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## Fits the Bradley-Terry Model to Potentially Large and Sparse Networks of Comparison Data

Facilities are provided for fitting the simple, unstructured Bradley-Terry model to networks of binary comparisons. The implemented methods are designed to scale well to large, potentially sparse, networks. A fairly high degree of scalability is achieved through the use of EM and MM algorithms, which are relatively undemanding in terms of memory usage (relative to some other commonly used methods such as iterative weighted least squares, for example). Both maximum likelihood and Bayesian MAP estimation methods are implemented. The package provides various standard methods for a newly defined 'btfit' model class, such as the extraction and summarisation of model parameters and the simulation of new datasets from a fitted model. Tools are also provided for reshaping data into the newly defined "btdata" class, and for analysing the comparison network, prior to fitting the Bradley-Terry model. This package complements, rather than replaces, the existing 'BradleyTerry2' package. (BradleyTerry2 has rather different aims, which are mainly the specification and fitting of "structured" Bradley-Terry models in which the strength parameters depend on covariates.)

 Name Description btdata Create a btdata object btfit Fits the Bradley-Terry model codes_to_counts Converts data frame with a code for wins to counts of wins coef.btfit Extract coefficients of a 'btfit' object btprob Calculates Bradley-Terry probabilities citations Statistics Journal Citation Data from Stigler (1994) fitted.btfit Fitted Method for "btfit" select_components Subset a btdata object BT_EM Fit the Bradley-Terry model using the EM or MM algorithm BradleyTerryScalable A package for fitting the Bradley-Terry model to (potentially) large and sparse data sets. toy_data A toy data set for the BradleyTerryScalable package vcov.btfit Calculate variance-covariance matrix for a btfit object simulate_BT This function simulates one or more pseudo-random datasets from a specified Bradley-Terry model. Counts are simulated from independent binomial distributions, with the binomial probabilities and totals specified through the function arguments. summary.btfit Summarizing Bradley-Terry Fits No Results!