The Bradley-Terry model is regression type model that estimates the relative abilities of 'players' & predicts the probability player $i$ will beat player $j$ in a competition based on the outcomes of observed matches.

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### Design Matrix for a Bradley Terry Model

I am working on a problem using a Bradley Terry Model and was asked to derive the design matrix of for this model applied to some data, but I am not sure how to do this using this data. Are there any ...
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### What are the undefined constants and functions in Stern's 2011 paper?

I'm reading the 2011 paper on ranking called Moderated Paired Comparisons by Steven E. Stern and there are no definitions given for some of the constants and functions in equation 1. As you can see, ...
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### Bradley-Terry models in R with multiple batches of random effects?

I want to fit Bradley-Terry models in R looked into the BradleyTerry2 package. However, as they write in their vignettes: (Note that a random intercept is the only ...
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### asking humans to rank items

I have around 50 items and I need to ask human graders to rank them. Is there any good resource on how to design this crowd sourcing task? For example, it will be tiresome to ask humans to rank 50 ...
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### compare two bradley terry models

I have pairwise comparisons data that I converted into Bradley terry parameters. If I have BT parameters from two different occasions, what is the right way to test the null hypothesis that both ...
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Both the Bradley-Terry model and Gradient boosted trees can be used to learn a ranking from pairwise comparisons (e.g. with libraries choix and XGboost). How do they relate to each other? Is there ...
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### non-parametric circular statistics

I am working on a research question of color preference (which can be represented in a circular space). I have divided the circular space into 16 equally spaced bins and done a pairwise comparison ...
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### How to summarise the ordering pattern of a set of four stimuli by participants?

I did an experiment where I asked 13 participants to order 4 stimuli (let's call them stimulus A, B, C and D), so there are 24 possible ways to order 4 items. Now I would like to know how to analyze ...
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### Measuring individual player effectiveness in 2-player per team sports

I've got a spreadsheet of some team scores. First team to 10 points wins. There are 2 players on each team. The players play with different teammates all the time, although they are not chosen ...
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### Multinomial choice with binary observations

Is there a standard name for a multinomial choice model where the observations are in the form of binary questions such as "do you prefer A to B" and "do you prefer B to D"? This seems like a common ...
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### How to model pairwise preference with both strong and weak preferences?

I have large comparison data in form In a pairwise comparison data each data point compares two alternatives. For instance: A > B (A is preferred to B, A and B are classes, not numbers) A > B B > A ...
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This is a softmax probability distribution: $$P(i| w_1, w_2, \ldots, w_n) = \frac{exp(w_i)}{\sum_{i=1}^n exp(w_i)}.$$ It known also as Boltzmann distribution. It is used in generalized Bradley-Terry ...