The predicted variable is a categorical response, named
resp with ranges ‘1’, ‘2’, ‘3’, and ‘4’ (nominal labels,
not numerical values). The predictor is a categorical/nominal
variable named group, with ranges ‘A’ by means of ‘Okay’.
Discover these points of the info:
-
The proportion of response ‘2’ equals response ‘3’
inside every group, and throughout all teams.
Particularly, in each group, p(‘2’) = p(‘3’) = 0.25. -
The proportions of responses ‘1’ and ‘4’ are symmetric
reflections of one another, with p(‘1’|A) = p(‘4’|Okay), p(‘1’|B) =
p(‘4’|J), and so forth.
Due to the a number of teams, this can be a pure setting to attempt
a hierarchical mannequin that shares data throughout teams, and can
present shrinkage throughout teams. Due to the symmetry within the knowledge,
the hierarchical mannequin ought to symmetrically shrink the response ‘1’
proportions nearer to 0.25, and do the identical for the response ‘4’
proportions.
I name brm() with the same old hierarchical
method = resp | trials(n) ~ 1 + (1 | group).
We will get the posterior predictions and make a plot:
Discover these points of the posterior
predictions:
-
Opposite to the info, the proportion of response ‘2’ is
not the identical throughout teams, and the proportion of response ‘3’ is just not
the identical throughout teams. -
Opposite to the info, inside each group, p(‘1’) =
p(‘2’) = p(‘3’). -
Opposite to the info, the proportion of response ‘1’
doesn’t symmetrically mirror response ‘4’.
Within the full doc linked under, I clarify why this occurs and I suggest an answer. Has this drawback been identified earlier than? Has this resolution been proposed earlier than?
To see the complete description of the problem, click on the hyperlink under to obtain the HTML file. Then discover the downloaded HTML file in your laptop and double-click it to open it in your browser:
https://drive.google.com/uc?export=obtain&id=1z_hGTzkkIlMJ0Tk2ONCH96bZh10l0gMr
(In case you’re reluctant to click on a direct obtain hyperlink, you’ll find the HTML doc on the following hyperlink, after which manually obtain it https://drive.google.com/file/d/1z_hGTzkkIlMJ0Tk2ONCH96bZh10l0gMr/view?usp=drive_link.)
I’ve posted this on the Stan Boards, so if you’re on this subject it’s possible you’ll need to monitor the feedback there:
