Generalized Context Model

Description

Constructs a Generalized Context Model.

Usage

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GCM(learning,response,parameters=list(w=NULL,lambda=1,r=1,q=1,gamma=NULL),
fixed,data,subset,ntimes=NULL,replicate=TRUE,remove.intercept=FALSE)

Arguments

learning

an object of class formula (or one that can be coerced to that class): a symbolic description of the learning model to be fitted. For more details of model speecification, see lm or glm.

response

an object of class formula (or one that can be coerced to that class): a symbolic description of the response model to be fitted. Only the left hand side of the formula will be used. For more details of model specification, see lm or glm.

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?

Details

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[t-k], k=1,...,t-1.

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.

Value

An object of class GCM.

References

Nosofsky, R.M. (1986). Attention, Similarity, and the Identification-Categorization Relationship. Journal of Experimental Psychology: General, 115, 39-57.

Examples

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## 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)