General Recognition Theory

Description

Functions to generate and analyze data for psychology experiments based on the General Recognition Theory.

Details

This package is written based mostly on the GRT Toolbox for MATLAB by Alfonso-Reese (2006), although many functions have been renamed and modified from the original in order to make them more general and “R-like.”

The functions grtrnorm and grtMeans are used for design categorization experiments and generating stimuli. The functions glc, gcjc, gqc, and grg are used for fitting the general linear classifier, the general conjunctive classifier, the general quadratic classifier, and the general random guessing model, respectively. The glc, gcjc, and gqc have plot methods (plot.glc, plot.gcjc, plot.gqc, plot3d.glc, plot3d.gqc).

For a complete list of functions, use library(help = "catlearn").

Author(s)

Kazunaga Matsuki

Maintainer: Andy Wills andy@willslab.co.uk

References

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.

Extract 'glc' or 'gcjc' coefficients

Description

Extracts the coefficients from the model object glc, glcStruct, or gcjc.

Usage

## S3 method for class 'glc'
coef(object, ...)

## S3 method for class 'glcStruct'
coef(object, ...)

## S3 method for class 'gcjc'
coef(object, ...)

Arguments

Details

Both the object glc and glcStruct contain the parameters for the decision boundary in the form:

a_1x_1 + a_2x_2 \ldots a_nx_n + b = 0

This function transforms and returns the coefficients of the function solved with respect the x_n.

For the object gcjc, a list of two coefficients (Intercepts) are returned.

Examples

data(subjdemo_2d)
fit.2dl <- glc(response ~ x + y, data=subjdemo_2d,
    category=subjdemo_2d$category, zlimit=7)
plot(fit.2dl, fitdb=FALSE)
abline(coef(fit.2dl), col = "red")
abline(coef(fit.2dl$initpar))

fit.1dx <- update(fit.2dl, . ~ . -y)
abline(v=coef(fit.1dx), col="green")

fit.1dy <- update(fit.2dl, . ~ . -x)
abline(h=coef(fit.1dy), col="blue")

Calculate d' (d-prime)

Description

Obtain the standardized distance between the two probability distributions, known as d' or sensitivity index.

Usage

dprime(x,
    category,
    response,
    par = list(),
    zlimit = Inf,
    type = c("SampleIdeal", "Observer"))

dprimef(means, covs, noise=NULL)

Arguments

Details

The function dprime estimates d' from sample data sets, whereas the function dprimef calculates it from population parameters.

In dprime, if any parts of the argument par are missing, the function will estimate an optimal linear decision bound from supplied x and category. The argument response is not used if type is SampleIdeal.

Author(s)

Author of the original Matlab routines: Leola Alfonso-Reese

Author of R adaptation: Kazunaga Matsuki

References

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

Examples

data(subjdemo_2d)
d2 <- subjdemo_2d
db <- glcStruct(noise=10, coeffs=c(0.514,-0.857),bias=-0.000154)
dprime(d2[,2:3], d2$category, d2$response, par = db, zlimit=7, type='SampleIdeal')

mc <- mcovs(category ~ x + y, data=d2)
dprimef(mc$means, mc$covs)

extractAIC method for class 'glc', 'gqc', 'gcjc', and 'grg'

Description

Extract Akaike's An Information Criteria from a General Linear, Quadratic, or Conjunctive Classifier, or a General Random Guessing model

Usage

## S3 method for class 'glc'
extractAIC(fit, scale, k = 2, ...)

## S3 method for class 'gqc'
extractAIC(fit, scale, k = 2, ...)

## S3 method for class 'gcjc'
extractAIC(fit, scale, k = 2, ...)

## S3 method for class 'grg'
extractAIC(fit, scale, k = 2, ...)

Arguments

Details

As with the default method, the criterion used is

AIC = - 2\log L + k \times \mbox{df},

where L is the likelihood and df is the degrees of freedom (i.e., the number of free parameters) of fit.

