# generalized Generalized Context Model

### Description

Constructs a generalized version of the Generalized Context Model.

### Usage

1 2 3 4 5 | ```
gGCM(learning,response,level=c("nominal","interval"),distance=c("cityblock",
"euclidian","minkowski"),similarity=c("exponential","gaussian","general"),
sampling=c("uniform","power","exponential"),parameters=list(w=NULL,lambda=1,
r=1,q=1,gamma=NULL,theta=NULL,sdy=NULL,sdr=NULL),fixed,data,subset,ntimes=NULL,
replicate=TRUE,base=NULL,remove.intercept=FALSE)
``` |

### Arguments

`learning` |
an object of class |

`response` |
an object of class |

`level` |
the measurement level of the dependent variable, either nominal or interval. |

`distance` |
either the name of a standard distance function, or a function which returns a T*T matrix with distances between the cues. See details. |

`similarity` |
either the name of a standard similarity function, or a function which converts the T*T distance matrix to a T*T similarity matrix. See datails. |

`sampling` |
either the name of a standard sampling function, or a function which returns a T*T matrix with sampling weights. See details. |

`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. |

`base` |
assign one of the levels of the criterion variable the role of base category. |

`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 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.

The model implemented by `gGCM`

extends the original GCM (Nosofsky, 1986)
by allowing (1) a continuous criterion, and (2) memory decay of exemplars.

### Value

An object of class `gGCMinterval`

or `gGCMnominal`

.

### References

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

Speekenbrink, M. \& Shanks, D.R. (2010). Learning in a changing environment. Journal of Experimental Psychology: General.

### Examples

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 <- gGCM(y~x1+x2+x3+x4,response=r~1,data=controls,ntimes=rep(200,16),remove.intercept=TRUE)
## estimate free parameters
## Not run: mod <- fit(mod)
summary(mod)
# now a model with a general minkowski distance function, and an exponential
# memory decay. Using numerical predictors and removing the intercept (-1) in
# the model formula removes the need for the remove.intercept argument.
mod <- gGCM(y~as.numeric(x1==1)+as.numeric(x2==1)+as.numeric(x3==1)+
as.numeric(x4==1)-1,response=r~1,distance="minkowski",sampling="uniform",data=controls,
ntimes=rep(200,16))
``` |