-free meal selection by 12pp (90% CI: 0.08 to 0.16). That’s quite a bit lower than the absolute increase in your random selection example (20pp).
So even though the results in odds ratio results were similar to one that might be expected under random selection, the absolute increase in number of meat-free meal selections was quite a bit lower. That inconsistency arises because participants in the study were opting for a high number of meat-free meals even when there were only two meat-free options.
Thanks! Would interpreting this as “here was a group of people who, on average, preferred non-meat options, so giving them more non-meat options decreased how much meat they ate” be right?
I don’t think I would agree with that as a general explanation of the results.… in order for us to get the results we did, you’d need some people who were selecting meat when there two veg options to select meat-free when there are three veg options. The folks who always selected a meat-free dish (around 20% of respondents) don’t drive variation in meat-free meal selection across different menu types, and so can’t explain our results. Same applies to those who always selected meat-based dishes. Indeed the regression results on menu characteristics were identical when we excluded those respondents (see Table 10 of full-writeup).
But I think your quote above might be able to explain why the pp change in meat dishes chosen is lower than the change of menu options. Would probably make a few changes though (completeness at the expense of brevity).
“When offered more non-meat menu options (20pp increase), survey respondents selected fewer meat-based dishes (12pp decrease). Respondents, on average, selected a relatively low share of meat-based meals across the experiment. This is one reason why the fall in the share of meat-dishes is smaller than the change in the share of menu options.”
Thanks for the question @Jeff Kaufman .
The short answer is that our headline odds ratio (OR) on the number of meat-free meals was pretty close to one associated with your random choice example. But the absolute increase in meat-free meal selections arising from an extra veg option (around 12pp) was lower than in the random choice example (20pp). That inconsistency reflects the high number of meat-free meal selections made by participants in the study even when there were only two meat-free options.
Detail
In the random selection example you provided (meat-free selections increasing from 40% to 60%), the OR would be 2.25:
Odds Ratio=Odds_afterOdds_before=60%/40%40%/60%=2.25
That’s just below our estimate for the OR (2.33) on the additional meat-free meal coefficient, but well within the 90% CI (1.81 to 2.99).
When interpreting results presented in odds ratio space, its important to bear in mind that odds ratios don’t translate linearly into pp changes—the starting odds/probability matters. An OR of 2.25 is associated with a 20pp increase for a baseline probability of 40%, but only a 10pp increase for a baseline probability of 80%.
The last column of Table 10 in the full write-up on the RP website provides the results of a linear regression model, which is easier to interpret in probability space. That model suggests 56% of meal selections were meat-free in a theoretical menu containing two (non-analogue) meat-free options, and three (red) meat-based dishes. Adding an additional (non-analogue) meat-free option would increase meat-free meal selection by 12pp (90% CI: 0.08 to 0.16). That’s quite a bit lower than the absolute increase in your random selection example (20pp).
So even though the results in odds ratio results were similar to one that might be expected under random selection, the absolute increase in number of meat-free meal selections was quite a bit lower. That inconsistency arises because participants in the study were opting for a high number of meat-free meals even when there were only two meat-free options.
Thanks! Would interpreting this as “here was a group of people who, on average, preferred non-meat options, so giving them more non-meat options decreased how much meat they ate” be right?
I don’t think I would agree with that as a general explanation of the results.… in order for us to get the results we did, you’d need some people who were selecting meat when there two veg options to select meat-free when there are three veg options. The folks who always selected a meat-free dish (around 20% of respondents) don’t drive variation in meat-free meal selection across different menu types, and so can’t explain our results. Same applies to those who always selected meat-based dishes. Indeed the regression results on menu characteristics were identical when we excluded those respondents (see Table 10 of full-writeup).
But I think your quote above might be able to explain why the pp change in meat dishes chosen is lower than the change of menu options. Would probably make a few changes though (completeness at the expense of brevity).
“When offered more non-meat menu options (20pp increase), survey respondents selected fewer meat-based dishes (12pp decrease). Respondents, on average, selected a relatively low share of meat-based meals across the experiment. This is one reason why the fall in the share of meat-dishes is smaller than the change in the share of menu options.”