Biased associative model with learning by elimination — uncfam

A variant of uncfam() (Kachergis et al. 2012's uncertainty- and familiarity-biased associative model) that adds inference by elimination (mutual exclusivity) to how a trial's associative weight is allocated. If the other words and objects on a trial are already confidently paired with each other, the remaining word and object probably go together, so their pairing should draw attention even though it is still weak. In uncfam(), by contrast, an already-strong pair on the trial draws weight away from such a pairing.

Usage

uncfam_elimination(X, B, C, eps)

Arguments

X: Associative weight to distribute
B: Weighting of uncertainty vs. familiarity
C: Decay
eps: Weight of elimination inference (0 = identical to uncfam())

Value

An object of class xslMod

Details

On each trial, each on-trial pair $(w', o')$ has a mutual confidence $q(w', o') = P(o'|w') P(w'|o')$, from the row- and column-normalized associations. A pair $(w, o)$ gets elimination support $s(w, o) = \sum_{w' \ne w, o' \ne o} q(w', o')$: how much of the rest of the trial is accounted for by other pairs. The share of the trial's weight $X$ given to $(w, o)$ is then $$\frac{b(w, o) + \epsilon s(w, o)}{1 + \epsilon \sum s}$$ where $b(w, o)$ is uncfam()'s normalized familiarity-and-uncertainty share, so eps = 0 reproduces uncfam() exactly.

Motivated by the initial-accuracy experiment (kachergis_initial_accuracy), where learners were more accurate on an initially mis-paired word the more of its study trials it shared with a word they already knew.

Examples

mod <- uncfam_elimination(X = .1, B = .98, C = 1, eps = 1)
xsl_run(mod, get_example_ambiguous_condition())
#> $fits
#> $fits[[1]]
#> $fits[[1]]$sims
#> NULL
#> 
#> $fits[[1]]$responses
#>           [,1]      [,2]      [,3]      [,4]
#> [1,] 0.3888889 0.3888889 0.3888889 0.3888889
#> 
#> $fits[[1]]$perf
#>         1         2         3         4 
#> 0.3888889 0.3888889 0.3888889 0.3888889 
#> 
#> $fits[[1]]$matrix
#>       1     2     3     4
#> 1 0.035 0.035 0.010 0.010
#> 2 0.035 0.035 0.010 0.010
#> 3 0.010 0.010 0.035 0.035
#> 4 0.010 0.010 0.035 0.035
#> 
#> $fits[[1]]$sse
#> [1] 0.04938272
#> 
#> $fits[[1]]$data
#> xslData object with label "example condition" and condition "ambiguous"
#>   training trials: 2
#>       test trials: 0
#>             words: 4
#>           objects: 4
#>        accuracies: 4
#> 
#> 
#> 
#> $sse
#> [1] 0.04938272
#> 
#> $unweighted_sse
#> [1] 0.04938272
#>