### Abstract

The construction of dominance hierarchies for animal societies is an important aspect of understanding the nature of social relationships, and the models to calculate dominance ranks are many. However, choosing the appropriate model for a given data set may appear daunting to the average behaviourist, especially when many of these models assume linearity of dominance. Here, we present a method to test whether or not a data set fits the assumption of linearity using the Bradley-Terry model as a representative of the class of models that assume linearity. Our method uses the geometry of a posterior distribution of possible rankings given the data by using a random walk on this distribution. This test is intuitive, efficient, particularly for large number of individuals, and represents an improvement over previous linearity tests because it takes into account all information (i.e. both linear and apparently circular or nonlinear information) from the data with few restrictions due to high dimensionality. Such a test is not only useful in determining whether a linear hierarchy is relevant to a given animal society, but is necessary in justifying the results of any analysis for which the assumption of linearity is made, such as the Bradley-Terry model. If the assumption of linearity is not met, other methods for ranking, such as the beta random field method proposed by Fushing et al. (2011, PLoS One, 6, e17817) should be considered.

Original language | English (US) |
---|---|

Pages (from-to) | 1523-1531 |

Number of pages | 9 |

Journal | Animal Behaviour |

Volume | 84 |

Issue number | 6 |

DOIs | |

State | Published - Dec 2012 |

### Fingerprint

### Keywords

- Bradley-Terry
- Goodness of fit
- Linearity
- Paired comparisons
- Ranking
- Rhesus macaque

### ASJC Scopus subject areas

- Animal Science and Zoology
- Ecology, Evolution, Behavior and Systematics

### Cite this

**Using Markov chain Monte Carlo (MCMC) to visualize and test the linearity assumption of the Bradley-Terry class of models.** / Shev, Aaron; Hsieh, Fushing; Beisner, Brianne; Mccowan, Brenda.

Research output: Contribution to journal › Article

*Animal Behaviour*, vol. 84, no. 6, pp. 1523-1531. https://doi.org/10.1016/j.anbehav.2012.09.026

}

TY - JOUR

T1 - Using Markov chain Monte Carlo (MCMC) to visualize and test the linearity assumption of the Bradley-Terry class of models

AU - Shev, Aaron

AU - Hsieh, Fushing

AU - Beisner, Brianne

AU - Mccowan, Brenda

PY - 2012/12

Y1 - 2012/12

N2 - The construction of dominance hierarchies for animal societies is an important aspect of understanding the nature of social relationships, and the models to calculate dominance ranks are many. However, choosing the appropriate model for a given data set may appear daunting to the average behaviourist, especially when many of these models assume linearity of dominance. Here, we present a method to test whether or not a data set fits the assumption of linearity using the Bradley-Terry model as a representative of the class of models that assume linearity. Our method uses the geometry of a posterior distribution of possible rankings given the data by using a random walk on this distribution. This test is intuitive, efficient, particularly for large number of individuals, and represents an improvement over previous linearity tests because it takes into account all information (i.e. both linear and apparently circular or nonlinear information) from the data with few restrictions due to high dimensionality. Such a test is not only useful in determining whether a linear hierarchy is relevant to a given animal society, but is necessary in justifying the results of any analysis for which the assumption of linearity is made, such as the Bradley-Terry model. If the assumption of linearity is not met, other methods for ranking, such as the beta random field method proposed by Fushing et al. (2011, PLoS One, 6, e17817) should be considered.

AB - The construction of dominance hierarchies for animal societies is an important aspect of understanding the nature of social relationships, and the models to calculate dominance ranks are many. However, choosing the appropriate model for a given data set may appear daunting to the average behaviourist, especially when many of these models assume linearity of dominance. Here, we present a method to test whether or not a data set fits the assumption of linearity using the Bradley-Terry model as a representative of the class of models that assume linearity. Our method uses the geometry of a posterior distribution of possible rankings given the data by using a random walk on this distribution. This test is intuitive, efficient, particularly for large number of individuals, and represents an improvement over previous linearity tests because it takes into account all information (i.e. both linear and apparently circular or nonlinear information) from the data with few restrictions due to high dimensionality. Such a test is not only useful in determining whether a linear hierarchy is relevant to a given animal society, but is necessary in justifying the results of any analysis for which the assumption of linearity is made, such as the Bradley-Terry model. If the assumption of linearity is not met, other methods for ranking, such as the beta random field method proposed by Fushing et al. (2011, PLoS One, 6, e17817) should be considered.

KW - Bradley-Terry

KW - Goodness of fit

KW - Linearity

KW - Paired comparisons

KW - Ranking

KW - Rhesus macaque

UR - http://www.scopus.com/inward/record.url?scp=84870469827&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84870469827&partnerID=8YFLogxK

U2 - 10.1016/j.anbehav.2012.09.026

DO - 10.1016/j.anbehav.2012.09.026

M3 - Article

AN - SCOPUS:84870469827

VL - 84

SP - 1523

EP - 1531

JO - Animal Behaviour

JF - Animal Behaviour

SN - 0003-3472

IS - 6

ER -