Questions tagged [bradley-terry-model]
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.
45
questions
2
votes
1
answer
104
views
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, ...
- 33
0
votes
0
answers
27
views
Efficient sampling of tournament match-ups for Bradley-Terry modeling
I am training an AI to learn to play a game through reinforcement learning. The procedure has produced a set of $N$ agents: $A_1, A_2, \ldots A_N$. I wish to estimate a skill rating $\beta_i$ for each ...
- 753
1
vote
0
answers
35
views
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 ...
- 31
3
votes
0
answers
44
views
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 ...
- 131
0
votes
2
answers
122
views
What would be the statistically relevant patterns among $25, 18, 15, 12, 10, 8, 6, 4, 2, 1, =101{\it ?}$
Here is the current Formula One World Championship points scoring systems—
Currently in Formula 1, there is a lot of talk about this and whether it is adequate or if it should be changed.
$$\begin{...
user354475
1
vote
0
answers
98
views
How to incorporate score margins into the Weng-Lin ranking models?
I'm trying to figure out how to incorporate this formula from this paper into the Weng-Lin update rule algorithms:
\begin{align}
\mathcal{P}[i \text{ beats } j] &= \frac{\exp{\lambda_i}}{\exp{\...
- 33
1
vote
1
answer
62
views
What is the first argument in BradleyTerry2 BTm function when data is in two columns?
I have a data frame with two columns. The first column contains the name of an object that won a contest with another object, and the second one contains the name of the loser. I want to fit the ...
- 113
2
votes
1
answer
121
views
Opposing effects in LME4 formulae (Bradley-Terry model)
Suppose I'm modelling a two-player game, and I want to estimate the probability $p$ of the first player winning, given the players involved. I want to do this using the formula $$p_{ij} = \textrm{...
- 1,085
2
votes
0
answers
54
views
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 ...
- 83
3
votes
0
answers
136
views
When should one use Bradley-Terry instead of gradient boosted trees for pairwise ranking
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 ...
- 173
3
votes
0
answers
62
views
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 ...
- 83
1
vote
0
answers
93
views
Likelihood Formulation of a Time Dynamic Bradley Terry Model with Random Effects
Let us assume a mixed logit model with a binary dependent variable $y_{i, t } $ that is explained by a fixed effect matrix X and a simple random intercept for each individual $i$
$y_{i,t}^* = x_{i,t}'...
- 523
3
votes
1
answer
1k
views
Weighted Pairwise Comparison With Table-like Heterogeneous Data - Is Bradley-Terry Model The Right Choice?
I came across this library Choix. I want to do Pairwise Comparison on data that looks like this to output a ranking from best to worst.
Let's call this X:
...
- 335
3
votes
0
answers
75
views
Why is model unidentifiability a problem?
I am new to the concept of model identifiability, but from my understanding it is possible to learn the true parameter values of the model after obtaining an infinite number of observations from it. ...
- 151
5
votes
1
answer
452
views
Inference on and quasi variances in Bradley-Terry-models
Upfront
I am not a statistician but a medical doctor. I have a working knowledge of statistical methods in my field, but this is my first time with pairwise comparisons and due to a lack of formal ...
- 8,305
1
vote
0
answers
63
views
4
votes
2
answers
594
views
logistic regression for competitive games
I am interested in using logistic regression to model a competitive game.
The data looks something like this:
...
- 438
2
votes
0
answers
170
views
Estimating probability of winning for each player based on ranking data of previous tournaments
The question could also be: "estimating the true ability of each player", though I think that already implies some assumptions.
In this paper I saw some references to Rankade and TrueSkill used by ...
- 720
3
votes
0
answers
1k
views
Statistical Analysis of Multiple Paired Preference Tests
I have four different methods 'A', 'B', 'C' and 'D' for generating synthetic videos, and I have crowdsourced 6 paired preference tests, one for each combination, where respondents were presented with ...
- 141
4
votes
1
answer
461
views
Decision tree: What is the most important next feature?
Summary: A decision tree (aka identification tree) is trained on a training set with a largish number of features (tens) and a large number of classes (thousands+). It turns out that every feature is ...
- 253
0
votes
1
answer
772
views
Correct standard error and p-values for Bradley-Terry model applied to ranking data ("rank-breaking")
One way to analyze ranking data is to use the Bradley-Terry data by converting ranks to pairwise comparisons (e.g. a>b>c becomes a>b, b>c, a>c) This is called "rank-breaking" in the machine learning ...
1
vote
1
answer
396
views
Paired Comparison Testing for Best Color
Suppose I have a set of 5 colors and 3 judges whose job is to choose their favorite color in the set. Each judge will be shown a screen with 2/5 colors and then another new pair of colors from the set ...
- 504
2
votes
1
answer
250
views
How to find the Fisher information matrix for a Bradley-Terry model
I'm using a Bradley-Terry model to rank items based on pairwise comparisons. The model estimates a score for each item $p_i = e^{\beta_i}$. I want to get an idea of the uncertainty of each items score....
