goalmodel: Fitting models for goals
In opisthokonta/goalmodel: Prediction Models For Goals Scored

goalmodel

R Documentation

Fitting models for goals

Description

goalmodel is used to fit models of goals scored in sports competitions. At a minimum this function estimates 'attack' and 'defence' ratings for all teams, but other covariates can be included, as well as other adjustments. The underlying statistical model can be either a Poisson, Negative Binomial, or Gaussian model.

Usage

goalmodel(
  goals1,
  goals2,
  team1,
  team2,
  x1 = NULL,
  x2 = NULL,
  hfa = TRUE,
  dc = FALSE,
  rs = FALSE,
  hurdle = FALSE,
  fixed_params = NULL,
  weights = NULL,
  model = "poisson",
  optim_method = "BFGS"
)

Arguments

`goals1`	Numeric, non-negative integer. The number of goals scored by team 1.
`goals2`	Numeric, non-negative integer. The number of goals scored by team 2.
`team1`	Vector of team names.
`team2`	Vector of team names.
`x1`	Matrix of additional covariates associated with team 1.
`x2`	Matrix of additional covariates associated with team 2.
`hfa`	Logical (TRUE by default). Include a (home field) advantage for team 1.
`dc`	Logical (FALSE by default). If TRUE an adjustment for low scoring goals is included in the model.
`rs`	Logical (FALSE by default). If TRUE an adjustment for teams to over and under estimate the opponent.
`hurdle`	Logical (FALSE by default). If TRUE, 0-0 results will be modeled using a separate parameter (a hurdle model).
`fixed_params`	A list with parameters that should be kept constant while the other parameters are estimated from data.
`weights`	Numeric vector of weigths that determine the influence of each match on the final parameter estimates.
`model`	String indicating whether the goals follow a 'poisson' model (default), a Negative Binomial ('negbin'), Conway-Maxwell-Poisson ('cmp') or a Gaussian ('gaussian') model.
`optim_method`	String indicating which optimization method to use in case the model can't be fitted with gml.fit(). See `optim` for more details.

Details

Fixed parameters must be given as a list that is similar as the one returned from this function. See the 'value' section.

Value

A list of class 'goalmodel'. The list contains the following components:

parameters - A list of parameters.
loglikelihood - The value of the log-likelihood at the maximum.
npar_est - Number of parameters that has been estimated.
npar_fixed - Number of parameter that was fixed to a constant value during model fitting.
aic - Akaike's Information Criterium.
r_squared - A pseudo r-squared; The proportion of variability in the observed goals that the model explains.
all_teams - A character vector with the names of all the teams in the data.
ngames - Number of games in the data.
est_time - The time it took to fit the model.
model = A string indicating whether a Poisson or Negative Binomial model was used.
fixed_params - A list with the parameters that was kept constant during model fitting.
converged - Logical indicating if the model fitting converged.
maxgoal - The greatest number of goals seen in the data. Used by the prediction functions.
fitter - String indicating wether the model was fitted with the built-in glm.fit() function.

The parameters list contain both the fixed and estimated parameters. It contains the following compnents:

attack - A named mumeric of the attack parameters.
defense - A named mumeric of the attack parameters.
intercept - A length 1 numeric with the intercept.

The following parameter components are optional, and depends on what kind of model is fitted.

hfa - If hfa=TRUE, an unnamd length 1 numeric with the home field advantage.
rho - If dc=TRUE, an unnamd length 1 numeric with the Dixon-Coles adjustment.
gamma - If rs=TRUE, an unnamd length 1 numeric with the Rue-Salvesen adjustment.
beta - If additional covarites are used, this is a named mumeric of the regression coefficients.
dispersion - The dispersion parameter in the Negative Binomial model or the Conway-Maxwell-Poisson model.
sigma - The standard deviation in a Gaussian model.
hurdle - The hurdle parameter.