Value

A numeric vector of length 2 including:

Examples

data(subjdemo_2d)
#fit a 2d suboptimal model
fit.2dl <- glc(response ~ x + y, data=subjdemo_2d, 
    category=subjdemo_2d$category, zlimit=7)
extractAIC(fit.2dl)

Draw a gray-scale Gabor Patch

Description

Draw a gray-scale Gabor Patch

Usage

gaborPatch(sf, 
    theta = 0, 
    rad = (theta * pi)/180, 
    pc = 1, 
    sigma = 1/6, 
    psi = 0, 
    grating = c("cosine", "sine"), 
    npoints = 100, 
    trim = 0, 
    trim.col = .5,
    ...)

Arguments

Details

The arguments theta and rad is the same thing but in different units. If both are supplied, rad takes the precedence.

Value

invisibly returns the matrix of the plotted values.

Note

This function is written just for fun; it is not optimized for speed or for performance.

References

Fredericksen, R. E., Bex, P. J., & Verstraten, F. A. J. (1997). How Big is a Gabor and Why Should We Care? Journal of the Optical Society of America A. 14, 1–12.

Gabor Filter. (2010, June 5). In Wikipedia, the free encyclopedia. Retrieved July 7, 2010, from http://en.wikipedia.org/wiki/Gabor_filter

Examples

# An imitation of Fredericksen et al.'s (1997) Fig 1.
# that demonstrate the relation between peak contrast
# and perceived size of the Gabor

op <- par(mfcol = c(3, 3), pty = "m", mai = c(0,0,0,0))
for(i in c(.85, .21, .06)){
    for(j in c(1/6, 1/7, 1/8)){
        gaborPatch(20, pc = i, sigma = j)
    }
}
par(op)

## Not run: 
# a typical plot of the stimuli and category structure
# often seen in artificial category-learning literatures.
m  <-  list(c(268, 157), c(332, 93))
covs  <-  matrix(c(4538, 4351, 4351, 4538), ncol = 2)
II <- grtrnorm(n = 40, np = 2, means = m, covs = covs,
   clip.sd = 4, seed = 1234)
II$sf <- .25+(II$x1/50)
II$theta <- II$x2*(18/50)

plot(II[,2:3], xlim = c(-100,600), ylim = c(-200,500), 
    pch = 21, bg = c("white","gray")[II$category])
abline(a = -175, b = 1)

library(Hmisc)
idx <- c(20, 31, 35, 49, 62)
xpos <- c(0, 100, 300, 350, 550)
ypos <- c(50, 300, 420, -120, 50)
for(i in 1:5)
{
    j = idx[i]
    segments(x0=II[j,"x1"], y0=II[j,"x2"], x1=xpos[i], y1=ypos[i])
    subplot(gaborPatch(sf=II[j,"sf"], theta=II[j,"theta"]), x=xpos[i], y=ypos[i])
}

## End(Not run)

General Conjunctive Classifier

Description

Fit a general conjunctive classifier.

Usage

gcjc(formula, data, category, par, config = 1, zlimit = Inf,
    fixed = list(), equal.noise = TRUE, opt = c("nlminb", "optim"), 
    lower=-Inf, upper=Inf, control=list())

Arguments

Details

If par is not fully specified in the argument, the function attempts to calculate the initial parameter values based on means by category or by response.

The default lower and upper values are selected based on the range of the data input so that the decision bound is found within the range of the data and convergence can be reached.

Value

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

References

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

See Also

glc, logLik.gcjc, coef.gcjc, plot.gcjc

Examples

data(subjdemo_cj)

m.cj <- gcjc(response ~ x1 + x2, data=subjdemo_cj, 
  config=2, category=subjdemo_cj$category, zlimit=7)

General Conjunctive Classifier structure

Description

A list of model parameters that specify a conjunctive decision bound, containing noise, coeffs, and bias.

Usage

gcjcStruct(noise, bias, config=c(1,2,3,4))

Arguments

Value

object of class gcjcStruct, which is a list of a named list containing noise, coeffs, and bias.

See Also

gcjc, coef.glcStruct, logLik.glcStruct

Examples

params <- gcjcStruct(noise=10, bias=c(100, 200), config=1)

General Linear Classifier

Description

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

Usage

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())

Arguments

Details

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.

Value

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

References

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.

See Also

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

Examples

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)

General Linear Classifier structure

Description

A named list of model parameters that specify a linear decision bound, containing noise, coeffs, and bias.

