glc: General Linear Classifier
In grt: General Recognition Theory

Description Usage Arguments Details Value References See Also Examples

Fit a general linear classifier (a.k.a. linear decison-bound model).

glc(formula, data, category, par = list(), zlimit = Inf,
    covstruct=c("unstructured", "scaledIdentity", "diagonal", "identity"),
    fixed = list(), opt = c("nlminb", "optim"), 
    lower=-Inf, upper=Inf, control=list())

`formula`	A formula of the form `response ~ x1 + x2 + ...`, where the response specifies the grouping factor (generally a participant's response) and the right hand side specifies the relevant dimensions or features of the stimuli.
`data`	A data frame from which variables specified in `formula` are taken.
`category`	(Optional.) A factor specifying the true category membership of the stimuli.
`par`	object of class `glcStruct` or named list containing a set of initial parameters (i.e., `noise`, `coeffs`, `bias`) used to fit the data.
`zlimit`	numeric. The z-scores (or discriminant scores) beyond the specified value will be truncated. Default to `Inf`.
`covstruct`	An optional character string. Only used when the initial parameters are not fully specified. see `ldb`.
`fixed`	A named list of logical vectors specifying whether each of `noise`, `coeffs`, and `bias` parameters should be fixed to the initial value. Default to `list(noise=FALSE, coeffs=FALSE, bias=FALSE`. A fatal error will be returned if set to all `TRUE`.
`opt`	A character string specifying the optimizer to be used: either `nlminb` (the default) or `optim`. If “optim”, “L-BFGS-B” method is used (see ‘Details’ of `optim`) .
`lower, upper`	Bounds on the parameters. see ‘Details’ for default values.
`control`	A list of control parameters passed to the internal optimization function. See ‘Details’ of `nlminb` or `optim`.

If par is not fully specified in the argument, the function attempts to calculate the initial parameter values by internally calling the functions mcovs and ldb. If category is also not specified, the response specified in the formula is used as the grouping factor in mcovs.

The default lower and upper values vary depending on the dimension of the model (i.e., the number of variables in the right hand side of formula). In all cases, default lower and upper values for the noise parameter is .001 and 500 respectively. In cases when an one-dimensional model is fitted, lower and upper bounds for the bias parameters are selected based on the range of the data input so that the decision bound is found within the reasonable range of the data and convergence can be reached. In all other cases, coeffs and bias has no limits.

When an one-dimensional model is being fit, fixed$coeffs always becomes TRUE.

object of the class glc, i.e., a list containing the following components:

`terms`	the `terms` object used.
`call`	the matched call.
`model`	the design matrix used to fit the model.
`category`	the category vector as specified in the input.
`initpar`	the initial parameter used to fit the model.
`par`	the fitted parameter.
`logLik`	the log-likelihood at convergence.

Alfonso-Reese, L. A. (2006) General recognition theory of categorization: A MATLAB toolbox. Behavior Research Methods, 38, 579-583.

Ashby, F. G., & Gott, R. E. (1988). Decision rules in the perception and categorization of multidimensional stimuli. Journal of Experimental Psychology: Learning, Memory, & Cognition, 14, 33-53.

Ashby, F. G. (1992) Multidimensional models of perception and cognition. Lawrence Erlbaum Associates.

gqc, ldb, logLik.glc, coef.glc, predict.glc, scale.glc, plot.glc, plot3d.glc

data(subjdemo_2d)
d2 <- subjdemo_2d
#fit a 2d suboptimal model
fit.2dl <- glc(response ~ x + y, data=d2, category=d2$category, zlimit=7)
#fit a 1d model (on the dimention 'y') on the same dataset
fit.1dy <- glc(response ~ y, data=d2, category=d2$category, zlimit=7)
#or using update()
#fit.1dy <- update(fit.2dl, . ~ . -x)

#fit a 2d optimal model
fit.2dlopt <- glc(response ~ x + y, data=d2, category=d2$category, zlimit=7, 
    fixed=list(coeffs=TRUE, bias=TRUE))

#calculate AIC and compare
AIC(fit.2dl, fit.1dy, fit.2dlopt)