EloRating (version 0.46.18)

optimizek: optimize the k parameter

Description

optimize the k parameter

Usage

optimizek(
  eloobject,
  krange = c(2, 400),
  optimode = "loop",
  resolution = 100,
  itype = NULL,
  daterange = NULL,
  burnin = 0,
  doplot = FALSE,
  progbar = FALSE,
  ...
)

Value

a list with two items: (1) $best, a data frame with one line, in which the maximal log likelihood is returned alongside the one or several corresponding k values, and (2) $complete, a data frame with all the values tested and their log likelihoods

Arguments

eloobject

output from elo.seq or from fastelo

krange

either a vector of length 2, giving the range of k values to be tested, or a named list with vectors of length 2, in which each list item is named according to different interaction types (see the intensity= argument in elo.seq)

optimode

character, either "loop" or "optimize". See details.

resolution

numeric, the number of steps between the range of k values to be tested. Currently only a single value can be supplied here and in case krange is a list this value will be applied to all items in this list

itype

character or factor containing the different interaction types, which is only relevant if krange is a list. The content of itype and the names of krange have to match!

daterange

character or Date of length 2, provides a date range for optimization. Only relevant in case eloobject is the result of elo.seq()

burnin

numeric, the number of interactions to be excluded from the calculation of the (log) likelihood. This parameter is ignored if a date range is supplied. By default burnin = 0, i.e. all interactions are considered.

doplot

logical, should a plot be returned. Works only if optimode = "loop", and only if there are maximally two different interaction types

progbar

logical, should a progress bar be displayed, not yet implemented

...

additional arguments for the plot and text functions, e.g. for setting cex or lwd

Details

this function attempts to find the objectively best k parameter. This is done by a maximum likelihood approach in which the likelihood is represented by the individual winning probabilities. In a perfect situation, in each interaction the winner would have a winning probability of 1, whereas in the worst case, in each interaction the winner would have a winning probability of 0.

There are two major approaches to find the best k. One does it 'by hand', i.e. by means of a loop trying many different k values (specified by resolution), recalculating the ratings (and associated winning probabilities) and return the likelihood for each k value. The second approach uses the optimize function, but this is not yet implemented.

One thing to note is that you can use interaction-level k values, i.e. if you have interactions of different types (e.g. fights vs. displacements) you can try to find the optimal k for each interaction type. This is achieved in the ("loop" approach by trying different combinations of k values. Because of the combinatorial nature of this approach, the number of individual sequences to be fitted increases sharply with higher resolutions: if you have two different interaction types and use a resolution of 5, the function will need to run 25 (= 5 * 5) iterations. If you use a more reasonable resolution of 100 the number of iterations will be already 10000. Also note that in that case the actual plotting of the results might take a lot of time in such cases. Just try with low values first to see whether it works as expected and the potentially increase the resolution.

References

franz2015aEloRating

mcmahan1984EloRating

Examples

data(adv2)
res <- elo.seq(winner = adv2$winner, loser = adv2$loser, Date = adv2$Date)
optimizek(eloobject = res, krange = c(50, 400), resolution = 200, doplot = TRUE)$best

# with a burnin value set:
optimizek(eloobject = res, krange = c(50, 400), resolution = 200, burnin = 15, doplot = TRUE)$best

# using different interaction intensities
myks <- list(displace = 20, fight = 200)
res <- elo.seq(winner = adv2$winner, loser = adv2$loser, Date = adv2$Date,
               k = myks, intensity = adv2$intensity)
optimizek(eloobject = res, optimode = "loop",
          krange = list(fight = c(50, 600), displace = c(20, 200)),
          resolution = 100, itype = adv2$intensity, main = 'bla')$best