Usage

glcStruct(noise, coeffs, bias)

Arguments

Value

object of class glcStruct, i.e., a named list containing noise, coeffs, and bias. Returned values are normalized, such that each value are divided by the euclidean norm of the coeffs vector, and the sum of coeffs^2 is 1.

See Also

glc, coef.glcStruct, logLik.glcStruct, old2new_par, new2old_par

Examples

params <- glcStruct(noise=10, coeffs=c(1, -1), bias=0)

General Quadratic Classifier

Description

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

Usage

gqc(formula,
    data,
    category,
    par = list(),
    zlimit = Inf,
    fixed = list(),
    opt = c("nlminb", "optim"),
    lower=-Inf,
    upper=Inf,
    control=list())

Arguments

Details

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 qdb. The response specified in the formula is used as the grouping factor in mcovs.

Value

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

References

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.

See Also

glc, qdb, logLik.gqc, logLik.gqcStruct, plot.gqc, plot3d.gqc

Examples

data(subjdemo_2d)
fit.2dq <- gqc(response ~ x + y, data=subjdemo_2d,
    category=subjdemo_2d$category, zlimit=7)

General Quadratic Classifier structure.

Description

A named list of model parameters that specify a quadratic decision bound, containing pnoise, cnoise, coeffs, and bias.

Usage

gqcStruct(pnoise, cnoise, coeffs, bias)

Arguments

Value

object of class gqcStruct, i.e., a named list containing pnoise, cnoise, coeffs, and bias.

See Also

gqc, logLik.gqcStruct

Examples

params <- gqcStruct(pnoise=10, cnoise=100, coeffs=c(1,2,3,4,5), bias=6)

General Random Guessing model

Description

General Random Guessing model

Usage

grg(response, fixed = FALSE, k = 2)

Arguments

Details

The function assumes that there are two categories (e.g, ‘A’ and ‘B’) to which each stimulus belongs.

Fixed Random Guessing model assumes that participant responded randomly without response bias; for each stimulus, probability of responding ‘A’ and ‘B’ is .5. There are no free parameters in this model (i.e., df = 0).

General Random Guessing model assumes that participants responded randomly but is biased toward one response. The model estimates the response bias (df = 1).

Value

object of class grg, which is a list object containing:

References

Ashby, F. G., & Crossley, M. J. (2010). Interactions between declarative and procedural-learning categorization systems. Neurobiology of Learning and Memory, 94, 1-12.

See Also

glc, gqc, extractAIC.grg

Examples

data(subjdemo_2d)
fit.grand <- grg(subjdemo_2d$response, fixed=FALSE)

fit.frand <- grg(subjdemo_2d$response, fixed=TRUE)

Obtain means of two multivariate normal populations satisfying certain criteria

Description

Obtain means of two multivariate normal populations having the specified covariance structure and centroid, and with which classification based on the optimal decision boundary satisfies the supplied probability of correct classification.

Usage

grtMeans(covs, centroid, optldb, p.correct, initd = 5, stepsize = 1)

Arguments

Value

Author(s)

Author of the original Matlab routine ‘Design2dGRTexp’: Leola Alfonso-Reese

Author of R adaptation: Kazunaga Matsuki

References

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

See Also

ldb.p.correct

Examples

foo <- grtMeans(diag(c(625,625)), centroid=c(200, 200*.6), 
    optldb=c(.6,-1,0), p.correct=.85)

Sample from multiple multivariate normal distributions

Description

Generate one or more samples from the two or more specified multivariate normal distributions.

Usage

grtrnorm(n,
        np = 2,
        means = list(rep(0,np), rep(0,np)), 
        covs = diag(rep(1,np)), 
        clip.sd = Inf,
        tol = 1e-6,
        empirical = TRUE, 
        seed = NULL,
        response.acc = NULL)

Arguments

Details

This function is essentially a wrapper to the mvrnorm function in MASS package.

If the optional response.acc argument is supplied, hypothetical random classification responses with specified accuracy will be generated.

Value

a data frame containing a column of numeric category labels and column(s) of sampled values for each variable, and optionally, a column of hypothetical responses.

