Compute a Colley matrix model for a matchup.

elo.colley(
formula,
data,
family = "binomial",
weights,
na.action,
subset,
k = 1,
...,
running = FALSE,
skip = 0
)

## Arguments

formula A formula. See the help page for formulas for details. A data.frame in which to look for objects in formula. Arguments passed to glm. A vector of weights. Note that these weights are used in the Colley matrix creation, but not the regression. A function which indicates what should happen when the data contain NAs. An optional vector specifying a subset of observations. The fraction of a win to be assigned to the winning team. See "details". Arguments passed to glm. Logical, denoting whether to calculate "running" projected probabilities. If true, a model is fit for group 1 on its own to predict group 2, then groups 1 and 2 to predict 3, then groups 1 through 3 to predict 4, etc. Groups are determined in formula. Omitting a group term re-runs a glm model to predict each observation (a potentially time-consuming operation!) Integer, denoting how many groups to skip before fitting the running models. This is helpful if groups are small, where glm would have trouble converging for the first few groups. The predicted values are then set to 0.5 for the skipped groups.

## Details

See the vignette for details on this method. The differences in assigned scores (from the coefficients of the Colley matrix regression) are fed into a logistic regression model to predict wins or (usually) a linear model to predict margin of victory. In this setting, 'k' indicates the fraction of a win to be assigned to the winning team (and the fraction of a loss to be assigned to the losing team); setting k = 1 (the default) emits the "Bias Free" ranking method presented by Colley. It is also possible to adjust the regression by setting the second argument of adjust(). As in elo.glm, the intercept represents the home-field advantage. Neutral fields can be indicated using the neutral() function, which sets the intercept to 0.

## References

Colley W.N. Colley's Bias Free College Football Ranking Method: The Colley Matrix Explained. 2002.

glm, summary.elo.colley, score, mov, elo.model.frame
elo.colley(score(points.Home, points.Visitor) ~ team.Home + team.Visitor, data = tournament,