Constructs a Generalized Context Model.
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learning 
an object of class 
response 
an object of class 
parameters 
an (optional) named list with (starting) values of the parameters. If no values are supplied, defaults are used. 
fixed 
a logical vector indicating whether model parameters are fixed or free 
data 
data frame containing the variables listed in the formula argument. 
subset 
subset of data to fit model to. 
ntimes 
a vector with number of observations for each replication. 
replicate 
logical to indicate whether model parameters are identical for each replication in ntimes. 
remove.intercept 
(logical) should the intercept term be removed from the x matrix of the model? 
The Generalized Context Model (Nosofsky, 1986) is an exemplar model. It predicts the value of a criterion at t based on the similarity of a probe cue x[t] to stored cues x[tk], k=1,...,t1.
The similarity between two cues is computed as
s(x[t],x[k]) = exp(lambda * d(x[t],x[k])^(q) )
where d(x[t],x[k]) is the generalized Minkowski distance
d(x[t],x[k]) = (sum[j] w[j]  x[jt]  x[jk] ^(r))^(1/r)
When making a response to cue x[t], first the overall similarity to each of the previously encountered exemplars of each of the levels of outcome y is determined as
The GCM can be seen as a mixture model. Each encountered exemplar adds a new component to the mixture. The mixture proportions are defined by the similarities. See the package manual for more information.
A more general version of the GCM is implemented by gGCM
.
An object of class GCM
.
Nosofsky, R.M. (1986). Attention, Similarity, and the IdentificationCategorization Relationship. Journal of Experimental Psychology: General, 115, 3957.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16  ## open weather prediction data
data(WPT)
controls < subset(WPT,id %in% paste("C",1:16,sep=""))
## initialize model, use remove.intercept=TRUE so that the x matrix will contain
## four columns.
mod < GCM(y~x1+x2+x3+x4,response=r~1,data=controls,
fix=list(r=TRUE,q=TRUE),ntimes=rep(200,16),
remove.intercept=TRUE)
## Not run:
## estimate free parameters
## discount (ignore) first 5 responses in each series
## as these can give deterministic predictions
mod < fit(mod,discount=5)
## End(Not run)
summary(mod)

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