How does one correctly interpret the population-level effect estimate for a monotonic (ordinal categorical) predictor variable.
For example, in the relevant vignette on the topic the simplex parameters are interpreted (as % of total effect) but I don’t see any interpretation for the aforementioned estimate…
I could see it as either the effect of going from level 0 to level n for a monotonic predictor with n levels ~or~ the average effect of going from any level to the next from 1, 2, …, n-1, to n. But I’m really just speculating…
The population-level estimate b of a monotonic effect indicates the response difference between the maximum and minimum category. See also https://psyarxiv.com/9qkhj
In that case…the intercept is the log-odds for the minimum category for each ordinal predictor + zero values for any continuous predictors + reference value for any nominal, categorical predictors?
Hey, thank you… but I still don’t “see” it.
I will consider the vignette (I know you gave a paper, but the vignette is simpler, should also be simpler to understand what is what).
I understand that the simplex parameters are cumulative percentages of the effects. But there the range goes from 30 (which is about the intercept) to 75, but the estimate is around 16 only. I still don’t get it.
Thank you again for ALL your help.
Sorry, I my query was quite confusing.
Considering your Vignette " Estimating Monotonic Effects with brms",
The Intercept is 32, which is about the average of the first class. The maximum class average is close to 75, which would make the maximum difference around 40.
That would be then the maximum effect (in a model that is solely Intercept + mo(income)), the difference between minimum and maximum classes. However, the population-effect monicome = 14.
Even the difference between the minimum and the next class is close to 30, while the first simplex parameter is 0.63.
So I fail to interpret what this 14 represents.
Thank you for great package and great support!
I think now I understood, in practical terms:
Population-level parameter of the monotonic effect = Total effect / (# of categories - 1)
So in the first model of the Vignette, there are 4 categories of income, i.e. “baseline” + 3 categories.
The population-level effect average 14.29 means the total effect = 14.29*3 = 43 (approximately).
And if categories are represented as integer numbers, is not about the number of categories, per se, but the integer difference. By that I mean: if for any reason one has a variables with categories c(11,14,15), although there are 3 categories, as integer variable brms will take the full range of 5 categories (11,12,13,14,15), and the population-level effect = (effect[5] - effect[1])/4
Have I understood now?
just double-checking since this response is marked as the solution (I think @guisamor made the same point below): according to Figure 1 in your paper (Buerkner & Charpentier, 2019, https://psyarxiv.com/9qkhj), the response difference between the maximum and minimum category is b * D (number of categories - 1), isn’t it?
If so, the population-level estimate b would indicate the response difference between the maximum and minimum category divided by D (the number of categories - 1), correct?
@tiflo this is a helpful/clear way of describing it. Interested to know if it is correct. That also means the population level estimate is essentially the average of each step difference along the ordinal predictor, right?