Author(s)

Author of the original Matlab routines: Leola Alfonso-Reese

Author of R adaptation: Kazunaga Matsuki

References

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

Examples

m <- list(c(268,157), c(332, 93))
covs <- matrix(c(4538, 4351, 4351, 4538), ncol=2)
II <- grtrnorm(n=80, np=2, means=m, covs=covs)


m <- list(c(283,98),c(317,98),c(283,152),c(317,152))
covs <- diag(75, ncol=2, nrow=2)
CJ <- grtrnorm(n=c(8,16,16,40), np=4, means=m, covs=covs)
CJ$category <- c(1,1,1,2)[CJ$category]

Linear Decision Bound

Description

Find coefficients of the ideal linear decision boundary given the means and covariance of two categories.

Usage

ldb(means, covs, 
    covstruct = c("unstructured", "scaledIdentity", "diagonal", "identity"),
    noise = 10)

Arguments

Details

The order of vectors in the list means matters as the sign of coeffs and bias in the output will be reversed.

The argument noise is only for convenience; the supplied value is simply bypassed to the output for the subsequent use, i.e., as object of class glcStruct.

Value

The object of class glcStruct

Author(s)

Author of the original Matlab routine ‘lindecisbnd’: Leola Alfonso-Reese

Author of R adaptation: Kazunaga Matsuki

References

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

See Also

mcovs, qdb, glcStruct, glc

Examples

m <- list(c(187, 142), c(213.4, 97.7))
covs <- diag(c(625, 625))
foo <- ldb(means=m, covs=covs)

Probability of correct classification based on the optimal linear decision bound.

Description

Estimates the probability of correct classification under the condition in which the optimal linear decision boundary is used to categorize the samples from two multivariate normal populations with the specified parameters

Usage

ldb.p.correct(means, covs, noise = 0)

Arguments

Author(s)

Author of the original Matlab routine ‘linprobcorr’: Leola Alfonso-Reese

Author of R adaptation: Kazunaga Matsuki

References

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

Examples

foo <- grtMeans(diag(c(625,625)), centroid=c(200, 200*.6), 
    optldb=c(.6,-1,0), p.correct=.85)
ldb.p.correct(foo$means, foo$covs)

lines Method for class 'gqc'

Description

Add a quadratic decision boundary line through the current plot.

Usage

## S3 method for class 'gqcStruct'
lines(x, 
    xlim = c(0,1), ylim = c(0,1), 
    npoints = 100, col = "black", 
    ...)

Arguments

Value

an invisible list of x- and y-coordinates of the line:

See Also

plot.gqc, {plot3d.gqc}

Examples

data(subjdemo_2d)
fit.2dq <- gqc(response ~ x + y, data=subjdemo_2d, 
     category=subjdemo_2d$category, zlimit=7)
plot(fit.2dq, fitdb=FALSE, initdb=FALSE)
lines(fit.2dq$par, xlim=c(0,400), ylim=c(0,400), col="red")
lines(fit.2dq$initpar, xlim=c(0,400), ylim=c(0,400), col="blue")

Log-Likelihood of a 'glc' or 'gcjc' Object

Description

Extract the log-likelihood of the fitted general linear or conjunctive classifier model.

Usage

## S3 method for class 'glc'
logLik(object, ...)

## S3 method for class 'gcjc'
logLik(object, ...)

Arguments

Value

The log-likelihood for the general linear or conjunctive classifier represented by the estimated parameters in object

Note

This function is intended for indirect internal use by functions such as AIC. To obtain the log-likelihood of the fitted model applied to new dataset, use logLik.glcStruct or logLik.gcjcStruct

See Also

glc, logLik.glcStruct, gcjc, logLik.gcjcStruct

Examples

data(subjdemo_2d)
fit <- glc(response ~ x + y, data=subjdemo_2d, 
    category=subjdemo_2d$category, zlimit=7)
logLik(fit)

Log-Likelihood of a 'glcStruct' or 'gcjcStruct' Object

Description

Calculate the log-likelihood of the general linear or conjunctive classifier model applied to a data set.

