DC_static_parameters_estimation.R

#_______________________________________________________________________________         
#   About: parameters estimation for Dixon-Coles model (static version)
#          Coefficients have a "named-list" structure
#          - Attack      --> DC_static_parameters$att
#          - Defence     --> DC_static_parameters$def
#          - Home effect --> DC_static_parameters$home
#          - Dep. effect --> DC_static_parameters$rho
#_______________________________________________________________________________          

#-------------------------------------------------------------------------------
# Import data, functions and libraries
serieA_2122<- read.csv("data/serieA_21-22.csv")
teams <- names(table(serieA_2122[,"HomeTeam"]))

source("functions/DC_relist_params.R")
source("functions/DC_tau.R")
source("functions/loglike/DC_static_loglike.R")

library(dplyr) # needed for the function "DC_relist_params()" and to use %>%
#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------
#Parameters estimation

#Initial guess
parameters_guess <- list(
    att = rep(0, length(teams)-1) %>% `names<-`(teams[2:length(teams)]),
    def = rep(0, length(teams)-1) %>% `names<-`(teams[2:length(teams)]),
    home = 2,
    rho = 0)
# Notice that the number of parameters is 2n instead of 2n+2 because of the sum-to-zero costraints
# The function "DC_relist_params()" will manage this

# Optim preferences
user_dots <- list(maxit = 100,
                  method = "BFGS",
                  interval = "profile",
                  hessian = TRUE)

# Optimal parameters estimation
DC_static_opt= optim(par = unlist(parameters_guess),
                            fn = DC_static_loglike,
                            data=serieA_2122,
                            method = user_dots$method,
                            hessian = user_dots$hessian,
                            control = list(maxit = user_dots$maxit))
#-------------------------------------------------------------------------------
# Get parameters and hessian
#-------------------------------------------------------------------------------
# Remember to relist parameters
DC_static_parameters<-DC_relist_params(DC_static_opt$par)
# Hessian
DC_static_hessian<- DC_static_opt$hessian
#-------------------------------------------------------------------------------

#-------------------------------------------------------------------------------
# Save/load parameters
save(DC_static_parameters, file = "parameters/DC_static_parameters.RData")
save(DC_static_hessian, file="parameters/hessian/DC_static_hessian.RData")
#-------------------------------------------------------------------------------