qvcalc.BTabilities {BradleyTerry2}  R Documentation 
Quasi Variances for Estimated Abilities
Description
A method for qvcalc::qvcalc()
to compute a set of quasi variances (and
corresponding quasi standard errors) for estimated abilities from a
BradleyTerry model as returned by BTabilities()
.
Usage
## S3 method for class 'BTabilities'
qvcalc(object, ...)
Arguments
object 
a 
... 
additional arguments, currently ignored. 
Details
For details of the method see Firth (2000), Firth (2003) or Firth and de Menezes (2004). Quasi variances generalize and improve the accuracy of “floating absolute risk” (Easton et al., 1991). This device for economical model summary was first suggested by Ridout (1989).
Ordinarily the quasi variances are positive and so their square roots (the quasi standard errors) exist and can be used in plots, etc.
Value
A list of class "qv"
, with components
covmat 
The full variancecovariance matrix for the estimated abilities. 
qvframe 
A data frame with variables 
dispersion 

relerrs 
Relative errors for approximating the standard errors of all simple contrasts. 
factorname 
The name of the ID factor identifying players in the 
coef.indices 

modelcall 
The call to 
Author(s)
David Firth
References
Easton, D. F, Peto, J. and Babiker, A. G. A. G. (1991) Floating absolute risk: an alternative to relative risk in survival and casecontrol analysis avoiding an arbitrary reference group. Statistics in Medicine 10, 1025–1035.
Firth, D. (2000) Quasivariances in XlispStat and on the web. Journal of Statistical Software 5.4, 1–13. https://www.jstatsoft.org/article/view/v005i04.
Firth, D. (2003) Overcoming the reference category problem in the presentation of statistical models. Sociological Methodology 33, 1–18.
Firth, D. and de Menezes, R. X. (2004) Quasivariances. Biometrika 91, 65–80.
Menezes, R. X. de (1999) More useful standard errors for group and factor effects in generalized linear models. D.Phil. Thesis, Department of Statistics, University of Oxford.
Ridout, M.S. (1989). Summarizing the results of fitting generalized linear models to data from designed experiments. In: Statistical Modelling: Proceedings of GLIM89 and the 4th International Workshop on Statistical Modelling held in Trento, Italy, July 17–21, 1989 (A. Decarli et al., eds.), pp 262–269. New York: Springer.
See Also
qvcalc::worstErrors()
, qvcalc::plot.qv()
.
Examples
example(baseball)
baseball.qv < qvcalc(BTabilities(baseballModel2))
print(baseball.qv)
plot(baseball.qv, xlab = "team",
levelNames = c("Bal", "Bos", "Cle", "Det", "Mil", "NY", "Tor"))