Usage

## S3 method for class 'glcStruct'
logLik(object, response, x, zlimit = Inf, ...)

## S3 method for class 'gcjcStruct'
logLik(object, response, x, zlimit = Inf, ...)

Arguments

Value

The log-likelihood for the general linear or conjunctive classifier described by object fitted against the dataset given by response and x.

Note

The value of attributes, attr(, "df") (degrees of freedom) is calculated based on the assumption that all the parameters in object are free to vary.

See Also

gqc, gqcStruct, logLik.glc, logLik.gcjc

Examples

m <- list(c(187, 142), c(213, 98))
covs <- diag(625, ncol=2, nrow=2)
db <- ldb(means=m, covs=covs, noise=10)
data(subjdemo_2d)
logLik(db, subjdemo_2d$response, x=subjdemo_2d[2:3], zlimit=7)

Log-Likelihood of a 'gqc' Object

Description

Extract the log-likelihood of the fitted general quadratic classifier model.

Usage

## S3 method for class 'gqc'
logLik(object, ...)

Arguments

Value

The log-likelihood for the general quadratic classifier represented by the estimated parameters in object

Note

This function is intended for indirect internal use by functions such as AIC. To obtain the log-likelihood of the fitted model applied to new dataset, use logLik.gqcStruct

See Also

gqc, logLik.gqcStruct

Log-Likelihood of a 'gqcStruct' Object

Description

Calculate the log-likelihood of the general quadratic classifier model applied to a data set.

Usage

## S3 method for class 'gqcStruct'
logLik(object, response, x, zlimit = Inf, ...)

Arguments

Value

The log-likelihood for the general quadratic classifier described by object fitted against the dataset given by response and x.

Note

The value of attributes, attr(, "df") (degrees of freedom) is calculated based on the assumption that all the parameters in object are free to vary.

See Also

gqc, gqcStruct, logLik.gqc

Examples

m <- list(c(187, 142), c(213, 98))
covs <- list(diag(625, ncol=2, nrow=2), diag(600, ncol=2, nrow=2))
db <- qdb(means=m, covs=covs)
data(subjdemo_2d)
logLik(db, subjdemo_2d$response, x=subjdemo_2d[2:3], zlimit=7)

Calculate sample means and covariance(s) of multivariate data

Description

Calculate sample means and covariance(s) of multivariate data

Usage

## Default S3 method:
mcovs(x, grouping, pooled=TRUE, ...)

## S3 method for class 'formula'
mcovs(formula, data, pooled=TRUE, ...)

Arguments

Value

A list containing:

Convert 'new' to 'old' glcStruct format

Description

Converts the glcStruct in ‘new’ format to ‘old’ format whereby a vector of angle is converted to coeffs.

Usage

new2old_par(x)

angle2cart(angle)

Arguments

Value

For new2old_par, object of class glcStruct.

For angle2cart, vector.

Author(s)

Author of the original Matlab routines: Leola Alfonso-Reese

Author of R adaptation: Kazunaga Matsuki

References

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

See Also

old2new_par cart2angle glcStruct

Examples

m <- list(c(187, 142), c(213.4, 97.7))
covs <- diag(c(625, 625))
foo <- ldb(means=m, covs=covs)
bar <- old2new_par(foo)
new2old_par(bar)

angle2cart(bar$angle)

Convert 'old' to 'new' glcStruct format

Description

Converts glcStruct in the 'old' to 'new' format for more efficient optimization where coeffs vectors are converted to a vector of angle with length of (coeffs) - 1

Usage

old2new_par(x)

cart2angle(cart)

Arguments

Value

For old2new_par, object of class glcStruct.

For cart2angle, vector.

Author(s)

Author of the original Matlab routines: Leola Alfonso-Reese

Author of R adaptation: Kazunaga Matsuki

References

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

Examples

m <- list(c(187, 142), c(213.4, 97.7))
covs <- diag(c(625, 625))
foo <- ldb(means=m, covs=covs)
old2new_par(foo)

cart2angle(foo$coeffs)

Plot Method for Class 'gcjc'

Description

Plot the fitted data set and decision boundary.

Usage

## S3 method for class 'gcjc'
plot(x, fitdb = TRUE, initdb = FALSE, xlim = NULL, ylim = NULL, bg, pch, ...)

Arguments

Details

This function produces a scatter plot of data matrix in the x and (optionally) decision boundary specified within (i.e., x$par and/or x$initpar).

