flatlizards {BradleyTerry2}

Augrabies Male Flat Lizards: Contest Results and Predictor Variables

Description

Data collected at Augrabies Falls National Park (South Africa) in September-October 2002, on the contest performance and background attributes of 77 male flat lizards (Platysaurus broadleyi). The results of exactly 100 contests were recorded, along with various measurements made on each lizard. Full details of the study are in Whiting et al. (2006).

Usage

flatlizards

Format

This dataset is a list containing two data frames: flatlizards$contests and flatlizards$predictors.

The flatlizards$contests data frame has 100 observations on the following 2 variables:

winner

a factor with 77 levels lizard003 ... lizard189.

loser

a factor with the same 77 levels lizard003 ... lizard189.

The flatlizards$predictors data frame has 77 observations (one for each of the 77 lizards) on the following 18 variables:

id

factor with 77 levels (3 5 6 ... 189), the lizard identifiers.

throat.PC1

numeric, the first principal component of the throat spectrum.

throat.PC2

numeric, the second principal component of the throat spectrum.

throat.PC3

numeric, the third principal component of the throat spectrum.

frontleg.PC1

numeric, the first principal component of the front-leg spectrum.

frontleg.PC2

numeric, the second principal component of the front-leg spectrum.

frontleg.PC3

numeric, the third principal component of the front-leg spectrum.

badge.PC1

numeric, the first principal component of the ventral colour patch spectrum.

badge.PC2

numeric, the second principal component of the ventral colour patch spectrum.

badge.PC3

numeric, the third principal component of the ventral colour patch spectrum.

badge.size

numeric, a measure of the area of the ventral colour patch.

testosterone

numeric, a measure of blood testosterone concentration.

SVL

numeric, the snout-vent length of the lizard.

head.length

numeric, head length.

head.width

numeric, head width.

head.height

numeric, head height.

condition

numeric, a measure of body condition.

repro.tactic

a factor indicating reproductive tactic; levels are resident and floater.

Details

There were no duplicate contests (no pair of lizards was seen fighting more than once), and there were no tied contests (the result of each contest was clear).

The variables head.length, head.width, head.height and condition were all computed as residuals (of directly measured head length, head width, head height and body mass index, respectively) from simple least-squares regressions on SVL.

Values of some predictors are missing (NA) for some lizards, ‘at random’, because of instrument problems unconnected with the value of the measurement being made.

Source

The data were collected by Dr Martin Whiting, http://whitinglab.com/people/martin-whiting/, and they appear here with his kind permission.

References

Turner, H. and Firth, D. (2012) Bradley-Terry models in R: The BradleyTerry2 package. Journal of Statistical Software, 48(9), 1–21.

Whiting, M. J., Stuart-Fox, D. M., O'Connor, D., Firth, D., Bennett, N. C. and Blomberg, S. P. (2006). Ultraviolet signals ultra-aggression in a lizard. Animal Behaviour 72, 353–363.

See Also

BTm()

Examples

##
##  Fit the standard Bradley-Terry model, using the bias-reduced
##  maximum likelihood method:
##
result <- rep(1, nrow(flatlizards$contests))
BTmodel <- BTm(result, winner, loser, br = TRUE, data = flatlizards$contests)
summary(BTmodel)
##
##  That's fairly useless, though, because of the rather small
##  amount of data on each lizard.  And really the scientific
##  interest is not in the abilities of these particular 77
##  lizards, but in the relationship between ability and the
##  measured predictor variables.
##
##  So next fit (by maximum likelihood) a "structured" B-T model in
##  which abilities are determined by a linear predictor.
##
##  This reproduces results reported in Table 1 of Whiting et al. (2006):
##
Whiting.model <- BTm(result, winner, loser, 
                     ~ throat.PC1[..] + throat.PC3[..] +
                         head.length[..] + SVL[..],
                     data = flatlizards)
summary(Whiting.model)
##
##  Equivalently, fit the same model using glmmPQL:
##
Whiting.model <- BTm(result, winner, loser,
                     ~ throat.PC1[..] + throat.PC3[..] +
                         head.length[..] + SVL[..] + (1|..), 
                     sigma = 0, sigma.fixed = TRUE, data = flatlizards)
summary(Whiting.model)
##
##  But that analysis assumes that the linear predictor formula for
##  abilities is _perfect_, i.e., that there is no error in the linear
##  predictor.  This will always be unrealistic.
##
##  So now fit the same predictor but with a normally distributed error
##  term --- a generalized linear mixed model --- by using the BTm
##  function instead of glm.
##
Whiting.model2 <- BTm(result, winner, loser,
                      ~ throat.PC1[..] + throat.PC3[..] +
                          head.length[..] + SVL[..] + (1|..), 
                      data = flatlizards, trace = TRUE)
summary(Whiting.model2)
##
##  The estimated coefficients (of throat.PC1, throat.PC3,
##  head.length and SVL are not changed substantially by
##  the recognition of an error term in the model; but the estimated
##  standard errors are larger, as expected.  The main conclusions from
##  Whiting et al. (2006) are unaffected.
##
##  With the normally distributed random error included, it is perhaps
##  at least as natural to use probit rather than logit as the link
##  function:
##
require(stats)
Whiting.model3 <- BTm(result, winner, loser, 
                      ~ throat.PC1[..] + throat.PC3[..] +
                          head.length[..] + SVL[..] + (1|..),
                      family = binomial(link = "probit"),
                      data = flatlizards, trace = TRUE)
summary(Whiting.model3)
BTabilities(Whiting.model3)
##  Note the "separate" attribute here, identifying two lizards with
##  missing values of at least one predictor variable 
##
##  Modulo the usual scale change between logit and probit, the results
##  are (as expected) very similar to Whiting.model2.