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.

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26 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{...
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GLM based on the Bradley–Terry model's probability

I have caluclated the Bradley–Terry probabilities for binary outcomes (around 2,000 cases are in my sample). I see that this probability is quite well distingushing the binary outcomes: Then I use ...
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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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Paired Comparisons and Ranked Lists

Here is a brief description of my experiment, to help you understand the data and question Individuals perform pairwise 2AFC (alternative forced choice) comparisons between two categories of items at ...
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39 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 ...
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33 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 ...
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39 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}'...
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1answer
159 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: ...
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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. ...
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1answer
266 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 ...
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458 views

logistic regression for competitive games

I am interested in using logistic regression to model a competitive game. The data looks something like this: ...
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149 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 ...
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790 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 ...
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1answer
346 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 ...
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1answer
401 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 ...
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1answer
240 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 ...
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1answer
131 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....
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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 ...
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99 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 ...
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1answer
172 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 ...
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1answer
470 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,...
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1answer
108 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 ...
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1answer
47 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 ...
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293 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 ...
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2answers
516 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 ...
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1answer
4k 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....
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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 ...
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489 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....
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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 ...
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1answer
217 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 ...
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1answer
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 ...
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1answer
917 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 ?
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4answers
5k 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 ...
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1answer
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 $i$, ...
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2answers
216 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 ...
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4answers
2k 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 ...
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1answer
529 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 ...
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1answer
278 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 ...
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3answers
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 ...