Examples

m <- list(c(100,200),c(100,100),c(200,100),c(200,200))
covs <- diag(30^2, ncol=2, nrow=2)
set.seed(1)
CJ <- grtrnorm(n=c(50,20,10,20), np=4, means=m, covs=covs)
CJ$category <- c(1,2,2,2)[CJ$category]
#create ramdom responses with 80% accuracy
CJ$response <- CJ$category
set.seed(1)
incorrect <- sample(1:100, size=20)
CJ$response[incorrect] <- abs(CJ$response[incorrect] - 3)

#now fit the model
m.cj <- gcjc(response ~ x1 + x2, data=CJ, config=2, category=CJ$category, zlimit=7)

plot(m.cj)

Plot Method for Class 'glc'

Description

Plot the fitted data set and linear decision boundary.

Usage

## S3 method for class 'glc'
plot(x, fitdb = TRUE, initdb = FALSE, xlim = NULL, ylim = NULL, bg, pch, ...)

Arguments

Details

This function produces a scatter plot of data matrix in the x and (optionally) decision boundary specified within (i.e., x$par and/or x$initpar).

The look of the plot differs depending on the dimension of the model. If the dimension is 1, the model matrix is plotted on the y-axis, and category vector (as in x$category) is plotted on the x axis. If the dimension is 2, scatter plot of the model matrix is plotted. If the dimension is 3, plot3d.glc is called to create a 3D scatter plot. If the dimension is greater than 3, an error message will be returned.

See Also

plot3d.glc

Examples

data(subjdemo_2d)
fit.2dl <- glc(response ~ x + y, data=subjdemo_2d, 
    category=subjdemo_2d$category, zlimit=7)
plot(fit.2dl)

#if one wants to plot decision bounds in
# colors different from the defaults
plot(fit.2dl, fitdb=FALSE)
abline(coef=coef(fit.2dl$par), col="orange")
abline(coef=coef(fit.2dl$initpar), col="purple")

plot Method for Class 'gqc'

Description

Plot the fitted data set and quadratic decision boundary.

Usage

## S3 method for class 'gqc'
plot(x, fitdb = TRUE, initdb = FALSE, 
    xlim = NULL, ylim = NULL, bg, pch, npoints = 100, ...) 

Arguments

Details

This function produces a scatter plot of data matrix in the x and (optionally) decision boundary (i.e., x$par and/or x$initpar).

The look of the plot differs depending on the dimension of the model. If the dimension is 2, scatter plot of the model matrix is plotted. If the dimension is 3, plot3d.gqc is called to create a 3D scatter plot. In all other cases, an error message will be returned.

See Also

lines.gqcStruct, {plot3d.gqc}

Examples

data(subjdemo_2d)
fit.2dq <- gqc(response ~ x + y, data=subjdemo_2d, 
    category=subjdemo_2d$category, zlimit=7)
plot(fit.2dq)

plot3d Method for Class 'glc'

Description

plot the fitted 3D data set and linear decision boundary.

Usage

## S3 method for class 'glc'
plot3d(x, fitdb = TRUE, initdb = FALSE,
    lims = NULL, alpha = .5, ...)

Arguments

Details

This function produces a 3D scatter plot of data matrix in the x and (optionally) decision boundary specified within (i.e., x$par and/or x$initpar), using points3d and quads3d in the rgl package respectively.

References

Daniel Adler, Oleg Nenadic and Walter Zucchini (2003) RGL: A R-library for 3D visualization with OpenGL

See Also

plot.glc, plot3d.gqc

Examples

## Not run: 
data(subjdemo_3d)
fit.3dl <- glc(response ~ x + y + z, data=subjdemo_3d,
    category=subjdemo_3d$category, zlimit=7)
plot3d(fit.3dl)

## End(Not run)

plot3d Method for Class 'gqc'

Description

plot the fitted 3D data set and quadratic decision boundaries.

Usage

## S3 method for class 'gqc'
plot3d(x, fitdb = TRUE, initdb = FALSE,
    lims = NULL, npoints = 100, alpha = .5,
    fill = TRUE, smooth = FALSE, ...)