- 21
5
votes
0
answers
229
views
Bradley-Terry model for unequal team comparisons
I'm trying to predict the outcome of a sports match between two teams. I have data on wins and losses for all teams in the league. I intend to use a Bradley-Terry model to find the relative rankings ...
- 4,657
2
votes
0
answers
115
views
How to adjust ratings of N items by pairwise comparisons
I have been keeping a list of movies I've seen in a spreadsheet and assigning them numerical rankings that approximate how I feel about them. A few years ago I implemented a program to read in the ...
- 1,237
1
vote
1
answer
254
views
What is the argument for running maximum likelihood estimation on Bradley-Terry models?
I have thought about estimating ratings for teams in a sport competition under the BT probability model. Some of the following may lack rigor, or possibly be sloppy, but I hope the key idea gets ...
3
votes
1
answer
693
views
Pairwise comparison with Bradley-Terry
I am performing a pairwise comparison test for the perceived weight of objects. I want to estimate the difference between each pair, say, A - B. I suspect that the underlying distributions of A, and B,...
- 33
4
votes
1
answer
145
views
I have 12 items to get into a single rank order. Can I get this from having a few hundred people see a set of 10 of the possible pairs of items?
I attempted to run a study where people had to rank order 12 statements from best to worst. However, it was extremely messy and difficult for people to rank that many items. Now, my professor and I ...
- 61
0
votes
1
answer
60
views
Approaches to predict probability of "game result"
Sorry for undetermined terms, I just never got familiar with this type of tasks.
Suppose I have a dataset with $M$ results of games between $N$ teams ($M \ge N$). Like
...
1
vote
0
answers
386
views
Logistic regression for paired comparisons
I am not a statistician; I'm an engineer, so much of this is a foreign language to me, though it seems like it wouldn't be that hard to understand if explained in a different way.
I am trying to ...
- 585
2
votes
2
answers
537
views
Predictive Models for the Soccer World Cup 2014
The Goldman Sachs model was already discussed here. I wonder whether there are other statistical forecasts publicly available, or even better, models including raw data. Specifically, I thought that ...
- 2,275
8
votes
1
answer
5k
views
How to calculate ratings/rankings from Paired comparison / Pairwise comparison of large data-sets?
As part of my graduate thesis (area: psychology) I have gathered preference data. The data includes approximately 50000 heads-up comparison between elementX and elementX. I have a total of 15 elements....
- 81
5
votes
0
answers
173
views
How many comparisons do I need to rank using Bradley-Terry?
I have recently learned about a method for ranking items based on comparisons called the Bradley-Terry method. I am using it to rank about 500 items.
I am wondering how many comparisons do I need to ...
- 933
14
votes
2
answers
698
views
Converting a list of partial rankings into a global ranking
I'm working on something like the following problem. I have a bunch of users and N books. Each user creates an ordered ranking of all the books he's read (which is likely a subset of the N books), e.g....
- 9,560
1
vote
0
answers
2k
views
How to test the accuracy of a predictive model?
I am trying to find the best way to test the accuracy of a predictive model for the outcome of a game between two random teams. The model presents a chance for each game that team A will win (win ...
- 11
9
votes
1
answer
588
views
How do I get a group of people to collectively rank a set of objects?
I work for an organization that oversees around 180 schools across the country. We regularly collect outcome data from these schools and rank them. I have been asked to do a survey of the national ...
- 191
3
votes
1
answer
2k
views
How to set up data for Bradley-Terry model in R? [closed]
I am trying to use the package BradleyTerry2 in R to assess sports teams. I am using the paper "Bradley-Terry Models in R: The BradleyTerry2 Package" written by Turner and Firth to guide me. I have ...
- 33
-1
votes
1
answer
1k
views
Bradley-Terry models by using R? [closed]
I want your help to Apply the Bradley-Terry models on any particular sport or any other idea of an application by using R. I am not familiar with R, can anyone help me ?
19
votes
4
answers
6k
views
How to get started with rating and ranking based on pairwise competition data?
I'm interesting in learning about how to rate and rank individuals in a group who only interact/compete in a pairwise fashion (i.e., systems like the ELO rating system for chess).
Are there are any ...
- 2,732
9
votes
1
answer
4k
views
How to fit Bradley–Terry–Luce model in R, without complicated formula?
The Bradley–Terry–Luce(BTL) model states that $p_{ji} = logit^{-1}(\delta_j - \delta_i)$, where $p_{ij}$ is the probability that object $j$ is judged to be "better", heavier, etc, than object $i$, ...
- 213
2
votes
2
answers
222
views
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 ...
- 1,703
19
votes
4
answers
3k
views
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 ...
- 191
8
votes
1
answer
658
views
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 ...
- 1,632
8
votes
1
answer
298
views
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
...
- 1,392
3
votes
3
answers
2k
views
Is there a SoftMax distribution with confidence parameters?
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 ...
- 1,392