Log Likelihood Method
Now suppose we use the individual method to estimate the four PVL parameters from a single participant on the IGT task. On each of the 100 trials, we observe a choice of one of the four possible decks from this participant. If deck j was chosen on trial t, that is we observe Dj(t)=1, then according to the PVL model, the probability (likelihood) of observing this choice equals pj(t) computed using (4.1), (4.2a), (4.2b) and (4.3). The log likelihood contributed by that trial then equals LL(t)=ln[pj(t)] using the predicted probability for the observation Dj(t)=1. The log likelihood for the observed choice on each trial is computed in the same manner, and all these are summed across trials to produce the total log likelihood, which is a function of the parameter vector Φ=(α, β, γ, θ)