Arguments

Details

This function produces a 3D scatter plot of data matrix of x and (optionally) quadratic decision boundaries specified within (i.e., x$par and/or x$initpar), using points3d function in the rgl package and contour3d function in the misc3d package respectively.

References

Daniel Adler, Oleg Nenadic and Walter Zucchini (2003) RGL: A R-library for 3D visualization with OpenGL

See Also

plot.gqc, {plot3d.gqc}

Examples

## Not run: 
data(subjdemo_3d)
fit.3dq <- gqc(response ~ x + y + z, data=subjdemo_3d,
    category=subjdemo_3d$category, zlimit=7)
plot3d(fit.3dq)

## End(Not run)

predict method for General Linear Classifier

Description

Predicted classification based on ‘glc’ model object.

Usage

## S3 method for class 'glc'
predict(object, newdata, seed = NULL, ...)

Arguments

Details

The function predict (or ‘simulate’) classification response of an observer whose noise and linear decision bounds are specified in object.

The predicted category labels are matched with those used for the fit in object.

If newdata is missing, the predictions are made on the data used for the fit.

Value

a vector of labels of categories to which each sample in newdata is predicted to belong, according to the model in object.

Author(s)

Author of the original Matlab routines: Leola Alfonso-Reese

Author of R adaptation: Kazunaga Matsuki

References

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

Examples

data(subjdemo_2d)
fit.2dl <- glc(response ~ x + y, data=subjdemo_2d, 
    category=subjdemo_2d$category, zlimit=7)

m <- list(c(187, 142), c(213.4, 97.7))
covs <- diag(c(900, 900))
newd <- grtrnorm(n=20, np=2, means=m, covs=covs, seed=1234)
predict(fit.2dl, newd[,2:3], seed=1234)

Quadratic Decision Bound

Description

Find coefficients of the ideal quadratic decision boundary given the means and covariance of two categories.

Usage

qdb(means, covs, pnoise = 10, cnoise = 100, sphere = FALSE)

Arguments

Details

The order of vectors in the list means and covs matters as the sign of coeffs and bias object in the output will be reversed.

The argument pnoise and cnoise is only for convenience; the supplied value is simply bypassed to the output for the subsequent use, i.e., as object of class gqcStruct.

Value

object of class gqcStruct

Author(s)

Author of the original Matlab routine ‘quaddecisbnd’: Leola Alfonso-Reese

Author of R adaptation: Kazunaga Matsuki

References

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

See Also

mcovs, qdb, gqcStruct, gqc

Examples

m <- list(c(187, 142), c(213.4, 97.7))
covs <- list(diag(c(625, 625)), diag(c(625, 625)))
foo <- qdb(means=m, covs=covs)

the proportion correct of the quadratic decision boundary.

Description

Calculate the proportion correct obtained by categorizing samples form one multivariate normal population using the quadratic decision boundary.

Usage

qdb.p.correct(x, qdb, refpts = colMeans(x))

Arguments

Details

The function assumes that all the points specified in x belong to just one category.

Author(s)

Author of the original Matlab routine ‘quadbndpercorr’: Leola Alfonso-Reese

Author of R adaptation: Kazunaga Matsuki

References

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

Examples

data(subjdemo_2d)
tmp <- split(subjdemo_2d, subjdemo_2d$category)
mc <- mcovs(category ~ x + y, data=subjdemo_2d, pooled=FALSE)
db <- qdb(mc$means, mc$covs)
qdb.p.correct(tmp[[1]][,2:3], db)

Scale method for the class 'glc' and 'gqc'

Description

Return the discriminant scores obtained by applying the general linear classifier to the fitted data.

Usage

## S3 method for class 'glc'
scale(x, initdb = FALSE, zlimit = Inf, ...)
## S3 method for class 'gqc'
scale(x, initdb = FALSE, zlimit = Inf, ...)

Arguments

Note

The generic function scale is redefined to accept arguments other than x, center, and scale.

Examples

data(subjdemo_2d)
fit.2dl <- glc(response ~ x + y, data=subjdemo_2d, 
    category=subjdemo_2d$category, zlimit=7)
scale(fit.2dl)

fit.2dq <- gqc(response ~ x + y, data=subjdemo_2d, 
    category=subjdemo_2d$category, zlimit=7)
scale(fit.2dq)


## Not run: 
#plots using the discriminant scores
require(Hmisc)
options(digits=3)
fit.2dl <- glc(response ~ x + y, data=subjdemo_2d, 
    category=subjdemo_2d$category, zlimit=7)
# z-scores based on the initial decision bound
# split by the true category membership
zinit <- split(scale(fit.2dl, initdb=TRUE), subjdemo_2d$category)
histbackback(zinit)

# z-scores based on the fitted decision bound
# split by the participants' response
zfit1 <- split(scale(fit.2dl, initdb=FALSE), subjdemo_2d$category)
histbackback(zfit1)

# z-scores based on the fitted decision bound
# split by the true category membership
zfit2 <- split(scale(fit.2dl, initdb=FALSE), subjdemo_2d$response)
histbackback(zfit2)

## End(Not run)

Sample dataset of a categorization experiment with 1D stimuli.

Description

A sample one dimensional stimulus set and response data of a hypothetical participant in a two-category classification experiment involving 500 trials.

Usage

subjdemo_1d

Format

This data frame contains 500 rows and the following columns:

category

label of the category to which each stimulus belongs.

x

value on the dimension 'x'

response

classification response of a participant.

Source

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

References

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

Sample dataset of a categorization experiment with 2D stimuli.

Description

A sample two dimensional stimulus set and response data of a hypothetical participant in a two-category classification experiment involving 500 trials.

Usage

subjdemo_2d

Format

This data frame contains 500 rows and the following columns:

category

label of the category to which each stimulus belongs.

x

value on the dimension 'x'

y

value on the dimension 'y'

response

classification response of a participant.

Source

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

References

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

Sample dataset of a categorization experiment with 3D stimuli.

Description

A sample one dimensional stimulus set and response data of a hypothetical participant in a two-category classification experiment involving 500 trials.

Usage

subjdemo_3d

Format

This data frame contains 500 rows and the following columns:

category

label of the category to which each stimulus belongs.

x

value on the dimension 'x'

y

value on the dimension 'y'

z

value on the dimension 'z'

response

classification response of a participant.

Source

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

References

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

Sample dataset of a categorization experiment with 2D conjunctive stimuli.

Description

A sample two dimensional stimulus set and response data of a hypothetical participant in a two-category classification experiment involving 100 trials.

Usage

subjdemo_cj

Format

This data frame contains 100 rows and the following columns:

category

label of the category to which each stimulus belongs.

x1

value on the dimension 'x1'

x2

value on the dimension 'x2'

response

classification response of a participant.

Examples

##### the data was generated using following codes:
m <- list(c(100,200),c(100,100),c(200,100),c(200,200))
covs <- diag(30^2, ncol=2, nrow=2)
set.seed(1)
subjdemo_cj <- grtrnorm(n=c(50,20,10,20), np=4, means=m, covs=covs)
subjdemo_cj$category <- c(1,2,2,2)[subjdemo_cj$category]
##### create ramdom responses with 80% accuracy
subjdemo_cj$response <- subjdemo_cj$category
set.seed(1)
incorrect <- sample(1:100, size=20)
subjdemo_cj$response[incorrect] <- abs(subjdemo_cj$response[incorrect] - 3)

##### plotting the dataset
with(subjdemo_cj, plot(x2 ~ x1, bg=category, pch=response))
abline(h=150, lty=2)
abline(v=150, lty=2)

Un-scale or re-center the scaled or centered Matrix-like object

Description

This function revert a Matrix-like object that is scaled or centered via scale.default to data with the original scale/center.

Usage

unscale(x)

Arguments

Value

a matrix that are re-centered or un-scaled, based on the value of attributes "scaled:center" and "scaled:scale" of x. If neither of those attributes is specified, x is returned.

See Also

scale

Examples

require(stats)
x <- matrix(1:10, ncol=2)
unscale(z <- scale(x))

#maybe useful for truncating
trunc <- 1
z[abs(z) > trunc] <- sign(z[abs(z) > trunc])*trunc
unscale(z)